diff --git a/Annexe-Exercices/Annexe-Exercices.tex b/Annexe-Exercices/Annexe-Exercices.tex index 8174600..44d7b91 100644 --- a/Annexe-Exercices/Annexe-Exercices.tex +++ b/Annexe-Exercices/Annexe-Exercices.tex @@ -950,7 +950,7 @@ Attention, cette ``procédure\index{procédure}'', qui présente beaucoup d'avan La masse m constitue évidemment le système. On choisit un système d'axes vertical et horizontal dirigé vers le haut et dans le sens de l'accélération. Les forces extérieures exercées sur la masse sont au nombre de trois~: son poids P, la réaction du plan R et la force F. - \begin{figure}[h] + \begin{figure}[ht] \caption[Force inclinée]{Une force inclinée}\label{forceinclinee} \smallskip \begin{center} @@ -991,7 +991,7 @@ Attention, cette ``procédure\index{procédure}'', qui présente beaucoup d'avan Quelles sont les tensions exercées par chaque câble sur les murs ? Réponses~: \SI{77,63}{\newton} et \SI{84,24}{\newton}. \begin{solos} Commençons par trouver les forces exercées par les câbles sur la lampe. Considérons donc la lampe comme système. Pour des câbles souples la force est exercée le long du câble. La situation est donc celle de la figure \ref{lampe}. - \begin{figure}[h] + \begin{figure}[ht] \caption[Lampe suspendue]{Une lampe suspendue}\label{lampe} \smallskip \begin{center} @@ -1032,7 +1032,7 @@ Attention, cette ``procédure\index{procédure}'', qui présente beaucoup d'avan \begin{exos} Soient deux masses, la première, de valeur M=\SI{5}{\kilo\gram}, posée sur un plan horizontal sans frottements et la seconde, m=\SI{2}{\kilo\gram}, reliée à la première par une corde sans masse et pendant dans le vide, comme présenté sur la figure \ref{pendante}. - \begin{figure}[h] + \begin{figure}[ht] \caption[Masse pendante]{La masse pendante}\label{pendante} \smallskip \begin{center} @@ -1088,7 +1088,7 @@ On lâche la première à vitesse initiale nulle. Calculez la vitesse de la seco \medskip Une autre manière de résoudre le problème est de procéder avec méthode. Le système qu'on doit choisir est bien évidemment la masse m, puisque c'est de celle-ci qu'on cherche l'accélération pour en trouver la vitesse au bout de \SI{2}{\second}. - \begin{figure}[h] + \begin{figure}[ht] \centering \caption[Plan incliné]{Le plan incliné}\label{incline} \medskip @@ -1261,7 +1261,7 @@ On lâche la première à vitesse initiale nulle. Calculez la vitesse de la seco \begin{exos} Une poulie est accrochée au plafond par son axe de rotation. D'un côté elle soutient une masse m de \SI{5}{\kilo\gram} et de l'autre une autre poulie par l'intermédiaire d'une corde accrochée au plafond. À l'axe de rotation de cette dernière est suspendu une autre masse M de \SI{5}{\kilo\gram}. La figure \ref{deuxpoulies} présente la situation. - \begin{figure}[h] + \begin{figure}[ht] \centering \caption[Deux poulies]{Deux poulies}\label{deuxpoulies} \medskip @@ -1275,7 +1275,7 @@ On lâche la première à vitesse initiale nulle. Calculez la vitesse de la seco \medskip Imaginons une poulie suspendue à une corde qui dépasse de celle-ci des deux côtés d'une longueur L, comme présenté sur la figure \ref{cordepoulie}. La demi-circonférence de la poulie vaut aussi L. - \begin{figure}[h] + \begin{figure}[ht] \centering \caption[Corde poulie]{Corde et poulie}\label{cordepoulie} \medskip @@ -1289,7 +1289,7 @@ On lâche la première à vitesse initiale nulle. Calculez la vitesse de la seco \smallskip Pour le déterminer, il faut considérer qu'en tirant sur la corde pour la faire monter d'une hauteur L, on amène le point A qui est à l'origine au contact de la poulie à la place du point B du haut de la corde (voir figure \ref{cordepoulie}). Si la poulie restait à sa place, on aurait la situation de la figure \ref{cordepoulietiree}). Mais, elle est en réalité libre de monter. Ce qui reste fixe est le point C de la figure \ref{cordepoulie}. - \begin{figure}[h] + \begin{figure}[ht] \centering \caption[Corde tirée poulie]{Corde tirée et poulie}\label{cordepoulietiree} \medskip @@ -1297,7 +1297,7 @@ On lâche la première à vitesse initiale nulle. Calculez la vitesse de la seco \input{Annexe-Exercices/Images/cordepoulietiree.eps_tex} \end{figure} On a donc a répartir une longueur 2L de corde entre le point A de la figure \ref{cordepoulietiree} et le point C de la figure \ref{cordepoulie}. Comme la demi-circonférence de la poulie vaut L, il reste une longueur L à répartir des deux côtés de la poulie, soit L/2 de chaque côté, comme le montre la figure \ref{cordepoulietireejuste}. - \begin{figure}[h] + \begin{figure}[ht] \centering \caption[Corde tirée poulie juste]{Corde tirée et poulie montée}\label{cordepoulietireejuste} \medskip @@ -1638,7 +1638,7 @@ On lâche la première à vitesse initiale nulle. Calculez la vitesse de la seco Le bloc se met soudain à glisser. Sachant que le c\oe fficient de frottement dynamique \(\mu\) à une valeur de 5\% inférieure au c\oe fficient statique, calculez l'accélération du bloc. Réponses~: \SI{0,62}{} et \SI{0,29}{\metre\per\second\squared} \begin{solos} La situation est celle de la figure \ref{inclinefrottement}. - \begin{figure}[h] + \begin{figure}[ht] \centering \caption[Frottements]{Frottements sur plan incliné}\label{inclinefrottement} \medskip @@ -1742,7 +1742,7 @@ On lâche la première à vitesse initiale nulle. Calculez la vitesse de la seco \begin{exos} À l'aide d'un chariot d'une masse M de \SI{4}{\kilo\gram}, on désire déplacer une masse m de \SI{3}{\kilo\gram} en la poussant latéralement, mais sans qu'elle touche le sol, comme présenté à la figure \ref{blocsuspendu}. - \begin{figure}[h] + \begin{figure}[ht] \centering \caption[Bloc suspendu]{Déplacement d'un bloc suspendu}\label{blocsuspendu} \medskip @@ -1755,7 +1755,7 @@ On lâche la première à vitesse initiale nulle. Calculez la vitesse de la seco Le poids du bloc de masse m vaut~: \[P_m=m\cdot g=3\cdot 9,81=\SI{29,43}{\newton}\] Pour que ce bloc ne tombe pas, il faut qu'une force verticale s'exerce vers le haut et compense le poids calculé ci-dessus, soit \(F_{fr}=P\). L'origine de cette force est évidemment le frottement entre les deux blocs. Or, celle-ci dépend de la force exercée par la masse M sur m, notée \(\overrightarrow{N}\), qui joue le rôle de la réaction R du sol pour un objet glissant horizontalement. La figure \ref{blocsuspenduforces} présente la situation qui permet d'exprimer la force de frottement et de déterminer la valeur N de la réaction. - \begin{figure}[h] + \begin{figure}[ht] \centering \caption[Forces sur bloc suspendu]{Forces sur le bloc suspendu}\label{blocsuspenduforces} \medskip diff --git a/Annexe-Exercices/Annexe-Exercices.tex.bak b/Annexe-Exercices/Annexe-Exercices.tex.bak index 14b4536..44d7b91 100644 --- a/Annexe-Exercices/Annexe-Exercices.tex.bak +++ b/Annexe-Exercices/Annexe-Exercices.tex.bak @@ -950,7 +950,7 @@ Attention, cette ``procédure\index{procédure}'', qui présente beaucoup d'avan La masse m constitue évidemment le système. On choisit un système d'axes vertical et horizontal dirigé vers le haut et dans le sens de l'accélération. Les forces extérieures exercées sur la masse sont au nombre de trois~: son poids P, la réaction du plan R et la force F. - \begin{figure}[h] + \begin{figure}[ht] \caption[Force inclinée]{Une force inclinée}\label{forceinclinee} \smallskip \begin{center} @@ -991,7 +991,7 @@ Attention, cette ``procédure\index{procédure}'', qui présente beaucoup d'avan Quelles sont les tensions exercées par chaque câble sur les murs ? Réponses~: \SI{77,63}{\newton} et \SI{84,24}{\newton}. \begin{solos} Commençons par trouver les forces exercées par les câbles sur la lampe. Considérons donc la lampe comme système. Pour des câbles souples la force est exercée le long du câble. La situation est donc celle de la figure \ref{lampe}. - \begin{figure}[h] + \begin{figure}[ht] \caption[Lampe suspendue]{Une lampe suspendue}\label{lampe} \smallskip \begin{center} @@ -1032,7 +1032,7 @@ Attention, cette ``procédure\index{procédure}'', qui présente beaucoup d'avan \begin{exos} Soient deux masses, la première, de valeur M=\SI{5}{\kilo\gram}, posée sur un plan horizontal sans frottements et la seconde, m=\SI{2}{\kilo\gram}, reliée à la première par une corde sans masse et pendant dans le vide, comme présenté sur la figure \ref{pendante}. - \begin{figure}[h] + \begin{figure}[ht] \caption[Masse pendante]{La masse pendante}\label{pendante} \smallskip \begin{center} @@ -1088,7 +1088,7 @@ On lâche la première à vitesse initiale nulle. Calculez la vitesse de la seco \medskip Une autre manière de résoudre le problème est de procéder avec méthode. Le système qu'on doit choisir est bien évidemment la masse m, puisque c'est de celle-ci qu'on cherche l'accélération pour en trouver la vitesse au bout de \SI{2}{\second}. - \begin{figure}[h] + \begin{figure}[ht] \centering \caption[Plan incliné]{Le plan incliné}\label{incline} \medskip @@ -1261,7 +1261,7 @@ On lâche la première à vitesse initiale nulle. Calculez la vitesse de la seco \begin{exos} Une poulie est accrochée au plafond par son axe de rotation. D'un côté elle soutient une masse m de \SI{5}{\kilo\gram} et de l'autre une autre poulie par l'intermédiaire d'une corde accrochée au plafond. À l'axe de rotation de cette dernière est suspendu une autre masse M de \SI{5}{\kilo\gram}. La figure \ref{deuxpoulies} présente la situation. - \begin{figure}[h] + \begin{figure}[ht] \centering \caption[Deux poulies]{Deux poulies}\label{deuxpoulies} \medskip @@ -1275,7 +1275,7 @@ On lâche la première à vitesse initiale nulle. Calculez la vitesse de la seco \medskip Imaginons une poulie suspendue à une corde qui dépasse de celle-ci des deux côtés d'une longueur L, comme présenté sur la figure \ref{cordepoulie}. La demi-circonférence de la poulie vaut aussi L. - \begin{figure}[h] + \begin{figure}[ht] \centering \caption[Corde poulie]{Corde et poulie}\label{cordepoulie} \medskip @@ -1289,7 +1289,7 @@ On lâche la première à vitesse initiale nulle. Calculez la vitesse de la seco \smallskip Pour le déterminer, il faut considérer qu'en tirant sur la corde pour la faire monter d'une hauteur L, on amène le point A qui est à l'origine au contact de la poulie à la place du point B du haut de la corde (voir figure \ref{cordepoulie}). Si la poulie restait à sa place, on aurait la situation de la figure \ref{cordepoulietiree}). Mais, elle est en réalité libre de monter. Ce qui reste fixe est le point C de la figure \ref{cordepoulie}. - \begin{figure}[h] + \begin{figure}[ht] \centering \caption[Corde tirée poulie]{Corde tirée et poulie}\label{cordepoulietiree} \medskip @@ -1297,7 +1297,7 @@ On lâche la première à vitesse initiale nulle. Calculez la vitesse de la seco \input{Annexe-Exercices/Images/cordepoulietiree.eps_tex} \end{figure} On a donc a répartir une longueur 2L de corde entre le point A de la figure \ref{cordepoulietiree} et le point C de la figure \ref{cordepoulie}. Comme la demi-circonférence de la poulie vaut L, il reste une longueur L à répartir des deux côtés de la poulie, soit L/2 de chaque côté, comme le montre la figure \ref{cordepoulietireejuste}. - \begin{figure}[h] + \begin{figure}[ht] \centering \caption[Corde tirée poulie juste]{Corde tirée et poulie montée}\label{cordepoulietireejuste} \medskip @@ -1638,7 +1638,7 @@ On lâche la première à vitesse initiale nulle. Calculez la vitesse de la seco Le bloc se met soudain à glisser. Sachant que le c\oe fficient de frottement dynamique \(\mu\) à une valeur de 5\% inférieure au c\oe fficient statique, calculez l'accélération du bloc. Réponses~: \SI{0,62}{} et \SI{0,29}{\metre\per\second\squared} \begin{solos} La situation est celle de la figure \ref{inclinefrottement}. - \begin{figure}[h] + \begin{figure}[ht] \centering \caption[Frottements]{Frottements sur plan incliné}\label{inclinefrottement} \medskip @@ -1742,7 +1742,7 @@ On lâche la première à vitesse initiale nulle. Calculez la vitesse de la seco \begin{exos} À l'aide d'un chariot d'une masse M de \SI{4}{\kilo\gram}, on désire déplacer une masse m de \SI{3}{\kilo\gram} en la poussant latéralement, mais sans qu'elle touche le sol, comme présenté à la figure \ref{blocsuspendu}. - \begin{figure}[h] + \begin{figure}[ht] \centering \caption[Bloc suspendu]{Déplacement d'un bloc suspendu}\label{blocsuspendu} \medskip @@ -1755,7 +1755,7 @@ On lâche la première à vitesse initiale nulle. Calculez la vitesse de la seco Le poids du bloc de masse m vaut~: \[P_m=m\cdot g=3\cdot 9,81=\SI{29,43}{\newton}\] Pour que ce bloc ne tombe pas, il faut qu'une force verticale s'exerce vers le haut et compense le poids calculé ci-dessus, soit \(F_{fr}=P\). L'origine de cette force est évidemment le frottement entre les deux blocs. Or, celle-ci dépend de la force exercée par la masse M sur m, notée \(\overrightarrow{N}\), qui joue le rôle de la réaction R du sol pour un objet glissant horizontalement. La figure \ref{blocsuspenduforces} présente la situation qui permet d'exprimer la force de frottement et de déterminer la valeur N de la réaction. - \begin{figure}[h] + \begin{figure}[ht] \centering \caption[Forces sur bloc suspendu]{Forces sur le bloc suspendu}\label{blocsuspenduforces} \medskip @@ -2074,7 +2074,7 @@ On lâche la première à vitesse initiale nulle. Calculez la vitesse de la seco \end{ex} \begin{ex} - On désire fournir \SI{3000}{\kilo\watt\hour} d'énergie pendant une année à chacun des ménages d'une ville de 30'000 habitants. Si le nombre moyen de personnes par ménage est de deux et demi, quel doit être le débit de la conduite d'eau d'une hauteur de \SI{74}{\metre} nécessaire pour cela. Le rendement vaut \(\eta=90\%\). Quel type de turbine faut-il choisir ? Réponse~: Francis. + On désire fournir \SI{3000}{\kilo\watt\hour} d'énergie pendant une année à chacun des ménages d'une ville de \num{30000} habitants. Si le nombre moyen de personnes par ménage est de deux et demi, quel doit être le débit de la conduite d'eau d'une hauteur de \SI{74}{\metre} nécessaire pour cela. Le rendement vaut \(\eta=90\%\). Quel type de turbine faut-il choisir ? Réponse~: Francis. \begin{sol} Le nombre de ménages est de \(30'000/2,5=12'000\). Il faut donc fournir une énergie de~: \[E=12'000\cdot 3'000=\SI{36000000}{\kilo\watt\hour}=\SI{36}{\giga\watt\hour}\] diff --git a/CoursMecaniqueOS.pdf b/CoursMecaniqueOS.pdf index 3959032..c6f8fbb 100644 Binary files a/CoursMecaniqueOS.pdf and b/CoursMecaniqueOS.pdf differ diff --git a/CoursMecaniqueOSDF.dvi b/CoursMecaniqueOSDF.dvi index b29f3cd..ff59842 100644 Binary files a/CoursMecaniqueOSDF.dvi and b/CoursMecaniqueOSDF.dvi differ diff --git a/CoursMecaniqueOSDF.ilg b/CoursMecaniqueOSDF.ilg index 095b4ec..1779d43 100644 --- a/CoursMecaniqueOSDF.ilg +++ b/CoursMecaniqueOSDF.ilg @@ -1,7 +1,7 @@ This is makeindex, version 2.15 [TeX Live 2016] (kpathsea + Thai support). Scanning style file ./Perso.ist...done (3 attributes redefined, 0 ignored). Scanning input file CoursMecaniqueOSDF.idx.....done (1213 entries accepted, 0 rejected). -Sorting entries............done (13289 comparisons). +Sorting entries............done (13271 comparisons). Generating output file CoursMecaniqueOSDF.ind.....done (935 lines written, 0 warnings). Output written in CoursMecaniqueOSDF.ind. Transcript written in CoursMecaniqueOSDF.ilg. diff --git a/CoursMecaniqueOSDF.ind b/CoursMecaniqueOSDF.ind index 83f7970..3862d10 100644 --- a/CoursMecaniqueOSDF.ind +++ b/CoursMecaniqueOSDF.ind @@ -1,55 +1,55 @@ \begin{theindex} {\bfseries{Symbols}\;\rule[3pt]{5cm}{0.2pt}}\smallskip\nopagebreak - \item \IeC {\'e}quation d'\IeC {\'e}tat, 141 - \item \IeC {\'e}vaporation, 139 + \item \IeC {\'e}quation d'\IeC {\'e}tat, 143 + \item \IeC {\'e}vaporation, 141 \indexspace {\bfseries{A}\;\rule[3pt]{5cm}{0.2pt}}\smallskip\nopagebreak \item absolu, 21 - \item abstract, 174 - \item acc\IeC {\'e}l\IeC {\'e}ration, 180 + \item abstract, 176 + \item acc\IeC {\'e}l\IeC {\'e}ration, 182 \item acc\IeC {\'e}l\IeC {\'e}ration, 39, 41, 42, 46, 47, 55, 58, 59, - 80, 81, 117 + 80, 81, 119 \subitem centrifuge, 81 - \subitem centrip\IeC {\`e}te, 81, 194, 196 + \subitem centrip\IeC {\`e}te, 81, 196, 198 \subitem instantan\IeC {\'e}e, 39 \subitem terrestre, 44, 45 \item acc\IeC {\'e}l\IeC {\'e}ration \subitem moyenne, 39 - \item accident nucl\IeC {\'e}aire, 110 - \item action, 105 + \item accident nucl\IeC {\'e}aire, 112 + \item action, 107 \item action \subitem \IeC {\`a} distance, 58 - \item activit\IeC {\'e}, 112 - \item agitation mol\IeC {\'e}culaire, 130 - \item Alexandrie, 167, 207 + \item activit\IeC {\'e}, 114 + \item agitation mol\IeC {\'e}culaire, 132 + \item Alexandrie, 169, 209 \item allongement, 70 - \item Alpha du Centaure, 207 - \item alternateur, 104, 105 - \item altitude, 189 + \item Alpha du Centaure, 209 + \item alternateur, 106, 107 + \item altitude, 191 \item altitude, 59, 84 \item amas \subitem de galaxies, 22 \item Androm\IeC {\`e}de, 23, 41 - \item anneau d'ast\IeC {\'e}ro\IeC {\"\i }des, 200 + \item anneau d'ast\IeC {\'e}ro\IeC {\"\i }des, 202 \item ann\IeC {\'e}e, 26 - \item annexe, 174, 175 + \item annexe, 176, 177 \item antimati\IeC {\`e}re, 36 \item apesanteur, 47, 62, 63 - \item aph\IeC {\'e}lie, 199 - \item apog\IeC {\'e}e, 27, 199 - \item Apollo, 170 + \item aph\IeC {\'e}lie, 201 + \item apog\IeC {\'e}e, 27, 201 + \item Apollo, 172 \item Apollo, 40, 41 - \item Arbeit, 118 + \item Arbeit, 119 \item Aristote, 42, 45, 51--55 - \item Assouan, 167 + \item Assouan, 169 \item astrog\IeC {\'e}n\IeC {\`e}se, 32 \item atome, 32, 33 \subitem naturel, 32 \item attraction, 40, 41, 45, 47, 55, 58 - \item Atwood, 211 + \item Atwood, 213 \item axe \subitem de rotation, 26 \subitem demi-grand, 48 @@ -59,111 +59,111 @@ \indexspace {\bfseries{B}\;\rule[3pt]{5cm}{0.2pt}}\smallskip\nopagebreak - \item balance, 197 + \item balance, 199 \item balance, 60 - \item balistique, 179 + \item balistique, 181 \item balistique, 44--46 \item balle, 44 - \item barrage, 104, 203, 205, 206 - \item barre de contr\IeC {\^o}le, 111, 113 - \item basse mer, 197, 198 - \item Beau de Rochas, 153 + \item barrage, 106, 205, 207, 208 + \item barre de contr\IeC {\^o}le, 113, 115 + \item basse mer, 199, 200 + \item Beau de Rochas, 155 \item b\IeC {\'e}ryllium, 33 - \item Bessel, 172 - \item Betz, 107 + \item Bessel, 174 + \item Betz, 109 \item big \subitem bang, 23, 33 - \item boiler, 108 - \item bombes \IeC {\`a} hydrog\IeC {\`e}ne, 113 + \item boiler, 110 + \item bombes \IeC {\`a} hydrog\IeC {\`e}ne, 115 \item bore, 33 \item boson, 35 \item Brah\IeC {\'e} \subitem Tycho, 48, 49 \item Bruno \subitem Giordano, 53, 54 - \item Bruno Giordano, 191--193 - \item but du travail pratique, 174 + \item Bruno Giordano, 193--195 + \item but du travail pratique, 176 \indexspace {\bfseries{C}\;\rule[3pt]{5cm}{0.2pt}}\smallskip\nopagebreak - \item canon, 179 - \item capacit\IeC {\'e} thermique, 138 + \item canon, 181 + \item capacit\IeC {\'e} thermique, 140 \item capsule, 40 \item carbone, 33 - \item Carnot Nicolas L\IeC {\'e}onard, 133 + \item Carnot Nicolas L\IeC {\'e}onard, 135 \item carr\IeC {\'e} \subitem de la distance, 58 \subitem du temps, 43 \item cart\IeC {\'e}sien, 37 - \item Cassini, 170, 171 + \item Cassini, 172, 173 \item cause \subitem du changement du mouvement, 57 - \subitem du mouvement, 55, 57, 117 + \subitem du mouvement, 55, 57, 119 \item ceinture \subitem d'ast\IeC {\'e}ro\IeC {\"\i }de, 25 \subitem de Kuiper, 25 - \item Celsius, 129 + \item Celsius, 131 \item centre \subitem de gravit\IeC {\'e}, 66 \subitem de l'univers, 52 \subitem de la terre, 52 - \item centre de gravit\IeC {\'e}, 195 + \item centre de gravit\IeC {\'e}, 197 \item centrifuge, 62 \item centrip\IeC {\`e}te, 62 - \item chaleur, 103, 129, 131, 132 - \subitem latente, 132 - \subitem sp\IeC {\'e}cifique, 131 - \item chaleur, 119 - \item chaleur latente, 139 + \item chaleur, 105, 131, 133, 134 + \subitem latente, 133, 134 + \subitem sp\IeC {\'e}cifique, 133 + \item chaleur, 121 + \item chaleur latente, 141 \item champ - \subitem de gravitation, 193 - \item chauffage, 108 - \subitem urbain, 110 - \item chemin, 122 - \item cheval vapeur, 100 + \subitem de gravitation, 195 + \item chauffage, 109 + \subitem urbain, 112 + \item chemin, 124 + \item cheval vapeur, 102 \item chiffres - \subitem significatifs, 243 + \subitem significatifs, 245 \item choc \subitem galactique, 23 \item chute \subitem libre, 3, 42, 44, 45, 58 - \item chute libre, 179 + \item chute libre, 181 \item cin\IeC {\'e}ma, 37 - \item cin\IeC {\'e}matique, 36, 37, 52, 80, 194 + \item cin\IeC {\'e}matique, 36, 37, 52, 80, 196 \subitem d'Aristote, 52 \item cinq \IeC {\'e}l\IeC {\'e}ments, 52 \item circonf\IeC {\'e}rence \subitem de la Terre, 64 - \subitem de la terre, 167, 169 + \subitem de la terre, 169, 171 \item circulaire, 37 - \item clart\IeC {\'e}, 173, 178 - \item Cl\IeC {\'e}om\IeC {\`e}de, 167 + \item clart\IeC {\'e}, 175, 180 + \item Cl\IeC {\'e}om\IeC {\`e}de, 169 \item c\oe fficient de frottement \subitem cin\IeC {\'e}tique, 69 \subitem statique, 69 - \item colatitude, 166 + \item colatitude, 168 \item combustion - \subitem des ordures, 108 - \subitem du m\IeC {\'e}thane, 114 + \subitem des ordures, 110 + \subitem du m\IeC {\'e}thane, 115 \item com\IeC {\`e}te, 26, 49 - \item concision, 173 - \item conclusion du travail pratique, 176 - \item conduction, 107 - \item conduite forc\IeC {\'e}e, 203 - \item conservation, 117, 120 - \subitem de l'\IeC {\'e}nergie, 120, 122 - \subitem de l'\IeC {\'e}nergie m\IeC {\'e}canique, 121 - \item conservation de l'\IeC {\'e}nergie, 102 - \item conservative, 122, 123 + \item concision, 175 + \item conclusion du travail pratique, 178 + \item conduction, 109 + \item conduite forc\IeC {\'e}e, 205 + \item conservation, 119, 122 + \subitem de l'\IeC {\'e}nergie, 122, 124 + \subitem de l'\IeC {\'e}nergie m\IeC {\'e}canique, 122 + \item conservation de l'\IeC {\'e}nergie, 104 + \item conservative, 124, 125 \item constante \subitem de la gravitation universelle, 58 \item construction \subitem de Proctor, 66, 67 - \item convection, 107 - \item conversion, 161 - \item coordonn\IeC {\'e}e, 165, 166 - \subitem sph\IeC {\'e}riques, 165 + \item convection, 109 + \item conversion, 163 + \item coordonn\IeC {\'e}e, 167, 168 + \subitem sph\IeC {\'e}riques, 167 \item coordonn\IeC {\'e}e, 22, 37 \subitem circulaire, 47, 80 \item corps @@ -174,44 +174,43 @@ \subitem aristot\IeC {\'e}licienne, 49 \subitem de Platon, 52 \item courbure, 45, 46 - \item courbure de l'espace, 191, 194 + \item courbure de l'espace, 193, 196 \item crat\IeC {\`e}re \subitem lunaire, 49 \item cristal, 70 \item cristallin, 49 - \item cro\IeC {\^u}te terrestre, 110 - \item croute terrestre, 199 + \item cro\IeC {\^u}te terrestre, 112, 201 \item cycle - \subitem d'Otto, 153 + \subitem d'Otto, 155 \indexspace {\bfseries{D}\;\rule[3pt]{5cm}{0.2pt}}\smallskip\nopagebreak - \item d\IeC {\'e}bit, 104 - \subitem am\IeC {\'e}nag\IeC {\'e}, 203 - \subitem de restitution, 203 + \item d\IeC {\'e}bit, 106 + \subitem am\IeC {\'e}nag\IeC {\'e}, 205 + \subitem de restitution, 205 \item d\IeC {\'e}c\IeC {\'e}l\IeC {\'e}ration, 57 - \item d\IeC {\'e}chet radioactif, 112 - \item d\IeC {\'e}construction, 106 - \item d\IeC {\'e}faut de masse, 111 + \item d\IeC {\'e}chet radioactif, 114 + \item d\IeC {\'e}construction, 108 + \item d\IeC {\'e}faut de masse, 113 \item degr\IeC {\'e} - \subitem Celsius, 129 - \subitem centigrade, 129 - \subitem Fahrenheit, 129 - \item degr\IeC {\'e} de libert\IeC {\'e}, 145 - \item Delambre, 168 - \item demi-vie, 112 + \subitem Celsius, 131 + \subitem centigrade, 131 + \subitem Fahrenheit, 131 + \item degr\IeC {\'e} de libert\IeC {\'e}, 147 + \item Delambre, 170 + \item demi-vie, 114 \item d\IeC {\'e}placement, 38 \item d\IeC {\'e}riv\IeC {\'e}e, 38 - \item description de l'exp\IeC {\'e}rience, 174 + \item description de l'exp\IeC {\'e}rience, 176 \item d\IeC {\'e}sint\IeC {\'e}gration, 33 \item deut\IeC {\'e}rium, 33 \item diam\IeC {\`e}tre - \subitem apparent, 27, 168 - \item dilatation du temps, 191 + \subitem apparent, 27, 170 + \item dilatation du temps, 193 \item dimension, 22, 37, 73 - \item discussion, 176 - \item dissipation de l'\IeC {\'e}nergie, 103 + \item discussion, 178 + \item dissipation de l'\IeC {\'e}nergie, 105 \item distance \subitem de freinage, 70 \subitem parcourue, 38 @@ -225,25 +224,25 @@ {\bfseries{E}\;\rule[3pt]{5cm}{0.2pt}}\smallskip\nopagebreak \item eau - \subitem chaude sanitaire, 108, 109 - \item \IeC {\'e}cart, 175, 244 - \subitem relatif, 244 - \subitem type, 245 - \item \IeC {\'e}chantillon, 246 + \subitem chaude sanitaire, 109, 110 + \item \IeC {\'e}cart, 177, 246 + \subitem relatif, 246 + \subitem type, 247 + \item \IeC {\'e}chantillon, 248 \item \IeC {\'e}clipse, 64 \subitem annulaire, 28 - \subitem de Lune, 169 - \subitem de Soleil, 169 + \subitem de Lune, 171 + \subitem de Soleil, 171 \subitem lunaire, 28 \subitem solaire, 28, 64 \subitem totale, 28 - \item \IeC {\'e}cliptique, 26--28, 165, 167, 198, 199 - \item EE, 162 + \item \IeC {\'e}cliptique, 26--28, 167, 169, 200, 201 + \item EE, 164 \item effet - \subitem de serre, 114 - \subitem photo\IeC {\'e}lectrique, 107, 109 + \subitem de serre, 116 + \subitem photo\IeC {\'e}lectrique, 109, 111 \item Eiffel, 53 - \item Einstein, 191 + \item Einstein, 193 \item Einstein, 47, 55 \item \IeC {\'e}lectron, 32, 33 \item \IeC {\'e}l\IeC {\'e}ment @@ -253,39 +252,39 @@ \subitem feu, 51 \item \IeC {\'e}lement \subitem terre, 51 - \item ellipse, 172, 199 + \item ellipse, 174, 201 \item ellipse, 26, 46 \item elliptique, 26 - \item enclassement, 245 - \item \IeC {\'e}nergie, 99, 117, 119, 129, 180 - \subitem \IeC {\'e}olienne, 106 - \subitem cin\IeC {\'e}tique, 101, 104, 107, 119, 120, 132 - \subitem de combustion, 113 - \subsubitem des d\IeC {\'e}chets, 206 - \subitem grise, 107, 109 - \subitem hydraulique, 103, 203 - \subitem interne, 132 - \subitem m\IeC {\'e}canique, 102, 120, 121 - \subitem non renouvelable, 110 - \subitem potentielle, 100, 104, 119, 120, 122, 127, 132 - \subitem renouvelable, 103 - \subitem solaire, 107 - \subsubitem \IeC {\'e}lectrique, 109 - \subsubitem thermique, 107, 108 - \item entropie, 156 - \item \IeC {\'e}olienne, 204, 205 - \item \IeC {\'e}picycle, 182 - \item \IeC {\'e}quateur, 183 - \subitem terrestre, 181 + \item enclassement, 247 + \item \IeC {\'e}nergie, 101, 119, 121, 131, 182 + \subitem \IeC {\'e}olienne, 108 + \subitem cin\IeC {\'e}tique, 103, 106, 109, 121, 122, 134 + \subitem de combustion, 115 + \subsubitem des d\IeC {\'e}chets, 208 + \subitem grise, 109, 112 + \subitem hydraulique, 105, 205 + \subitem interne, 134 + \subitem m\IeC {\'e}canique, 104, 122, 123 + \subitem non renouvelable, 112 + \subitem potentielle, 102, 106, 121, 122, 124, 129, 134 + \subitem renouvelable, 105 + \subitem solaire, 109 + \subsubitem \IeC {\'e}lectrique, 111 + \subsubitem thermique, 109, 110 + \item entropie, 158 + \item \IeC {\'e}olienne, 206, 207 + \item \IeC {\'e}picycle, 184 + \item \IeC {\'e}quateur, 185 + \subitem terrestre, 183 \item \IeC {\'e}quigravit\IeC {\'e}, 40 - \item \IeC {\'e}quinoxe, 198 - \item \IeC {\'e}quipartition de l'\IeC {\'e}nergie, 145 - \item \IeC {\'E}ratosth\IeC {\`e}ne, 64, 167, 207 - \item erreur, 175, 176 - \subitem syst\IeC {\'e}matique, 176 - \item erreur, 244 - \subitem relative, 244 - \subitem syst\IeC {\'e}matique, 244 + \item \IeC {\'e}quinoxe, 200 + \item \IeC {\'e}quipartition de l'\IeC {\'e}nergie, 147 + \item \IeC {\'E}ratosth\IeC {\`e}ne, 64, 169, 209 + \item erreur, 177, 178 + \subitem syst\IeC {\'e}matique, 178 + \item erreur, 246 + \subitem relative, 246 + \subitem syst\IeC {\'e}matique, 246 \item espace \subitem courbe, 47 \subitem interstellaire, 23 @@ -295,89 +294,90 @@ \item \IeC {\'E}toile \subitem Polaire, 26 \item \IeC {\'e}toile, 23, 24, 26 - \subitem \IeC {\`a} neutrons, 24, 177 + \subitem \IeC {\`a} neutrons, 24, 179 \subitem du matin, 26 \subitem du soir, 26 \subitem filante, 26 - \subitem nouvelle, 177 + \subitem nouvelle, 179 \item Everest, 59 - \item excentricit\IeC {\'e}, 172 - \item exemple de calcul, 176 + \item excentricit\IeC {\'e}, 174 + \item exemple de calcul, 178 \item exoplan\IeC {\`e}te, 24 - \item EXP, 162 - \item expansion, 177 + \item EXP, 164 + \item expansion, 179 \item expansion, 22, 23, 41 - \item extrados, 106 + \item extrados, 108 \indexspace {\bfseries{F}\;\rule[3pt]{5cm}{0.2pt}}\smallskip\nopagebreak - \item Fahrenheit, 129 + \item Fahrenheit, 131 \item fermion, 35 - \item filaments, 177 - \item fioul, 113 - \item fission, 111, 112 - \item fluide caloriporteur, 108, 112 - \item forage, 110, 206 + \item filaments, 179 + \item fioul, 115 + \item fission, 113, 114 + \item fluide caloporteur, 113 + \item fluide caloriporteur, 110 + \item forage, 112, 208 \item force, 52, 54, 55, 62, 81 \subitem \IeC {\'e}lectrique, 32, 33, 58 \subitem \IeC {\'e}lectromagn\IeC {\'e}tique, 58 - \subitem centrifuge, 61, 62, 67, 193, 194 + \subitem centrifuge, 61, 62, 67, 195, 196 \subitem centrip\IeC {\`e}te, 61--63, 81 - \subitem conservative, 101, 103, 122, 123 - \subitem d'inertie, 61, 67, 68, 193--197 - \subitem de frottement, 101, 119 - \subitem de gravitation, 32, 47, 58--60, 194 - \subitem de mar\IeC {\'e}e, 197 + \subitem conservative, 103, 105, 124, 125 + \subitem d'inertie, 61, 67, 68, 195--199 + \subitem de frottement, 103, 121 + \subitem de gravitation, 32, 47, 58--60, 196 + \subitem de mar\IeC {\'e}e, 199 \subitem de r\IeC {\'e}action, 69 - \subitem dissipative, 101, 103 + \subitem dissipative, 103, 105 \subitem ext\IeC {\'e}rieure, 56, 57 \subitem faible, 58 - \subitem fictive, 61, 63, 193, 194 + \subitem fictive, 61, 63, 195, 196 \subitem fondamentale, 35, 58 - \subitem forte, 32, 58, 111 - \subitem inertielle, 193 - \subitem non conservative, 122 - \item foyer, 172 + \subitem forte, 32, 58, 113 + \subitem inertielle, 195 + \subitem non conservative, 124 + \item foyer, 174 \item foyer \subitem d'une ellipse, 48 \item freinage, 57 - \item frottement, 102 - \item frottement, 42, 44, 47, 54, 57, 69, 121, 122 + \item frottement, 104 + \item frottement, 42, 44, 47, 54, 57, 69, 123, 124 \subitem sec, 69 - \item fusion, 113, 129, 139 + \item fusion, 115, 131, 141 \item fusion, 33 \indexspace {\bfseries{G}\;\rule[3pt]{5cm}{0.2pt}}\smallskip\nopagebreak \item galaxie, 23, 24, 41 - \item Galil\IeC {\'e}e, 43, 49, 53, 179, 191 + \item Galil\IeC {\'e}e, 43, 49, 53, 181, 193 \item Galilei \subitem Galileo, 43 \item gaz - \subitem \IeC {\`a} effet de serre, 106, 107, 110, 114 - \subitem carbonique, 114 - \subitem naturel, 108, 114 + \subitem \IeC {\`a} effet de serre, 108, 109, 112, 116 + \subitem carbonique, 116 + \subitem naturel, 110, 115 \item gaz \subitem interstellaire, 33 \item g\IeC {\'e}ante \subitem rouge, 24, 33 \item g\IeC {\'e}ocentrique, 54 - \item g\IeC {\'e}ostationnaire, 62, 189 - \item g\IeC {\'e}othermie, 110, 205 + \item g\IeC {\'e}ostationnaire, 62, 191 + \item g\IeC {\'e}othermie, 112, 207 \item Giordano \subitem Bruno, 23 - \item gnomon, 167 + \item gnomon, 169 \item Grande \subitem Ourse, 26 - \item grandeur, 177 + \item grandeur, 179 \item grandeur - \subitem conserv\IeC {\'e}e, 117 + \subitem conserv\IeC {\'e}e, 119 \item graphe \subitem horaire, 43 - \item graphe horaire, 178 - \item graphique, 175 + \item graphe horaire, 180 + \item graphique, 177 \item gravitation, 3, 23, 41 \subitem universelle, 47 \item gravit\IeC {\'e}, 41 @@ -399,63 +399,63 @@ \item imminence \subitem de glissement, 69 - \item immobilit\IeC {\'e} de la terre, 182 + \item immobilit\IeC {\'e} de la terre, 184 \item impulsion, 95 - \item incertitude, 169, 175, 176, 178, 246 - \subitem \IeC {\'e}nergie cin\IeC {\'e}tique, 249 - \subitem \IeC {\'e}nergie potentielle, 249 - \subitem absolue, 246, 248 - \subitem addition, 248 - \subitem division, 248 - \subitem multiplication, 247, 248 - \subitem multiplication par un entier, 247, 248 - \subitem puissance, 248 - \subitem relative, 247, 248 - \subitem somme, 247 - \subitem soustraction, 247, 248 - \subitem vitesse chute libre, 249 - \item inertie, 181--183 + \item incertitude, 171, 177, 178, 180, 248 + \subitem \IeC {\'e}nergie cin\IeC {\'e}tique, 251 + \subitem \IeC {\'e}nergie potentielle, 251 + \subitem absolue, 248, 250 + \subitem addition, 250 + \subitem division, 250 + \subitem multiplication, 249, 250 + \subitem multiplication par un entier, 249, 250 + \subitem puissance, 250 + \subitem relative, 249, 250 + \subitem somme, 249 + \subitem soustraction, 249, 250 + \subitem vitesse chute libre, 251 + \item inertie, 183--185 \item inertie, 53 \item infini, 23 \item interaction \subitem fondamentale, 35 - \item intrados, 106 - \item invariance, 193, 194 - \subitem du temps, 192 - \subitem formelle, 193, 194 - \item Io, 199 - \item irrigation, 106 + \item intrados, 108 + \item invariance, 195, 196 + \subitem du temps, 194 + \subitem formelle, 195, 196 + \item Io, 201 + \item irrigation, 108 \indexspace {\bfseries{J}\;\rule[3pt]{5cm}{0.2pt}}\smallskip\nopagebreak - \item joule, 99 + \item joule, 101 \item Jupiter, 26 \indexspace {\bfseries{K}\;\rule[3pt]{5cm}{0.2pt}}\smallskip\nopagebreak - \item Kelvin, 130 + \item Kelvin, 132 \item Kepler - \subitem troisi\IeC {\`e}me loi, 171 + \subitem troisi\IeC {\`e}me loi, 173 \item Kepler, 48, 49 \subitem Johanes, 49 \subitem premi\IeC {\`e}re loi, 48 \subitem seconde loi, 48 \subitem troisi\IeC {\`e}me loi, 48 - \item kilowattheure, 103 + \item kilowattheure, 105 \item kin\IeC {\^e}ma, 37 - \item kWh, 103 + \item kWh, 105 \indexspace {\bfseries{L}\;\rule[3pt]{5cm}{0.2pt}}\smallskip\nopagebreak - \item latitude, 166 + \item latitude, 168 \item latitude, 22 \item Leibnitz, 59 \item L\IeC {\'e}onides, 26 \item lepton, 35 - \item liaison, 111 + \item liaison, 113 \item liaison \subitem interatomique, 70 \item licence @@ -464,13 +464,13 @@ \item ligne des n\oe uds, 28 \item limite \subitem de la deuxi\IeC {\`e}me loi, 61 - \item limite de Betz, 107, 205 - \item limite de Roche, 199 - \item liqu\IeC {\'e}faction, 139 + \item limite de Betz, 109, 207 + \item limite de Roche, 201 + \item liqu\IeC {\'e}faction, 141 \item lithium, 33 - \item Local Standard of Rest, 184 + \item Local Standard of Rest, 186 \item loi - \subitem de la gravitation universelle, 189 + \subitem de la gravitation universelle, 191 \item loi \subitem de l'action et de la r\IeC {\'e}action, 56 \subitem de l'inertie, 55 @@ -483,8 +483,8 @@ \subitem seconde, 55 \subitem seconde loi, 84 \subitem troisieme, 56 - \item loi des gaz parfaits, 141 - \item longitude, 166 + \item loi des gaz parfaits, 143 + \item longitude, 168 \item longitude, 22 \item Lune, 26, 40, 45, 63 \subitem Noire, 28 @@ -492,58 +492,58 @@ \indexspace {\bfseries{M}\;\rule[3pt]{5cm}{0.2pt}}\smallskip\nopagebreak - \item mar\IeC {\'e}e, 3, 65, 195 - \subitem c\IeC {\^o}ti\IeC {\`e}re, 65, 199 + \item mar\IeC {\'e}e, 3, 65, 197 + \subitem c\IeC {\^o}ti\IeC {\`e}re, 65, 201 \subitem champ vectoriel, 67 - \subitem d'\IeC {\'e}quinoxe, 198 + \subitem d'\IeC {\'e}quinoxe, 200 \subitem de basse mer, 65 - \subitem de d\IeC {\'e}clinaison, 199 + \subitem de d\IeC {\'e}clinaison, 201 \subitem de morte eau, 65 - \subitem de p\IeC {\'e}rig\IeC {\'e}e, 199 - \subitem de p\IeC {\'e}rih\IeC {\'e}lie, 199 + \subitem de p\IeC {\'e}rig\IeC {\'e}e, 201 + \subitem de p\IeC {\'e}rih\IeC {\'e}lie, 201 \subitem de pleine mer, 65 \subitem de vive eau, 65 - \subitem de vives et mortes eaux, 198 + \subitem de vives et mortes eaux, 200 \subitem haute, 66 \subitem oc\IeC {\'e}anique, 69 \subitem th\IeC {\'e}orie ondulatoire, 65 \subitem th\IeC {\'e}orie statique, 65 - \item mar\IeC {\'e}e noire, 110 - \item marnage, 198 - \item Mars, 170 + \item mar\IeC {\'e}e noire, 112 + \item marnage, 200 + \item Mars, 172 \item masse - \subitem critique, 111 - \subitem volumique, 104 + \subitem critique, 113 + \subitem volumique, 106 \item masse, 42, 56, 60 \subitem des astres, 64 - \item m\IeC {\^a}t, 205 - \item mazout, 113 + \item m\IeC {\^a}t, 207 + \item mazout, 115 \item MCU, 47, 51, 52, 62, 80, 81 \item m\IeC {\'e}canique, 36, 51 \subitem d'Aristote, 54 \subitem de Newton, 55 \item Mendele\IeC {\"\i }ev, 24 \item mesure - \subitem de distance, 167 + \subitem de distance, 169 \item m\IeC {\'e}t\IeC {\'e}ore, 26 - \item Michelson et Morley, 184 - \item minute d'arc, 161 + \item Michelson et Morley, 186 + \item minute d'arc, 163 \item mol\IeC {\'e}cule, 32 \item monde \subitem sublunaire, 51, 63 \subitem supralunaire, 63 - \item Mont Soleil, 106 - \item morte eau, 198 + \item Mont Soleil, 108 + \item morte eau, 200 \item moteur - \subitem \IeC {\`a} essence, 152 - \subitem \IeC {\`a} explosion, 152 - \item moteur id\IeC {\'e}al, 133 + \subitem \IeC {\`a} essence, 154 + \subitem \IeC {\`a} explosion, 154 + \item moteur id\IeC {\'e}al, 135 \item mouvement \subitem circulaire - \subsubitem uniforme, 189 - \subitem circulaire uniforme, 196 - \subitem rectiligne uniforme, 193 - \subitem simple, 178 + \subsubitem uniforme, 191 + \subitem circulaire uniforme, 198 + \subitem rectiligne uniforme, 195 + \subitem simple, 180 \item mouvement, 36, 37 \subitem acc\IeC {\'e}l\IeC {\'e}r\IeC {\'e}, 48 \subitem balistique, 48 @@ -562,11 +562,11 @@ \subitem simple, 39 \subitem uniforme, 48 \subitem violent, 52 - \item MRU, 178, 193 + \item MRU, 180, 195 \item MRU, 39, 40, 42, 44, 45, 47, 80 - \item MRUA, 178--180 + \item MRUA, 180--182 \item MRUA, 41, 42, 44--46 - \item multiple, 162 + \item multiple, 164 \indexspace {\bfseries{N}\;\rule[3pt]{5cm}{0.2pt}}\smallskip\nopagebreak @@ -575,7 +575,7 @@ \subitem blanche, 24 \subitem noire, 24 \item n\IeC {\'e}buleuse, 23 - \subitem du crabe, 177 + \subitem du crabe, 179 \subitem plan\IeC {\'e}taire, 24 \item neutrino \subitem \IeC {\'e}lectronique, 35 @@ -583,16 +583,16 @@ \item Newton, 41, 47, 51, 54, 57, 63 \subitem Isaac, 56 \item notation - \subitem d'ing\IeC {\'e}nieur, 162, 244 - \subitem scientifique, 162, 244 + \subitem d'ing\IeC {\'e}nieur, 164, 246 + \subitem scientifique, 164, 246 \item Nouvelle \subitem Lune, 28 \item nouvelle \subitem lune, 28 - \item nouvelle lune, 198 + \item nouvelle lune, 200 \item nuage \subitem de Oort, 26 - \item nucl\IeC {\'e}on, 111 + \item nucl\IeC {\'e}on, 113 \item nucl\IeC {\'e}on, 35 \indexspace @@ -600,12 +600,12 @@ \item obus, 44 \item onde, 33, 35 - \item opposition, 171 + \item opposition, 173 \item optique, 55 - \item orbite, 165, 189 - \subitem circulaire, 183 - \subitem de mars, 182 - \subitem elliptique, 171, 172, 182 + \item orbite, 167, 191 + \subitem circulaire, 185 + \subitem de mars, 184 + \subitem elliptique, 173, 174, 184 \item orbite, 26, 40, 62 \subitem circulaire, 47 \subitem de mars, 48 @@ -613,50 +613,50 @@ \subitem g\IeC {\'e}ostationnaire, 49, 84 \item ordonn\IeC {\'e}e, 39 \item ordre - \subitem de grandeur, 244 + \subitem de grandeur, 246 \item origine, 37 \item oxyg\IeC {\`e}ne, 33 \indexspace {\bfseries{P}\;\rule[3pt]{5cm}{0.2pt}}\smallskip\nopagebreak - \item pale, 106, 204, 205 + \item pale, 108, 206, 207 \item palier - \subitem de fusion, 132 - \subitem de liqu\IeC {\'e}faction, 132 - \subitem de solidification, 132 - \subitem de vaporisation, 132 + \subitem de fusion, 134 + \subitem de liqu\IeC {\'e}faction, 134 + \subitem de solidification, 134 + \subitem de vaporisation, 134 \item parabole, 42, 44, 46 - \item parallaxe, 170--172 - \subitem stellaire, 172 - \item param\IeC {\`e}tre, 177 - \item Paris-Cayenne, 171 - \item parsec, 161, 207 + \item parallaxe, 172--174 + \subitem stellaire, 174 + \item param\IeC {\`e}tre, 179 + \item Paris-Cayenne, 173 + \item parsec, 163, 209 \item particule, 33 \subitem \IeC {\'e}l\IeC {\'e}mentaire, 33, 34 - \item Partie th\IeC {\'e}orique, 174 - \item pc, 161 - \item pendule, 177 + \item Partie th\IeC {\'e}orique, 176 + \item pc, 163 + \item pendule, 179 \item pendule \subitem de Foucault, 54 - \item p\IeC {\'e}rig\IeC {\'e}e, 27, 199 - \item p\IeC {\'e}rih\IeC {\'e}lie, 199 - \item p\IeC {\'e}riode, 64, 84, 177, 189 + \item p\IeC {\'e}rig\IeC {\'e}e, 27, 201 + \item p\IeC {\'e}rih\IeC {\'e}lie, 201 + \item p\IeC {\'e}riode, 64, 84, 179, 191 \subitem de r\IeC {\'e}volution, 48 \subitem de rotation, 46 - \subitem sid\IeC {\'e}rale, 181, 183 + \subitem sid\IeC {\'e}rale, 183, 185 \subitem synodique, 64 - \item p\IeC {\'e}trole, 113 + \item p\IeC {\'e}trole, 115 \item phase \subitem de v\IeC {\'e}nus, 49 \subitem lunaire, 28 \item phases de V\IeC {\'e}nus, 54 \item physique \subitem quantique, 3 - \subitem th\IeC {\'e}orique, 127 + \subitem th\IeC {\'e}orique, 129 \item plan \subitem de l'\IeC {\'e}cliptique, 68 - \item plan inclin\IeC {\'e}, 179 + \item plan inclin\IeC {\'e}, 181 \item plan\IeC {\`e}te, 24, 26 \subitem extrasolaire, 24 \subitem jovienne, 26 @@ -665,56 +665,56 @@ \item Platon, 42, 51, 63 \item pleine \subitem Lune, 28 - \item pleine lune, 198 - \item pleine mer, 197, 198 - \item Pline l'Ancien, 167 - \item pluralit\IeC {\'e} des mondes, 192 + \item pleine lune, 200 + \item pleine mer, 199, 200 + \item Pline l'Ancien, 169 + \item pluralit\IeC {\'e} des mondes, 194 \item Pluton, 26 \item poids - \subitem relatif, 195, 197 - \item poids, 45, 58--60, 63, 122, 123 + \subitem relatif, 197, 199 + \item poids, 45, 58--60, 63, 124 \subitem apparent, 60, 62 - \item Polaire, 170 + \item Polaire, 172 \item poly\IeC {\`e}dre \subitem r\IeC {\'e}gulier, 49 - \item pompe \IeC {\`a} chaleur, 110 + \item pompe \IeC {\`a} chaleur, 112 \item pont \subitem du Gard, 44, 45 - \item population, 246 - \item portance, 106 - \item position, 165, 185 + \item population, 248 + \item portance, 108 + \item position, 167, 187 \item position, 37--39, 42, 56 \item positron, 36 \item premi\IeC {\`e}re loi - \subitem de la thermodynamique, 133 - \item premier principe, 133 + \subitem de la thermodynamique, 135 + \item premier principe, 135 \item premi\IeC {\`e}re loi, 55 \item principe - \subitem de conservation de l'\IeC {\'e}nergie, 102 + \subitem de conservation de l'\IeC {\'e}nergie, 104 \item principe \subitem d'incertitude, 34 \subitem d'ind\IeC {\'e}termination, 34 - \subitem de moindre action, 127 + \subitem de moindre action, 129 \item Principia \subitem mathematica, 55 - \item proc\IeC {\'e}dure, 210 + \item proc\IeC {\'e}dure, 212 \item produit - \subitem scalaire, 118 + \subitem scalaire, 120 \item proton, 32, 33 - \item Proxima du Centaure, 172 - \item pseudo-force, 194 - \subitem centrifuge, 195 + \item Proxima du Centaure, 174 + \item pseudo-force, 196 + \subitem centrifuge, 197 \item pseudo-force, 63, 67 \subitem centrifuge, 67, 69 \subitem d'inertie, 67 - \item Ptol\IeC {\'e}m\IeC {\'e}e, 182 - \item puissance, 99, 100 - \subitem de chute, 104 - \subitem install\IeC {\'e}e, 103, 203 + \item Ptol\IeC {\'e}m\IeC {\'e}e, 184 + \item puissance, 101, 102 + \subitem de chute, 106 + \subitem install\IeC {\'e}e, 105, 205 \subitem solaire - \subsubitem moyenne, 108 - \subsubitem utile, 108 - \item pulsar, 177 + \subsubitem moyenne, 110 + \subsubitem utile, 110 + \item pulsar, 179 \indexspace {\bfseries{Q}\;\rule[3pt]{5cm}{0.2pt}}\smallskip\nopagebreak @@ -730,92 +730,92 @@ {\bfseries{R}\;\rule[3pt]{5cm}{0.2pt}}\smallskip\nopagebreak \item radian, 26 - \item radioactivit\IeC {\'e}, 112 - \item rail inclin\IeC {\'e}, 178 + \item radioactivit\IeC {\'e}, 114 + \item rail inclin\IeC {\'e}, 180 \item rapport - \subitem de laboratoire, 173 - \subitem de travail pratique, 174 - \item rapport de compression, 154 - \item rayon de la Terre, 207 - \item r\IeC {\'e}action, 105 - \subitem en cha\IeC {\^\i }ne, 111 - \item r\IeC {\'e}f\IeC {\'e}rentiel, 183, 184 - \subitem absolu, 184 + \subitem de laboratoire, 175 + \subitem de travail pratique, 176 + \item rapport de compression, 156 + \item rayon de la Terre, 209 + \item r\IeC {\'e}action, 107 + \subitem en cha\IeC {\^\i }ne, 113 + \item r\IeC {\'e}f\IeC {\'e}rentiel, 185, 186 + \subitem absolu, 186 \subitem acc\IeC {\'e}l\IeC {\'e}r\IeC {\'e}, 61 \subitem en rotation, 63, 67 - \subitem inertiel, 62, 63, 67, 193 + \subitem inertiel, 62, 63, 67, 195 \subitem non acc\IeC {\'e}l\IeC {\'e}r\IeC {\'e}, 63 - \subitem non inertiel, 63, 67, 193, 194 + \subitem non inertiel, 63, 67, 195, 196 \subitem non-inertiel, 62 - \subitem tournant, 193, 195 - \item r\IeC {\`e}gle de Betz, 107, 204 - \item relativit\IeC {\'e}, 182 - \subitem restreinte, 184 - \item relativit\IeC {\'e}, 21, 191 - \subitem de Galil\IeC {\'e}e, 193 - \subitem g\IeC {\'e}n\IeC {\'e}rale, 3, 47, 51, 194 - \subitem galil\IeC {\'e}enne, 191, 194 - \subitem restreinte, 23, 51, 191, 193 + \subitem tournant, 195, 197 + \item r\IeC {\`e}gle de Betz, 109, 206 + \item relativit\IeC {\'e}, 184 + \subitem restreinte, 186 + \item relativit\IeC {\'e}, 21, 193 + \subitem de Galil\IeC {\'e}e, 195 + \subitem g\IeC {\'e}n\IeC {\'e}rale, 3, 47, 51, 196 + \subitem galil\IeC {\'e}enne, 193, 196 + \subitem restreinte, 23, 51, 193, 195 \item rendement - \subitem hydraulique, 104 - \subitem maximum, 133 - \subitem optique, 108 - \subitem photo\IeC {\'e}lectrique, 109 + \subitem hydraulique, 106 + \subitem maximum, 135 + \subitem optique, 110 + \subitem photo\IeC {\'e}lectrique, 111, 112 \item repos \subitem naturel, 52 \item ressort, 60, 70 - \item r\IeC {\'e}sultats, 174 - \item r\IeC {\'e}sum\IeC {\'e}, 174 + \item r\IeC {\'e}sultats, 176 + \item r\IeC {\'e}sum\IeC {\'e}, 176 \item r\IeC {\'e}tine, 49 - \item r\IeC {\'e}trogradation, 182 - \item Richer, 170 - \item Riehen, 110 + \item r\IeC {\'e}trogradation, 184 + \item Richer, 172 + \item Riehen, 112 \item rotation - \subitem de la Terre, 181 - \subitem de la terre, 181 - \subitem du Soleil, 183 - \item roue \IeC {\`a} aube, 105 + \subitem de la Terre, 183 + \subitem de la terre, 183 + \subitem du Soleil, 185 + \item roue \IeC {\`a} aube, 107 \indexspace {\bfseries{S}\;\rule[3pt]{5cm}{0.2pt}}\smallskip\nopagebreak \item saison, 26, 27 \subitem d'\IeC {\'e}clipse, 29 - \item satellite, 189 + \item satellite, 191 \item satellite, 3, 41, 47, 49, 54, 62, 84 \subitem de jupiter, 49 - \item Saturne, 200 - \item scaph\IeC {\'e}, 168 + \item Saturne, 202 + \item scaph\IeC {\'e}, 170 \item scolastique, 53 - \item second principe, 157 + \item second principe, 159 \item seconde - \subitem d'arc, 161 + \subitem d'arc, 163 \subitem loi - \subsubitem de Newton, 180, 189 - \item seconde loi, 193 - \item s\IeC {\'e}isme, 110 - \item SI, 161 + \subsubitem de Newton, 182, 191 + \item seconde loi, 195 + \item s\IeC {\'e}isme, 112 + \item SI, 163 \item signe - \subitem des \IeC {\'e}carts, 244 + \subitem des \IeC {\'e}carts, 246 \item silicium - \subitem monocristallin, 109 - \subitem polycristallin, 109 - \item Soleil, 181 + \subitem monocristallin, 111 + \subitem polycristallin, 111 + \item Soleil, 183 \item Soleil, 24--26 - \item soleil, 106 - \item solidification, 139 - \item solstice, 198 - \subitem d'\IeC {\'e}t\IeC {\'e}, 167 - \item sous-multiple, 162 - \item sph\IeC {\'e}rique, 165 + \item soleil, 108 + \item solidification, 141 + \item solstice, 200 + \subitem d'\IeC {\'e}t\IeC {\'e}, 169 + \item sous-multiple, 164 + \item sph\IeC {\'e}rique, 167 \item sph\IeC {\`e}re \subitem cristalline, 49 \item sph\IeC {\'e}rique, 37 - \item stade, 168 + \item stade, 170 \item statique, 69 - \item Strabon, 167 + \item Strabon, 169 \item structure - \subitem de rapport, 173 + \subitem de rapport, 175 \item structure, 21 \item subatomique, 32 \item sublunaire, 42, 45, 51 @@ -824,71 +824,71 @@ \item superg\IeC {\'e}ante, 24 \item supernovae, 24, 33 \item supralunaire, 42, 45 - \item Sy\IeC {\`e}ne, 167 + \item Sy\IeC {\`e}ne, 169 \item Syst\IeC {\`e}me - \subitem International d'unit\IeC {\'e}s, 161 + \subitem International d'unit\IeC {\'e}s, 163 \item syst\IeC {\`e}me - \subitem de coordonn\IeC {\'e}es circulaires, 165 + \subitem de coordonn\IeC {\'e}es circulaires, 167 \item syst\IeC {\`e}me \subitem d'axes, 37, 73 - \subitem internationnal, 130 + \subitem international, 132 \subitem solaire, 24 \indexspace {\bfseries{T}\;\rule[3pt]{5cm}{0.2pt}}\smallskip\nopagebreak - \item tableau, 175 + \item tableau, 177 \item tableau \subitem p\IeC {\'e}riodique, 24 \item tache \subitem solaire, 49 \item tache solaire, 54 - \item taux d'injection, 155 - \item Tchernobyl, 113 - \item temp\IeC {\'e}rature d'\IeC {\'e}quilibre, 140 - \item temp\IeC {\'e}rature, 129, 131, 133 + \item taux d'injection, 157 + \item Tchernobyl, 115 + \item temp\IeC {\'e}rature d'\IeC {\'e}quilibre, 142 + \item temp\IeC {\'e}rature, 131, 133, 134 \item temps, 21, 22, 43 \subitem de vol, 45 \item Terre, 26 \item th\IeC {\'e}or\IeC {\`e}me - \subitem d'addition des vitesses, 192 - \subitem de conservation, 99 - \subsubitem de l'\IeC {\'e}nergie cin\IeC {\'e}tique, 101 - \subsubitem de l'\IeC {\'e}nergie m\IeC {\'e}canique, 101 - \subitem de l'\IeC {\'e}nergie cin\IeC {\'e}tique, 101 + \subitem d'addition des vitesses, 194 + \subitem de conservation, 101 + \subsubitem de l'\IeC {\'e}nergie cin\IeC {\'e}tique, 103 + \subsubitem de l'\IeC {\'e}nergie m\IeC {\'e}canique, 103 + \subitem de l'\IeC {\'e}nergie cin\IeC {\'e}tique, 103 \item th\IeC {\'e}orie \subitem des humeurs, 51 - \item thermodynamique, 133 - \item titre, 174 + \item thermodynamique, 135 + \item titre, 176 \item toupie, 27 \item trajectoire, 26, 33, 35 \item transformation - \subitem de Galil\IeC {\'e}e, 194 - \subitem galil\IeC {\'e}enne, 192 - \item transition d'\IeC {\'e}tat, 139 - \item transmutation, 113 - \item travail, 99, 132 - \item travail, 117--120, 122, 123 - \subitem simple, 118 + \subitem de Galil\IeC {\'e}e, 196 + \subitem galil\IeC {\'e}enne, 194 + \item transition d'\IeC {\'e}tat, 141 + \item transmutation, 115 + \item travail, 101, 134 + \item travail, 119--122, 124, 125 + \subitem simple, 120 \item tropique - \subitem du Cancer, 167 + \subitem du Cancer, 169 \item trou \subitem noir, 24 \item trous \subitem noir, 3 - \item turbine, 104, 110, 112, 203 - \subitem Francis, 105 - \subitem Kaplan, 105 - \subitem Pelton, 105 - \item Tycho Brah\IeC {\'e}, 182 + \item turbine, 106, 112, 113, 205 + \subitem Francis, 107 + \subitem Kaplan, 107 + \subitem Pelton, 107 + \item Tycho Brah\IeC {\'e}, 184 \item type \subitem de force, 57 \indexspace {\bfseries{U}\;\rule[3pt]{5cm}{0.2pt}}\smallskip\nopagebreak - \item UA, 161 - \item unit\IeC {\'e}, 161 + \item UA, 163 + \item unit\IeC {\'e}, 163 \item unit\IeC {\'e} \subitem de longueur, 37 \item univers, 21, 23, 42, 45 @@ -897,39 +897,39 @@ \indexspace {\bfseries{V}\;\rule[3pt]{5cm}{0.2pt}}\smallskip\nopagebreak - \item valeur en eau, 138 - \item vapeur, 112 - \item vaporisation, 129, 139 - \item variable, 177 - \item variation de l'\IeC {\'e}nergie m\IeC {\'e}canique, 103 - \item vent, 106 + \item valeur en eau, 140 + \item vapeur, 114 + \item vaporisation, 131, 141 + \item variable, 179 + \item variation de l'\IeC {\'e}nergie m\IeC {\'e}canique, 105 + \item vent, 108 \item V\IeC {\'e}nus, 26 \item vitesse - \subitem angulaire, 196 - \subitem constante, 191 - \subitem lin\IeC {\'e}aire, 196 - \item vitesse, 35, 38, 42, 43, 47, 53, 117 + \subitem angulaire, 198 + \subitem constante, 193 + \subitem lin\IeC {\'e}aire, 198 + \item vitesse, 35, 38, 42, 43, 47, 53, 119 \subitem constante, 55 \subitem instantann\IeC {\'e}e, 38 \subitem moyenne, 38 \subitem scalaire, 47, 81 - \item vive eau, 198 + \item vive eau, 200 \item Voie \subitem Lact\IeC {\'e}e, 24, 41 - \item Voie Lact\IeC {\'e}e, 183 - \item volcanisme, 199 + \item Voie Lact\IeC {\'e}e, 185 + \item volcanisme, 201 \indexspace {\bfseries{W}\;\rule[3pt]{5cm}{0.2pt}}\smallskip\nopagebreak - \item watt, 100, 103 + \item watt, 102, 105 \indexspace {\bfseries{Z}\;\rule[3pt]{5cm}{0.2pt}}\smallskip\nopagebreak - \item z\IeC {\'e}nith, 167, 195, 198, 207 - \item z\IeC {\'e}ro, 121 - \subitem de l'\IeC {\'e}nergie potentielle, 125 - \item zone contamin\IeC {\'e}e, 113 + \item z\IeC {\'e}nith, 169, 197, 200, 209 + \item z\IeC {\'e}ro, 123 + \subitem de l'\IeC {\'e}nergie potentielle, 126 + \item zone contamin\IeC {\'e}e, 115 \end{theindex} diff --git a/CoursMecaniqueOSDF.log b/CoursMecaniqueOSDF.log index 2b75ab3..f2fe498 100644 --- a/CoursMecaniqueOSDF.log +++ b/CoursMecaniqueOSDF.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.14159265-2.6-1.40.17 (TeX Live 2016/Debian) (preloaded format=latex 2018.12.20) 2 APR 2019 23:08 +This is pdfTeX, Version 3.14159265-2.6-1.40.17 (TeX Live 2016/Debian) (preloaded format=latex 2018.12.20) 3 APR 2019 21:26 entering extended mode \write18 enabled. %&-line parsing enabled. @@ -915,9 +915,9 @@ Package etexcmds Info: Could not find \expanded. 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Cette constante est [] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - [58] Underfull \hbox (badness 1939) in paragraph at lines 365--366 - \T1/lmr/bx/sc/10 Exemple[] \T1/lmr/m/n/10 Dé-ter-mi-nez la perte de poids que + \T1/lmr/bx/n/10 Exemple[] \T1/lmr/m/n/10 Dé-ter-mi-nez la perte de poids que [] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - [59] File: ./Dynamique/Images/Ascenseur_neg.eps Graphic file (type eps) <./Dynamique/Images/Ascenseur_neg.eps> @@ -2849,67 +2555,22 @@ File: ./Dynamique/Images/Ascenseur_zero.eps Graphic file (type eps) <./Dynamique/Images/Ascenseur_zero.eps> File: ./Dynamique/Images/Ascenseur_pos.eps Graphic file (type eps) <./Dynamique/Images/Ascenseur_pos.eps> - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[60] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[61] +[60] [61] File: ./Dynamique/Images/MCU2.eps Graphic file (type eps) - <./Dynamique/Images/MCU2.eps> - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[62] + <./Dynamique/Images/MCU2.eps> [62] File: ./Cinematique/Images/newton_isaac_h5.eps Graphic file (type eps) - <./Cinematique/Images/newton_isaac_h5.eps> -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[63] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[64] +<./Cinematique/Images/newton_isaac_h5.eps> [63] [64] File: ./Dynamique/Images/PleineBasseMer1.eps Graphic file (type eps) - <./Dynamique/Images/PleineBasseMer1.eps> + +<./Dynamique/Images/PleineBasseMer1.eps> File: ./Dynamique/Images/PleineBasseMer2.eps Graphic file (type eps) -<./Dynamique/Images/PleineBasseMer2.eps> - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[65] +<./Dynamique/Images/PleineBasseMer2.eps> [65] Underfull \hbox (badness 1648) in paragraph at lines 621--622 []\T1/lmr/m/n/10 Pour com-prendre la dy-na-mique du sys-tème [] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - [66] File: ./Dynamique/Images/PleineBasseMerCG.eps Graphic file (type eps) <./Dynamique/Images/PleineBasseMerCG.eps> @@ -2918,79 +2579,35 @@ File: ./Dynamique/Images/ConstructionProctor.eps Graphic file (type eps) <./Dynamique/Images/ConstructionProctor.eps> File: ./Dynamique/Images/Proctor.eps Graphic file (type eps) <./Dynamique/Images/Proctor.eps> - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[67] - -Package amsmath Warning: Foreign command \atopwithdelims; -(amsmath) \frac or \genfrac should be used instead -(amsmath) on input line 667. - - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[68] +[67] [68] File: ./Dynamique/Images/ForceFrottement.eps Graphic file (type eps) <./Dynamique/Images/ForceFrottement.eps> File: ./Dynamique/Images/Frein_de_wagon.eps Graphic file (type eps) -<./Dynamique/Images/Frein_de_wagon.eps> - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[69] +<./Dynamique/Images/Frein_de_wagon.eps> [69] File: ./Dynamique/Images/Essieu_de_wagon.eps Graphic file (type eps) - <./Dynamique/Images/Essieu_de_wagon.eps> + +<./Dynamique/Images/Essieu_de_wagon.eps> File: ./Dynamique/Images/Ressort.eps Graphic file (type eps) <./Dynamique/Images/Ressort.eps> - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - [70] -Underfull \hbox (badness 10000) in paragraph at lines 810--829 +Underfull \hbox (badness 10000) in paragraph at lines 812--831 [] -Overfull \hbox (12.98033pt too wide) in paragraph at lines 832--863 +Overfull \hbox (12.98033pt too wide) in paragraph at lines 834--865 [] $[]$ [] [] -Underfull \hbox (badness 10000) in paragraph at lines 832--863 +Underfull \hbox (badness 10000) in paragraph at lines 834--865 [] -) +) [71 -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[71 - -] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[72] +] [72] \openout2 = `MecaniqueDim/MecaniqueDim.aux'. (./MecaniqueDim/MecaniqueDim.tex @@ -3010,63 +2627,26 @@ Underfull \vbox (badness 10000) has occurred while \output is active [] ] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - [74] File: ./MecaniqueDim/Images/Ballon.eps Graphic file (type eps) - <./MecaniqueDim/Images/Ballon.eps> - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[75] + <./MecaniqueDim/Images/Ballon.eps> [75] File: ./MecaniqueDim/Images/Planincline.eps Graphic file (type eps) - <./MecaniqueDim/Images/Planincline.eps> -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[76] +<./MecaniqueDim/Images/Planincline.eps> [76] File: ./MecaniqueDim/Images/Planincline2.eps Graphic file (type eps) - <./MecaniqueDim/Images/Planincline2.eps> -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[77] +<./MecaniqueDim/Images/Planincline2.eps> [77] File: ./MecaniqueDim/Images/Tirbalistique.eps Graphic file (type eps) - <./MecaniqueDim/Images/Tirbalistique.eps> -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[78] +<./MecaniqueDim/Images/Tirbalistique.eps> [78] File: ./MecaniqueDim/Images/Tira.eps Graphic file (type eps) - <./MecaniqueDim/Images/Tira.eps> + +<./MecaniqueDim/Images/Tira.eps> File: ./MecaniqueDim/Images/Tirb.eps Graphic file (type eps) <./MecaniqueDim/Images/Tirb.eps> File: ./MecaniqueDim/Images/Parabolesecurite.eps Graphic file (type eps) -<./MecaniqueDim/Images/Parabolesecurite.eps> - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[79] +<./MecaniqueDim/Images/Parabolesecurite.eps> [79] Underfull \vbox (badness 10000) has occurred while \output is active [] @@ -3074,62 +2654,24 @@ Underfull \hbox (badness 10000) in paragraph at lines 419--419 []\T1/lmr/bx/n/12 Mouvement cir-cu-laire uni- [] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - [80] File: ./Cinematique/Images/MCU.eps Graphic file (type eps) - <./Cinematique/Images/MCU.eps> - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[81] + <./Cinematique/Images/MCU.eps> [81] File: ./MecaniqueDim/Images/Viragesvmin0.eps Graphic file (type eps) - <./MecaniqueDim/Images/Viragesvmin0.eps> + +<./MecaniqueDim/Images/Viragesvmin0.eps> File: ./MecaniqueDim/Images/Viragesvminpas0.eps Graphic file (type eps) -<./MecaniqueDim/Images/Viragesvminpas0.eps> - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[82] +<./MecaniqueDim/Images/Viragesvminpas0.eps> [82] File: ./MecaniqueDim/Images/Viragesvmaxfinie.eps Graphic file (type eps) - <./MecaniqueDim/Images/Viragesvmaxfinie.eps> -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[83] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[84]) - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[85 +<./MecaniqueDim/Images/Viragesvmaxfinie.eps> [83] [84]) [85 ] \openout2 = `MecaniqueDifferentielle/MecaniqueDifferentielle.aux'. - (./MecaniqueDifferentielle/MecaniqueDifferentielle.tex [86 + +(./MecaniqueDifferentielle/MecaniqueDifferentielle.tex [86 @@ -3144,24 +2686,10 @@ Underfull \hbox (badness 3291) in paragraph at lines 16--17 [87 -] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[88] +] [88] File: ./MecaniqueDifferentielle/Images/Chutevisqueuse.eps Graphic file (type ep s) - <./MecaniqueDifferentielle/Images/Chutevisqueuse.eps> - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[89] + <./MecaniqueDifferentielle/Images/Chutevisqueuse.eps> [89] Underfull \hbox (badness 2932) in paragraph at lines 149--151 \T1/lmr/m/n/10 fé-ren-tielle est alors don-née par [] @@ -3177,24 +2705,11 @@ s) File: ./MecaniqueDifferentielle/Images/Masseoscillante.eps Graphic file (type e ps) -<./MecaniqueDifferentielle/Images/Masseoscillante.eps> - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[90] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[91] +<./MecaniqueDifferentielle/Images/Masseoscillante.eps> [90] [91] File: ./MecaniqueDifferentielle/Images/Massesuspendue.eps Graphic file (type ep s) - <./MecaniqueDifferentielle/Images/Massesuspendue.eps> + +<./MecaniqueDifferentielle/Images/Massesuspendue.eps> File: ./MecaniqueDifferentielle/Images/Masseoscillantesuspendue.eps Graphic fil e (type eps) @@ -3203,30 +2718,10 @@ Underfull \hbox (badness 1968) in paragraph at lines 305--307 \T1/lmr/m/n/10 C'est une équa-tion dif-fé-ren-tielle, à c÷f-fi-cients [] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[92]) - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[93] +[92]) [93] \openout2 = `QtiteMvt/QtiteMvt.aux'. - (./QtiteMvt/QtiteMvt.tex - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[94 + (./QtiteMvt/QtiteMvt.tex [94 @@ -3237,41 +2732,15 @@ Underfull \hbox (badness 2158) in paragraph at lines 50--50 []\T1/lmr/bx/n/14.4 Choc par-fai-te-ment élas- [] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - [96] Underfull \hbox (badness 1189) in paragraph at lines 160--162 []\T1/lmr/m/n/10 Comme exemple de choc par-fai-te-ment mou, [] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[97] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[98] (./QtiteMvt/Images/choc2dimimpact.eps_tex +[97] [98] (./QtiteMvt/Images/choc2dimimpact.eps_tex File: ./QtiteMvt/Images/choc2dimimpact.eps Graphic file (type eps) -<./QtiteMvt/Images/choc2dimimpact.eps>)) - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[99] +<./QtiteMvt/Images/choc2dimimpact.eps>)) [99] \openout2 = `Energie/Energie.aux'. (./Energie/Energie.tex [100 @@ -3290,94 +2759,29 @@ Underfull \vbox (badness 1337) has occurred while \output is active [] ] File: ./Energie/Images/ChevalVapeur.eps Graphic file (type eps) -<./Energie/Images/ChevalVapeur.eps> - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[102] +<./Energie/Images/ChevalVapeur.eps> [102] File: ./Energie/Images/En_cin_pot_circ.eps Graphic file (type eps) - <./Energie/Images/En_cin_pot_circ.eps> -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[103] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[104] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[105] +<./Energie/Images/En_cin_pot_circ.eps> [103] [104] [105] File: ./Energie/Images/Emosson.eps Graphic file (type eps) - <./Energie/Images/Emosson.eps> -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[106] +<./Energie/Images/Emosson.eps> [106] File: ./Energie/Images/Pelton.eps Graphic file (type eps) <./Energie/Images/Pelton.eps> File: ./Energie/Images/TurbinePelton.eps Graphic file (type eps) - <./Energie/Images/TurbinePelton.eps> -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[107] +<./Energie/Images/TurbinePelton.eps> [107] File: ./Energie/Images/Eolienne.eps Graphic file (type eps) <./Energie/Images/Eolienne.eps> File: ./Energie/Images/Aile.eps Graphic file (type eps) - <./Energie/Images/Aile.eps> - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[108] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[109] (./Energie/Images/SolaireThermique.pst) - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. +<./Energie/Images/Aile.eps> [108] [109] (./Energie/Images/SolaireThermique.pst) [110] File: ./Energie/Images/Photoelectric_effect.eps Graphic file (type eps) <./Energie/Images/Photoelectric_effect.eps> File: ./Energie/Images/CellulePhotoElectrique.eps Graphic file (type eps) -<./Energie/Images/CellulePhotoElectrique.eps> - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[111] +<./Energie/Images/CellulePhotoElectrique.eps> [111] Underfull \hbox (badness 1014) in paragraph at lines 466--467 []\T1/lmr/m/n/10 Deux autres points doivent aussi être abor- [] @@ -3401,42 +2805,16 @@ Underfull \hbox (badness 2197) in paragraph at lines 495--496 Underfull \vbox (badness 10000) has occurred while \output is active [] - - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[112] + [112] File: ./Energie/Images/ReacteurNucleaire.eps Graphic file (type eps) - <./Energie/Images/ReacteurNucleaire.eps> + +<./Energie/Images/ReacteurNucleaire.eps> Underfull \vbox (badness 10000) has occurred while \output is active [] - - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[113] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - + [113] [114] File: ./Energie/Images/Combustion_methane.eps Graphic file (type eps) - <./Energie/Images/Combustion_methane.eps> - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[115] + <./Energie/Images/Combustion_methane.eps> [115] Underfull \hbox (badness 10000) in paragraph at lines 614--635 [] @@ -3451,33 +2829,12 @@ Underfull \hbox (badness 10000) in paragraph at lines 638--667 [] -) +) [116 -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[116 - -] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[117] +] [117] \openout2 = `EnergieOS/EnergieOS.aux'. - (./EnergieOS/EnergieOS.tex - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[118 + (./EnergieOS/EnergieOS.tex [118 @@ -3495,75 +2852,28 @@ File: ./EnergieOS/Images/Travailvecteur.eps Graphic file (type eps) <./EnergieOS/Images/Travailvecteur.eps> File: ./EnergieOS/Images/Travailgeneral.eps Graphic file (type eps) -<./EnergieOS/Images/Travailgeneral.eps> - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[120] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[121] +<./EnergieOS/Images/Travailgeneral.eps> [120] [121] Overfull \hbox (2.66286pt too wide) in paragraph at lines 139--139 [] [] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - [122] Underfull \vbox (badness 3895) has occurred while \output is active [] - - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[123] + [123] Underfull \hbox (badness 1968) in paragraph at lines 277--277 []\T1/lmr/bx/n/14.4 Limite du théo-rème de [] File: ./EnergieOS/Images/TravailFerme.eps Graphic file (type eps) -<./EnergieOS/Images/TravailFerme.eps> - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[124] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[125] +<./EnergieOS/Images/TravailFerme.eps> [124] [125] Underfull \vbox (badness 1314) has occurred while \output is active [] - - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[126] + [126] \openout7 = `CoursMecaniqueOSDF-gnuplottex-fig1.gnuplot'. - Opening gnuplot stream CoursMecaniqueOSDF-gnuplottex-fig1.gnuplot + +Opening gnuplot stream CoursMecaniqueOSDF-gnuplottex-fig1.gnuplot runsystem(gnuplot CoursMecaniqueOSDF-gnuplottex-fig1.gnuplot 2>>CoursMecaniqueO SDF.gnuploterrors)...executed. @@ -3572,39 +2882,19 @@ n input line 470. (./CoursMecaniqueOSDF-gnuplottex-fig1.tex \plotpoint=\box114 -)) - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[127 +)) [127 ] \openout2 = `PhysiqueTheorique/PhysiqueTheorique.aux'. - (./PhysiqueTheorique/PhysiqueTheorique.tex -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[128 +(./PhysiqueTheorique/PhysiqueTheorique.tex [128 ] Chapitre 9. -[129]) - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[130 +[129]) [130 ] \openout2 = `Thermodynamique/Thermodynamique.aux'. @@ -3636,12 +2926,6 @@ Overfull \hbox (16.71072pt too wide) in paragraph at lines 187--188 [][] [] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - [134] Underfull \hbox (badness 10000) in paragraph at lines 213--233 @@ -3657,23 +2941,9 @@ Underfull \hbox (badness 10000) in paragraph at lines 236--260 [] -) +) [135 -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[135 - -] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[136] +] [136] \openout2 = `ThermodynamiqueOS/ThermodynamiqueOS.aux'. (./ThermodynamiqueOS/ThermodynamiqueOS.tex @@ -3703,49 +2973,15 @@ File: ./ThermodynamiqueOS/Images/Bilame.eps Graphic file (type eps) File: ./ThermodynamiqueOS/Images/DilatationVolumique2.eps Graphic file (type ep s) -<./ThermodynamiqueOS/Images/DilatationVolumique2.eps> - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[138] +<./ThermodynamiqueOS/Images/DilatationVolumique2.eps> [138] Underfull \hbox (badness 1028) in paragraph at lines 156--158 []\T1/lmr/m/n/10 Une pis-cine de [][][][][][][][] est rem-plie [] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[139] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[140] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[141] +[139] [140] [141] Underfull \vbox (badness 1226) has occurred while \output is active [] - - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[142] + [142] Underfull \hbox (badness 10000) in paragraph at lines 377--378 []\T1/lmr/m/n/10 A tem-pé-ra-ture [] @@ -3776,10 +3012,6 @@ Underfull \hbox (badness 1024) in paragraph at lines 547--548 []\T1/lmr/m/n/10 Cela consti-tue le prin-cipe d'équi-par-ti-tion de [] - -LaTeX Warning: Reference `diagrammepv' on page 147 undefined on input line 594. - - [147] File: ./ThermodynamiqueOS/Images/DiagTravailPVisobare.eps Graphic file (type ep s) @@ -3879,36 +3111,9 @@ Annexe A. -] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[162] +] [162] File: ./Annexe-UnitesInternationales/Images/Arc.eps Graphic file (type eps) - <./Annexe-UnitesInternationales/Images/Arc.eps> - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[163] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[164]) - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - + <./Annexe-UnitesInternationales/Images/Arc.eps> [163] [164]) [165] \openout2 = `Annexe-SystemeCoordonnees/Annexe-SystemeCoordonnees.aux'. @@ -3930,19 +3135,13 @@ Underfull \vbox (badness 10000) has occurred while \output is active [] ] File: ./Annexe-SystemeCoordonnees/Images/spherique.eps Graphic file (type eps) -<./Annexe-SystemeCoordonnees/Images/spherique.eps>) - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[168 +<./Annexe-SystemeCoordonnees/Images/spherique.eps>) [168 ] \openout2 = `Annexe-MesuresDistances/Annexe-MesuresDistances.aux'. - (./Annexe-MesuresDistances/Annexe-MesuresDistances.tex + +(./Annexe-MesuresDistances/Annexe-MesuresDistances.tex Annexe C. Underfull \hbox (badness 10000) in paragraph at lines 4--5 @@ -3974,14 +3173,7 @@ Underfull \hbox (badness 1048) in paragraph at lines 116--117 \T1/lmr/m/it/10 ob-ser-vâmes à Pa-ris trois Etoiles dans [] -[173]) - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[174 +[173]) [174 ] \openout2 = `Annexe-TravauxPratiques/Annexe-TravauxPratiques.aux'. @@ -4002,37 +3194,21 @@ Underfull \vbox (badness 10000) has occurred while \output is active [] ] - -LaTeX Warning: Reference `railhorizontal' on page 176 undefined on input line 6 -6. - File: ./Annexe-TravauxPratiques/Images/RailHorizontal.eps Graphic file (type ep s) + <./Annexe-TravauxPratiques/Images/RailHorizontal.eps> Underfull \hbox (badness 1648) in paragraph at lines 77--78 []\T1/lmr/m/n/10 Les ré-sul-tats doivent im-pé-ra-ti-ve-ment fi-gu-rer [] [176] - -LaTeX Warning: Reference `explegraphe' on page 177 undefined on input line 86. - File: ./Annexe-TravauxPratiques/Images/ExpleGraphe.eps Graphic file (type eps) -<./Annexe-TravauxPratiques/Images/ExpleGraphe.eps> - -LaTeX Warning: Reference `tableau' on page 177 undefined on input line 96. - -[177] [178] + <./Annexe-TravauxPratiques/Images/ExpleGraphe.eps> [177] [178] Underfull \hbox (badness 1205) in paragraph at lines 188--189 \T1/lmr/m/n/10 ouest) et me-su-rer suc-ces-si-ve-ment les dis-tances [] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - [179 ] @@ -4058,14 +3234,7 @@ Underfull \hbox (badness 7186) in paragraph at lines 307--308 []\T1/lmr/m/n/10 Verticalement, on a un [] -) - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[182] +) [182] \openout2 = `Annexe-Rotations/Annexe-Rotations.aux'. (./Annexe-Rotations/Annexe-Rotations.tex @@ -4096,20 +3265,7 @@ Underfull \hbox (badness 2753) in paragraph at lines 99--100 []\T1/lmr/m/n/10 car, comme la vi-tesse de la lu-mière vaut [] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[185]) - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[186 +[185]) [186 ] \openout2 = `Annexe-MRUA/Annexe-MRUA.aux'. @@ -4123,17 +3279,11 @@ e (type eps) -]) - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[188] +]) [188] \openout2 = `Annexe-ChuteLune/Annexe-ChuteLune.aux'. - (./Annexe-ChuteLune/Annexe-ChuteLune.tex + +(./Annexe-ChuteLune/Annexe-ChuteLune.tex Annexe G. (./Annexe-ChuteLune/Images/SchemaChuteLune.tex) Underfull \vbox (badness 10000) has occurred while \output is active [] @@ -4164,12 +3314,6 @@ Underfull \vbox (badness 10000) has occurred while \output is active [] ]) - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - [192 ] @@ -4189,31 +3333,11 @@ Underfull \hbox (badness 1107) in paragraph at lines 9--10 ] File: ./Annexe-Relativite/Images/TransGalilee.eps Graphic file (type eps) - <./Annexe-Relativite/Images/TransGalilee.eps> - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[194] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[195]) - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[196] + <./Annexe-Relativite/Images/TransGalilee.eps> [194] [195]) [196] \openout2 = `Annexe-Maree/Annexe-Maree.aux'. - (./Annexe-Maree/Annexe-Maree.tex + +(./Annexe-Maree/Annexe-Maree.tex Annexe J. File: ./Annexe-Maree/Images/Maree.eps Graphic file (type eps) <./Annexe-Maree/Images/Maree.eps> @@ -4229,32 +3353,12 @@ Underfull \vbox (badness 4441) has occurred while \output is active [] ] (./Annexe-Maree/Images/Systterrelune.pst) -(./Annexe-Maree/Images/Systterreluneeau.pst) - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[198] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[199] +(./Annexe-Maree/Images/Systterreluneeau.pst) [198] [199] File: ./Annexe-Maree/Images/Decalages.eps Graphic file (type eps) - <./Annexe-Maree/Images/Decalages.eps> + +<./Annexe-Maree/Images/Decalages.eps> File: ./Annexe-Maree/Images/ViveMorteEau.eps Graphic file (type eps) - -<./Annexe-Maree/Images/ViveMorteEau.eps> - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - + <./Annexe-Maree/Images/ViveMorteEau.eps> [200] Underfull \hbox (badness 2970) in paragraph at lines 142--143 []\T1/lmr/m/n/10 Au pé-ri-gée, la dis-tance Terre-Lune vaut : @@ -4263,19 +3367,12 @@ Underfull \hbox (badness 2970) in paragraph at lines 142--143 Underfull \vbox (badness 1005) has occurred while \output is active [] - - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[201] + [201] File: ./Annexe-Maree/Images/Roche.eps Graphic file (type eps) - <./Annexe-Maree/Images/Roche.eps> -File: ./Annexe-Maree/Images/LimiteRoche1.eps Graphic file (type eps) -<./Annexe-Maree/Images/LimiteRoche1.eps> +<./Annexe-Maree/Images/Roche.eps> +File: ./Annexe-Maree/Images/LimiteRoche1.eps Graphic file (type eps) + <./Annexe-Maree/Images/LimiteRoche1.eps> File: ./Annexe-Maree/Images/LimiteRoche2.eps Graphic file (type eps) <./Annexe-Maree/Images/LimiteRoche2.eps> @@ -4287,27 +3384,14 @@ File: ./Annexe-Maree/Images/LimiteRoche4.eps Graphic file (type eps) <./Annexe-Maree/Images/LimiteRoche4.eps> File: ./Annexe-Maree/Images/LimiteRoche5.eps Graphic file (type eps) -<./Annexe-Maree/Images/LimiteRoche5.eps> - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[202] +<./Annexe-Maree/Images/LimiteRoche5.eps> [202] Underfull \vbox (badness 3108) has occurred while \output is active [] -) - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[203] +) [203] \openout2 = `Annexe-Energies/Annexe-Energies.aux'. - (./Annexe-Energies/Annexe-Energies.tex [204 + +(./Annexe-Energies/Annexe-Energies.tex [204 @@ -4323,33 +3407,12 @@ Underfull \hbox (badness 1067) in paragraph at lines 34--35 [205 -] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[206] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[207] +] [206] [207] Underfull \hbox (badness 3724) in paragraph at lines 135--135 []\T1/lmr/bx/n/14.4 Énergie de com-bus-tion [] -) - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[208 +) [208 ] \openout2 = `Annexe-Exercices/Annexe-Exercices.aux'. @@ -4391,23 +3454,11 @@ Underfull \hbox (badness 1112) in paragraph at lines 327--328 []\T1/lmr/m/n/10 Un avion s'ap-proche d'un porte-avions à [] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - [210] Underfull \hbox (badness 3826) in paragraph at lines 545--556 []\T1/lmr/m/n/10 Une moto passe de [][] à [] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - [211] Underfull \hbox (badness 10000) in paragraph at lines 562--563 []\T1/lmr/m/n/10 Si on sup-pose sa vi-tesse ho-ri-zon-tale @@ -4448,27 +3499,12 @@ Overfull \hbox (8.10452pt too wide) in paragraph at lines 676--677 [] [] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - [212] (./Annexe-Exercices/Images/Poulie.tex) (./Annexe-Exercices/Images/pendante.eps_tex File: ./Annexe-Exercices/Images/pendante.eps Graphic file (type eps) -<./Annexe-Exercices/Images/pendante.eps>) - -LaTeX Warning: `h' float specifier changed to `ht'. - - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[213] (./Annexe-Exercices/Images/deuxpoulies.eps_tex +<./Annexe-Exercices/Images/pendante.eps>) [213] +(./Annexe-Exercices/Images/deuxpoulies.eps_tex File: ./Annexe-Exercices/Images/deuxpoulies.eps Graphic file (type eps) <./Annexe-Exercices/Images/deuxpoulies.eps>) @@ -4476,12 +3512,6 @@ Underfull \hbox (badness 1552) in paragraph at lines 1364--1401 []\T1/lmr/m/n/10 Reprenez la si-tua-tion du pro- [] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - [214] Underfull \hbox (badness 1603) in paragraph at lines 1552--1553 []\T1/lmr/m/n/10 Une voi-ture a une masse $\OML/lmm/m/it/10 m \OT1/lmr/m/n/10 = @@ -4501,17 +3531,7 @@ Underfull \hbox (badness 3439) in paragraph at lines 1743--1744 (./Annexe-Exercices/Images/blocsuspendu.eps_tex File: ./Annexe-Exercices/Images/blocsuspendu.eps Graphic file (type eps) -<./Annexe-Exercices/Images/blocsuspendu.eps>) - -LaTeX Warning: `h' float specifier changed to `ht'. - - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[215] +<./Annexe-Exercices/Images/blocsuspendu.eps>) [215] Output from handle ans going to Solutions.tex File ans already open @@ -4519,12 +3539,6 @@ Underfull \hbox (badness 1117) in paragraph at lines 1848--1849 []\T1/lmr/m/n/10 d'une voi-ture de masse [][] rou-lant à [] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - [216] Underfull \hbox (badness 10000) in paragraph at lines 2196--2203 []\T1/lmr/m/n/10 Un par-ti-cu-lier consomme @@ -4535,23 +3549,10 @@ Underfull \hbox (badness 10000) in paragraph at lines 2196--2203 [][] \T1/lmr/m/n/10 d'éner-gie élec-trique. Il dé-sire [] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[217] (./Solutions.tex - -LaTeX Warning: Reference `defecart' on page 218 undefined on input line 65. - -[218] [219] - -LaTeX Warning: Reference `defecart' on page 220 undefined on input line 150. - -[220] +[217] (./Solutions.tex [218] [219] [220] File: ./Annexe-Exercices/Images/GraphesMRU.eps Graphic file (type eps) - <./Annexe-Exercices/Images/GraphesMRU.eps> + +<./Annexe-Exercices/Images/GraphesMRU.eps> Underfull \hbox (badness 1838) in paragraph at lines 276--278 \T1/lmr/m/n/10 Les deux po-si-tions sont bien évi-dem-ment les [] @@ -4583,17 +3584,11 @@ File: ./Annexe-Exercices/Images/lampe.eps Graphic file (type eps) e.eps_tex File: ./Annexe-Exercices/Images/incline.eps Graphic file (type eps) -<./Annexe-Exercices/Images/incline.eps>) - -LaTeX Warning: `h' float specifier changed to `ht'. - -[235] [236] (./Annexe-Exercices/Images/cordepoulie.eps_tex +<./Annexe-Exercices/Images/incline.eps>) [235] [236] +(./Annexe-Exercices/Images/cordepoulie.eps_tex File: ./Annexe-Exercices/Images/cordepoulie.eps Graphic file (type eps) <./Annexe-Exercices/Images/cordepoulie.eps>) - -LaTeX Warning: `h' float specifier changed to `ht'. - (./Annexe-Exercices/Images/cordepoulietiree.eps_tex File: ./Annexe-Exercices/Images/cordepoulietiree.eps Graphic file (type eps) @@ -4602,29 +3597,18 @@ File: ./Annexe-Exercices/Images/cordepoulietiree.eps Graphic file (type eps) File: ./Annexe-Exercices/Images/cordepoulietireejuste.eps Graphic file (type ep s) -<./Annexe-Exercices/Images/cordepoulietireejuste.eps>) [237] - -LaTeX Warning: `h' float specifier changed to `ht'. - -[238] +<./Annexe-Exercices/Images/cordepoulietireejuste.eps>) [237] [238] Underfull \vbox (badness 2828) has occurred while \output is active [] [239] (./Annexe-Exercices/Images/inclinefrottement.eps_tex File: ./Annexe-Exercices/Images/inclinefrottement.eps Graphic file (type eps) -<./Annexe-Exercices/Images/inclinefrottement.eps>) - -LaTeX Warning: `h' float specifier changed to `ht'. - -[240] [241] (./Annexe-Exercices/Images/blocsuspenduforces.eps_tex +<./Annexe-Exercices/Images/inclinefrottement.eps>) [240] [241] +(./Annexe-Exercices/Images/blocsuspenduforces.eps_tex File: ./Annexe-Exercices/Images/blocsuspenduforces.eps Graphic file (type eps) -<./Annexe-Exercices/Images/blocsuspenduforces.eps>) - -LaTeX Warning: `h' float specifier changed to `ht'. - -[242] +<./Annexe-Exercices/Images/blocsuspenduforces.eps>) [242] Underfull \hbox (badness 1253) in paragraph at lines 599--601 \T1/lmr/m/n/10 par des-cente. Soit au to-tal, pour 5 des-centes [] @@ -4669,12 +3653,6 @@ Underfull \hbox (badness 1264) in paragraph at lines 71--72 \T1/lmr/m/n/10 moyenne des ba-guettes est plus ins-truc-tif. La [] - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - [246] \openout7 = `CoursMecaniqueOSDF-gnuplottex-fig2.gnuplot'. @@ -4685,14 +3663,7 @@ SDF.gnuploterrors)...executed. Package gnuplottex Info: CoursMecaniqueOSDF-gnuplottex-fig2.gnuplot converted o n input line 175. -(./CoursMecaniqueOSDF-gnuplottex-fig2.tex) - -Package Fancyhdr Warning: \headheight is too small (12.2pt): - Make it at least 12.80502pt. - We now make it that large for the rest of the document. - This may cause the page layout to be inconsistent, however. - -[247] [248] +(./CoursMecaniqueOSDF-gnuplottex-fig2.tex) [247] [248] Overfull \hbox (13.96065pt too wide) in paragraph at lines 284--284 [] [] @@ -5068,16 +4039,16 @@ LaTeX Font Warning: Some font shapes were not available, defaults substituted. LaTeX Warning: There were undefined references. -LaTeX Warning: There were multiply-defined labels. +LaTeX Warning: Label(s) may have changed. 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-(expliquer)g(la)h(c)n(h)n(ute)f(de)h(la)1802 4704 y(lune)1968 -4674 y FV(c)2029 4704 y FX(\(v)n(oir)d(aussi)f(page)h(63\).)1885 -4812 y(De)41 b(fa\347on)g(plus)g(d\351taill\351e,)h(mais)f -(partiellemen)n(t)g(in-)1802 4912 y(exacte)18 b(comme)h(nous)g(le)g(v)n +(la)1802 4412 y(T)-7 b(erre)28 b(tout)i(en)f(tournan)n(t)g(autour)g +(d'elle.)h(La)f(\034gure)f(2.8)1802 4512 y(pr\351sen)n(te)39 +b(l'illustration)2584 4482 y FW(51)2695 4512 y FY(utilis\351e)h(par)g +(Newton)h(dans)1802 4611 y(les)29 b(principia)g(de)h(1728)e(p)r(our)h +(expliquer)g(la)h(c)n(h)n(ute)f(de)h(la)1802 4711 y(lune)1968 +4681 y FW(c)2029 4711 y FY(\(v)n(oir)d(aussi)f(page)h(63\).)1885 +4819 y(De)41 b(fa\347on)g(plus)g(d\351taill\351e,)h(mais)f +(partiellemen)n(t)g(in-)1802 4919 y(exacte)18 b(comme)h(nous)g(le)g(v)n (errons)e(plus)i(tard,)g(on)f(p)r(ourrait)p 0 TeXcolorgray -1802 5015 734 4 v 1895 5091 a FE(c.)35 b(A)-8 b(v)n(ec)29 +1802 5021 734 4 v 1895 5098 a FE(c.)35 b(A)-8 b(v)n(ec)29 b(mes)f(plus)g(vifs)f(remerciemen)n(ts)i(\340)f(Emilio)f(Segr\350)h -(Vi-)1802 5170 y(sual)g(Arc)n(hiv)n(es)g(p)r(our)g(son)h(autorisation)g -(de)g(repro)r(duire)f(ici)f(cette)1802 5249 y(magni\034que)39 +(Vi-)1802 5177 y(sual)g(Arc)n(hiv)n(es)g(p)r(our)g(son)h(autorisation)g +(de)g(repro)r(duire)f(ici)f(cette)1802 5256 y(magni\034que)39 b(illustration)f(de)h(Newton)h(tir\351e)e(des)h(Principia)f(de)1802 -5328 y(1728)29 b(pr\351sen)n(tan)n(t)h(la)e(relation)g(en)n(tre)h(c)n -(h)n(ute)g(et)g(satellisation.)f(On)1802 5407 y(la)23 +5335 y(1728)29 b(pr\351sen)n(tan)n(t)h(la)e(relation)g(en)n(tre)h(c)n +(h)n(ute)g(et)g(satellisation.)f(On)1802 5414 y(la)23 b(trouv)n(e)i(aussi)e(dans)h(\(Lindemann,)g(1999,)h(p.)e(164\).)p -0 TeXcolorgray 0 TeXcolorgray 1719 5617 a FX(45)p 0 TeXcolorgray +0 TeXcolorgray 0 TeXcolorgray 1719 5624 a FY(45)p 0 TeXcolorgray eop end %%Page: 46 46 TeXDict begin 46 45 bop 0 TeXcolorgray 0 TeXcolorgray -116 267 a FQ(2.5.)55 b(MOUVEMENTS)27 b(SIMPLES)1202 b(CHAPITRE)28 -b(2.)55 b(LA)27 b(CIN\311MA)-7 b(TIQUE)p 116 301 3753 +116 269 a FR(2.5.)55 b(MOUVEMENTS)27 b(SIMPLES)1202 b(CHAPITRE)28 +b(2.)55 b(LA)27 b(CIN\311MA)-7 b(TIQUE)p 116 302 3753 4 v 0 TeXcolorgray 0 TeXcolorgray 0 TeXcolorgray 297 -589 a FK(Figure)29 b(2.7)h(\025)f FJ(L'id\351)l(e)f(de)g(la)f(chute)i -(de)f(la)f(Lune)p 0 TeXcolorgray 395 1996 a +596 a FK(Figure)29 b(2.7)h(\025)f FJ(L'id\351)l(e)f(de)g(la)f(chute)i +(de)f(la)f(Lune)p 0 TeXcolorgray 395 2003 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 395 1996 -a 395 1996 a + 395 2003 +a 395 2003 a tx@Dict begin { 57.21819 59.03915 } PutCoor PutBegin end - 395 1996 a @beginspecial @setspecial + 395 2003 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.56903 SLW 0 setgray 0 360 54.77126 54.77126 0.0 0.0 0 true Ellipse closepath gsave 0.56903 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end @endspecial -395 1996 a +395 2003 a tx@Dict begin PutEnd end - 395 1996 a 395 1996 a + 395 2003 a 395 2003 a tx@Dict begin gsave STV CP T /ps@rot 90. def grestore end - 395 1996 a 395 1996 + 395 2003 a 395 2003 a tx@Dict begin { 57.18974 141.97849 } PutCoor PutBegin end - 395 1996 a 395 1996 a + 395 2003 a 395 2003 a tx@Dict begin ps@rot RotBegin end - 395 1996 a @beginspecial @setspecial + 395 2003 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.56903 SLW 0 setgray 0 360 8.10901 8.10901 0.0 0.0 0 true Ellipse closepath gsave 0.56903 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end -@endspecial 395 1996 a +@endspecial 395 2003 a tx@Dict begin RotEnd end - 395 1996 a 395 1996 a + 395 2003 a 395 2003 a tx@Dict begin PutEnd end - 395 1996 + 395 2003 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.25 1. 2.84526 2. 1. .setopacityalpha Arrow @@ -835506,12 +835517,12 @@ a @beginspecial @setspecial 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end -@endspecial 395 1996 a +@endspecial 395 2003 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end 395 -1996 a 395 1996 a +2003 a 395 2003 a tx@Dict begin { 55.9947 106.61191 } PutCoor PutBegin end - 395 1996 a @beginspecial @setspecial + 395 2003 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { BeginArrow 1. 1. scale false 0.25 1. 2.84526 2. 1. .setopacityalpha Arrow EndArrow moveto } def /ArrowB { } def 0.42676 SLW 0 setgray /ArrowA { BeginArrow 1. @@ -835530,14 +835541,14 @@ cos exch sin moveto exch arc mtrx setmatrix gsave 0.42676 SLW 0 setgray end -@endspecial 395 1996 a +@endspecial 395 2003 a tx@Dict begin PutEnd end - 395 1996 a 395 1996 a + 395 2003 a 395 2003 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 395 1996 -a 395 1996 a + 395 2003 +a 395 2003 a tx@Dict begin { 61.62834 84.41887 } PutCoor PutBegin end - 395 1996 a @beginspecial @setspecial + 395 2003 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { BeginArrow 1. 1. scale false 0.25 1. 2.84526 2. 1. .setopacityalpha Arrow EndArrow moveto } def /ArrowB { } def 0.42676 SLW 0 setgray /ArrowA { BeginArrow 1. @@ -835556,28 +835567,28 @@ cos exch sin moveto exch arc mtrx setmatrix gsave 0.42676 SLW 0 setgray end @endspecial -395 1996 a +395 2003 a tx@Dict begin PutEnd end - 395 1996 a 395 1996 a + 395 2003 a 395 2003 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 395 1996 a 395 1996 + 395 2003 a 395 2003 a tx@Dict begin { 142.40529 56.76294 } PutCoor PutBegin end - 395 1996 a @beginspecial @setspecial + 395 2003 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.56903 SLW 0 setgray 0 360 8.10901 8.10901 0.0 0.0 0 true Ellipse closepath gsave 0.56903 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end @endspecial 395 -1996 a +2003 a tx@Dict begin PutEnd end - 395 1996 a 395 1996 a + 395 2003 a 395 2003 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 395 1996 a 395 1996 a + 395 2003 a 395 2003 a tx@Dict begin { 61.85597 61.59987 } PutCoor PutBegin end 395 -1996 a @beginspecial @setspecial +2003 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { BeginArrow 1. 1. scale false 0.25 1. 2.84526 2. 1. .setopacityalpha Arrow EndArrow moveto } def /ArrowB { } def 0.42676 SLW 0 setgray /ArrowA { BeginArrow 1. @@ -835595,14 +835606,14 @@ cos exch sin moveto exch arc mtrx setmatrix gsave 0.42676 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end -@endspecial 395 1996 +@endspecial 395 2003 a tx@Dict begin PutEnd end - 395 1996 a 395 1996 a + 395 2003 a 395 2003 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 395 1996 a 395 1996 a + 395 2003 a 395 2003 a tx@Dict begin { 61.40073 75.20021 } PutCoor PutBegin end - 395 1996 + 395 2003 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { BeginArrow 1. 1. scale false 0.25 1. 2.84526 2. 1. .setopacityalpha Arrow EndArrow moveto } @@ -835621,51 +835632,51 @@ cos exch sin moveto exch arc mtrx setmatrix gsave 0.42676 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end -@endspecial 395 1996 a +@endspecial 395 2003 a tx@Dict begin PutEnd end 395 -1996 a 395 1996 a +2003 a 395 2003 a tx@Dict begin { 57.18974 53.7754 } PutCoor PutBegin end - 395 1996 a 299 2025 a FX(T)-7 b(erre)395 -1996 y + 395 2003 a 299 2032 a FY(T)-7 b(erre)395 +2003 y tx@Dict begin PutEnd end - 395 1996 a 395 1996 a + 395 2003 a 395 2003 a tx@Dict begin { 57.18974 156.20479 } PutCoor PutBegin end - 395 1996 a 304 2025 a FX(Lune)395 -1996 y + 395 2003 a 304 2032 a FY(Lune)395 +2003 y tx@Dict begin PutEnd end - 395 1996 a 395 1996 a + 395 2003 a 395 2003 a tx@Dict begin { 72.55414 84.78877 } PutCoor PutBegin end - 395 1996 a 166 2025 a FX(Mouv)n(emen)n(ts) -395 1996 y + 395 2003 a 166 2032 a FY(Mouv)n(emen)n(ts) +395 2003 y tx@Dict begin PutEnd end - 395 1996 a 395 1996 a + 395 2003 a 395 2003 a tx@Dict begin { 131.73557 135.43442 } PutCoor PutBegin end - 395 1996 a 183 2025 -a FX(Mouv)n(emen)n(t)395 1996 y + 395 2003 a 183 2032 +a FY(Mouv)n(emen)n(t)395 2003 y tx@Dict begin PutEnd end - 395 1996 a 395 1996 a + 395 2003 a 395 2003 a tx@Dict begin { 137.14154 126.89864 } PutCoor PutBegin end -395 1996 a 229 2025 a FX(circulaire)395 1996 y +395 2003 a 229 2032 a FY(circulaire)395 2003 y tx@Dict begin PutEnd end - 395 1996 -a 395 1996 a + 395 2003 +a 395 2003 a tx@Dict begin { 39.83365 129.7439 } PutCoor PutBegin end - 395 1996 a 285 2025 a FX(Ch)n(ute)395 1996 + 395 2003 a 285 2032 a FY(Ch)n(ute)395 2003 y tx@Dict begin PutEnd end - 395 1996 a 395 1996 a + 395 2003 a 395 2003 a tx@Dict begin { 42.39436 120.35452 } PutCoor PutBegin end - 395 1996 a 314 2025 a FX(libre)395 -1996 y + 395 2003 a 314 2032 a FY(libre)395 +2003 y tx@Dict begin PutEnd end - 395 1996 a 395 1996 a + 395 2003 a 395 2003 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 395 1996 a 395 1996 a + 395 2003 a 395 2003 a tx@Dict begin { 58.01486 59.83582 } PutCoor PutBegin end 395 -1996 a @beginspecial @setspecial +2003 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.28453 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def 0.0 0.0 /yOrig ED /xOrig ED 53.00722 53.00722 /ry ED /rx ED /angleA /d @@ -835680,14 +835691,14 @@ cos exch sin moveto exch arc mtrx setmatrix gsave 0.28453 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end -@endspecial 395 1996 +@endspecial 395 2003 a tx@Dict begin PutEnd end - 395 1996 a 395 1996 a + 395 2003 a 395 2003 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 395 1996 a 395 1996 a + 395 2003 a 395 2003 a tx@Dict begin { 59.97809 61.05931 } PutCoor PutBegin end - 395 1996 + 395 2003 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.28453 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def 0.0 @@ -835703,14 +835714,14 @@ cos exch sin moveto exch arc mtrx setmatrix gsave 0.28453 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end -@endspecial 395 1996 a +@endspecial 395 2003 a tx@Dict begin PutEnd end 395 -1996 a 395 1996 a +2003 a 395 2003 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 395 1996 a 395 1996 a + 395 2003 a 395 2003 a tx@Dict begin { 60.83168 61.77061 } PutCoor PutBegin end - 395 1996 a @beginspecial + 395 2003 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.28453 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def 0.0 @@ -835726,14 +835737,14 @@ cos exch sin moveto exch arc mtrx setmatrix gsave 0.28453 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end -@endspecial 395 1996 a +@endspecial 395 2003 a tx@Dict begin PutEnd end - 395 1996 a 395 1996 + 395 2003 a 395 2003 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 395 1996 a 395 1996 a + 395 2003 a 395 2003 a tx@Dict begin { 142.12076 56.62067 } PutCoor PutBegin end - 395 1996 a @beginspecial @setspecial + 395 2003 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.28453 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def 0.0 0.0 /yOrig ED /xOrig ED 6.5441 6.5441 /ry ED /rx ED /angleA /d { add @@ -835748,14 +835759,14 @@ moveto exch arc mtrx setmatrix gsave 0.28453 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end -@endspecial 395 1996 a +@endspecial 395 2003 a tx@Dict begin PutEnd end - 395 1996 a 395 1996 a + 395 2003 a 395 2003 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 395 1996 -a 395 1996 a + 395 2003 +a 395 2003 a tx@Dict begin { 142.37682 56.7345 } PutCoor PutBegin end - 395 1996 a @beginspecial @setspecial + 395 2003 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.28453 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def 0.0 0.0 /yOrig ED /xOrig ED 5.5198 5.5198 /ry ED /rx ED /angleA /d { add @@ -835771,19 +835782,19 @@ exch sin moveto exch arc mtrx setmatrix gsave 0.28453 SLW 0 setgray end @endspecial -395 1996 a +395 2003 a tx@Dict begin PutEnd end - 395 1996 a 395 1996 a + 395 2003 a 395 2003 a tx@Dict begin { 80.52087 73.40773 } PutCoor PutBegin end - 395 1996 a 204 2017 -a FX(balistiques)395 1996 y + 395 2003 a 204 2024 +a FY(balistiques)395 2003 y tx@Dict begin PutEnd end - 395 1996 a 395 1996 a + 395 2003 a 395 2003 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end 395 -1996 a 395 1996 a +2003 a 395 2003 a tx@Dict begin { 56.90521 141.69398 } PutCoor PutBegin end - 395 1996 a @beginspecial @setspecial + 395 2003 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.28453 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def 0.0 0.0 /yOrig ED /xOrig ED 6.5441 6.5441 /ry ED /rx ED /angleA /d { add @@ -835798,14 +835809,14 @@ moveto exch arc mtrx setmatrix gsave 0.28453 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end -@endspecial 395 1996 a +@endspecial 395 2003 a tx@Dict begin PutEnd end - 395 1996 a 395 1996 a + 395 2003 a 395 2003 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 395 1996 -a 395 1996 a + 395 2003 +a 395 2003 a tx@Dict begin { 57.18974 141.97849 } PutCoor PutBegin end - 395 1996 a @beginspecial @setspecial + 395 2003 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.28453 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def 0.0 0.0 /yOrig ED /xOrig ED 5.5198 5.5198 /ry ED /rx ED /angleA /d { add @@ -835821,12 +835832,12 @@ exch sin moveto exch arc mtrx setmatrix gsave 0.28453 SLW 0 setgray end @endspecial -395 1996 a +395 2003 a tx@Dict begin PutEnd end - 395 1996 a 0 TeXcolorgray 0 TeXcolorgray 0 -TeXcolorgray 297 2251 a FK(Figure)29 b(2.8)h(\025)f FJ(L'id\351)l(e)f -(de)g(la)f(chute)i(de)f(la)f(Lune)600 2342 y(Il)6 b(lustr)l(ation)28 -b(des)g(Principia.)p 0 TeXcolorgray 266 4548 a @beginspecial + 395 2003 a 0 TeXcolorgray 0 TeXcolorgray 0 +TeXcolorgray 297 2258 a FK(Figure)29 b(2.8)h(\025)f FJ(L'id\351)l(e)f +(de)g(la)f(chute)i(de)f(la)f(Lune)600 2349 y(Il)6 b(lustr)l(ation)28 +b(des)g(Principia.)p 0 TeXcolorgray 266 4555 a @beginspecial 14 @llx 14 @lly 642 @urx 871 @ury 1842 @rwi @setspecial %%BeginDocument: ./Cinematique/Images/newton_isaac_h5.eps %!PS-Adobe-3.0 EPSF-3.0 @@ -969776,67 +969787,67 @@ end %%EOF %%EndDocument - @endspecial 0 TeXcolorgray 116 4805 a FX(dire)g(que)f(la)h(Lune)f(tom) + @endspecial 0 TeXcolorgray 116 4812 a FY(dire)g(que)f(la)h(Lune)f(tom) n(b)r(e)h(sur)f(la)h(T)-7 b(erre)26 b(d'une)i(hauteur)116 -4905 y(\351gale)36 b(\340)h(la)f(distance)h(T)-7 b(erre-Lune)36 -b(en)h(un)g(quart)f(de)h(la)116 5004 y(p)r(\351rio)r(de)32 +4911 y(\351gale)36 b(\340)h(la)f(distance)h(T)-7 b(erre-Lune)36 +b(en)h(un)g(quart)f(de)h(la)116 5011 y(p)r(\351rio)r(de)32 b(de)f(rotation)g(de)h(la)f(Lune)g(autour)g(de)h(la)f(T)-7 -b(erre)116 5104 y(\(cf.)29 b(\034gure)d(2.9\).)199 5208 +b(erre)116 5111 y(\(cf.)29 b(\034gure)d(2.9\).)199 5214 y(De)35 b(cette)f(mani\350re,)f(on)h(p)r(eut)g(calculer)f(la)h(v)-5 -b(aleur)33 b(de)116 5307 y(l'acc\351l\351ration)43 b(que)i(devrait)e(a) -n(v)n(oir)g(la)h(Lune)h(dans)f(sa)116 5407 y(c)n(h)n(ute)33 +b(aleur)33 b(de)116 5314 y(l'acc\351l\351ration)43 b(que)i(devrait)e(a) +n(v)n(oir)g(la)h(Lune)h(dans)f(sa)116 5414 y(c)n(h)n(ute)33 b(sur)g(la)g(T)-7 b(erre)32 b(p)r(our)g(\023)24 b(tom)n(b)r(er)g(\024) 33 b(d'un)h(quart)e(de)p 0 TeXcolorgray 0 TeXcolorgray -0 TeXcolorgray 0 TeXcolorgray 2201 589 a FK(Figure)d(2.9)g(\025)h +0 TeXcolorgray 0 TeXcolorgray 2201 596 a FK(Figure)d(2.9)g(\025)h FJ(Chute)e(de)g(la)f(Lune)h(sur)h(la)e(T)-6 b(err)l(e)p -0 TeXcolorgray 2321 1831 a +0 TeXcolorgray 2321 1838 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 2321 1831 a 2321 1831 a + 2321 1838 a 2321 1838 a tx@Dict begin { 56.62067 46.37775 } PutCoor PutBegin end 2321 -1831 a @beginspecial @setspecial +1838 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.42676 SLW 0 setgray 0 360 35.99252 35.99252 0.0 0.0 0 true Ellipse closepath gsave 0.42676 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end -@endspecial 2321 1831 +@endspecial 2321 1838 a tx@Dict begin PutEnd end - 2321 1831 a 2321 1831 a + 2321 1838 a 2321 1838 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 2321 1831 a 2321 1831 a + 2321 1838 a 2321 1838 a tx@Dict begin { 56.99055 128.03673 } PutCoor PutBegin end 2321 -1831 a @beginspecial @setspecial +1838 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.42676 SLW 0 setgray 0 360 8.25124 8.25124 0.0 0.0 0 true Ellipse closepath gsave 0.42676 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end -@endspecial 2321 1831 +@endspecial 2321 1838 a tx@Dict begin PutEnd end - 2321 1831 a 2321 1831 a + 2321 1838 a 2321 1838 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 2321 1831 a 2321 1831 a + 2321 1838 a 2321 1838 a tx@Dict begin { 140.27135 45.23962 } PutCoor PutBegin end 2321 -1831 a @beginspecial @setspecial +1838 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.42676 SLW 0 setgray 0 360 8.25124 8.25124 0.0 0.0 0 true Ellipse closepath gsave 0.42676 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end -@endspecial 2321 1831 +@endspecial 2321 1838 a tx@Dict begin PutEnd end - 2321 1831 a 2321 1831 a + 2321 1838 a 2321 1838 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 2321 1831 a 2321 1831 a + 2321 1838 a 2321 1838 a tx@Dict begin { 57.24663 45.29654 } PutCoor PutBegin end 2321 -1831 a @beginspecial @setspecial +1838 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { BeginArrow 1. 1. scale false 0.25 1. 2.84526 2. 1. .setopacityalpha Arrow EndArrow moveto } def /ArrowB { } def 0.28453 SLW 0 setgray /ArrowA { BeginArrow 1. @@ -969854,15 +969865,15 @@ cos exch sin moveto exch arc mtrx setmatrix gsave 0.28453 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end -@endspecial 2321 1831 +@endspecial 2321 1838 a tx@Dict begin PutEnd end - 2321 1831 a 2321 1831 a + 2321 1838 a 2321 1838 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 2321 1831 a 2321 1831 a + 2321 1838 a 2321 1838 a tx@Dict begin { 56.76294 46.49155 } PutCoor PutBegin end 2321 -1831 a @beginspecial @setspecial +1838 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.28453 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def 0.0 0.0 /yOrig ED /xOrig ED 34.54146 34.54146 /ry ED /rx ED /angleA /d @@ -969877,15 +969888,15 @@ cos exch sin moveto exch arc mtrx setmatrix gsave 0.28453 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end -@endspecial 2321 1831 +@endspecial 2321 1838 a tx@Dict begin PutEnd end - 2321 1831 a 2321 1831 a + 2321 1838 a 2321 1838 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 2321 1831 a 2321 1831 a + 2321 1838 a 2321 1838 a tx@Dict begin { 57.90106 46.9468 } PutCoor PutBegin end 2321 -1831 a @beginspecial @setspecial +1838 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.28453 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def 0.0 0.0 /yOrig ED /xOrig ED 33.71635 33.71635 /ry ED /rx ED /angleA /d @@ -969899,15 +969910,15 @@ CM def xOrig yOrig T rx ry scale 0 0 moveto exch dup dup cos exch sin moveto exch arc mtrx setmatrix gsave 0.28453 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end -@endspecial 2321 1831 +@endspecial 2321 1838 a tx@Dict begin PutEnd end - 2321 1831 a 2321 1831 a + 2321 1838 a 2321 1838 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 2321 1831 a 2321 1831 a + 2321 1838 a 2321 1838 a tx@Dict begin { 60.3195 48.59705 } PutCoor PutBegin end 2321 -1831 a @beginspecial @setspecial +1838 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.28453 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def 0.0 0.0 /yOrig ED /xOrig ED 34.76907 34.76907 /ry ED /rx ED /angleA /d @@ -969922,10 +969933,10 @@ cos exch sin moveto exch arc mtrx setmatrix gsave 0.28453 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end -@endspecial 2321 1831 +@endspecial 2321 1838 a tx@Dict begin PutEnd end - 2321 1831 a @beginspecial @setspecial + 2321 1838 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { BeginArrow 1. 1. scale false 0.25 1. 2.84526 2. 1. .setopacityalpha Arrow EndArrow moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.25 1. 2.84526 2. @@ -969939,28 +969950,28 @@ def /ArrowB { BeginArrow 1. 1. scale false 0.25 1. 2.84526 2. end @endspecial -2321 1831 a +2321 1838 a tx@Dict begin { 57.18974 38.69556 } PutCoor PutBegin end - 2321 1831 a 2225 1860 a FX(T)f(erre)2321 -1831 y + 2321 1838 a 2225 1866 a FY(T)f(erre)2321 +1838 y tx@Dict begin PutEnd end - 2321 1831 a 2321 1831 a + 2321 1838 a 2321 1838 a tx@Dict begin { 73.12318 92.47096 } PutCoor PutBegin end - 2321 1831 a 2225 1850 -a FC(d)2268 1862 y FB(T)9 b Fz(\000)p FB(L)2321 1831 + 2321 1838 a 2225 1857 +a FC(d)2268 1869 y FB(T)9 b Fz(\000)p FB(L)2321 1838 y tx@Dict begin PutEnd end - 2321 1831 a 2321 1831 a + 2321 1838 a 2321 1838 a tx@Dict begin { 117.50926 45.8087 } PutCoor PutBegin end - 2321 1831 a 2231 1860 a FX(Lune)2321 -1831 y + 2321 1838 a 2231 1866 a FY(Lune)2321 +1838 y tx@Dict begin PutEnd end - 2321 1831 a 2321 1831 a + 2321 1838 a 2321 1838 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 2321 1831 a 2321 1831 + 2321 1838 a 2321 1838 a tx@Dict begin { 140.49898 45.21118 } PutCoor PutBegin end - 2321 1831 a @beginspecial @setspecial + 2321 1838 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.28453 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def 0.0 0.0 /yOrig ED /xOrig ED 7.0847 7.0847 /ry ED /rx ED /angleA /d { add @@ -969975,14 +969986,14 @@ moveto exch arc mtrx setmatrix gsave 0.28453 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end @endspecial -2321 1831 a +2321 1838 a tx@Dict begin PutEnd end - 2321 1831 a 2321 1831 a + 2321 1838 a 2321 1838 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 2321 1831 a 2321 -1831 a + 2321 1838 a 2321 +1838 a tx@Dict begin { 139.7023 44.32916 } PutCoor PutBegin end - 2321 1831 a @beginspecial @setspecial + 2321 1838 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.28453 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def 0.0 0.0 /yOrig ED /xOrig ED 4.83693 4.83693 /ry ED /rx ED /angleA /d { @@ -969997,14 +970008,14 @@ moveto exch arc mtrx setmatrix gsave 0.28453 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end @endspecial -2321 1831 a +2321 1838 a tx@Dict begin PutEnd end - 2321 1831 a 2321 1831 a + 2321 1838 a 2321 1838 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 2321 1831 a 2321 -1831 a + 2321 1838 a 2321 +1838 a tx@Dict begin { 56.90521 128.32126 } PutCoor PutBegin end - 2321 1831 a @beginspecial @setspecial + 2321 1838 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.28453 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def 0.0 0.0 /yOrig ED /xOrig ED 7.0847 7.0847 /ry ED /rx ED /angleA /d { add @@ -970019,14 +970030,14 @@ moveto exch arc mtrx setmatrix gsave 0.28453 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end @endspecial -2321 1831 a +2321 1838 a tx@Dict begin PutEnd end - 2321 1831 a 2321 1831 a + 2321 1838 a 2321 1838 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 2321 1831 a 2321 -1831 a + 2321 1838 a 2321 +1838 a tx@Dict begin { 56.05162 127.75218 } PutCoor PutBegin end - 2321 1831 a @beginspecial @setspecial + 2321 1838 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.28453 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def 0.0 0.0 /yOrig ED /xOrig ED 4.83693 4.83693 /ry ED /rx ED /angleA /d { @@ -970041,213 +970052,213 @@ moveto exch arc mtrx setmatrix gsave 0.28453 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end @endspecial -2321 1831 a +2321 1838 a tx@Dict begin PutEnd end - 2321 1831 a 0 TeXcolorgray 2034 2084 a FX(tour.)23 + 2321 1838 a 0 TeXcolorgray 2034 2091 a FY(tour.)23 b(T)-7 b(r\350s)22 b(grossi\350remen)n(t,)f(en)i(confondan)n(t)g(la)g -(c)n(h)n(ute)g(de)2034 2184 y(la)j(Lune)g(a)n(v)n(ec)e(un)i(simple)g -(mouv)n(emen)n(t)f(balistique)h(don)n(t)2034 2283 y(la)f(comp)r(osan)n +(c)n(h)n(ute)g(de)2034 2190 y(la)j(Lune)g(a)n(v)n(ec)e(un)i(simple)g +(mouv)n(emen)n(t)f(balistique)h(don)n(t)2034 2290 y(la)f(comp)r(osan)n (te)f(v)n(erticale)h(est)g(un)h(MR)n(UA,)g(on)f(p)r(ourrait)2034 -2383 y(en)j(e\033et)g(\351crire)e(:)2226 2616 y FC(h)d -FL(=)g FC(d)2428 2628 y FB(T)9 b(er)r(r)r(e)p Fz(\000)p -FB(Lune)2841 2616 y FL(=)2939 2559 y(1)p 2939 2597 42 -4 v 2939 2673 a(2)2990 2616 y FC(a)18 b FG(\001)h FC(t)3124 -2581 y FF(2)3184 2616 y FL(=)3282 2559 y(1)p 3282 2597 -V 3282 2673 a(2)3333 2616 y FC(a)g FG(\001)3437 2499 -y Fr(\022)3508 2559 y FC(T)p 3508 2597 61 4 v 3517 2673 -a FL(4)3578 2499 y Fr(\023)3639 2516 y FF(2)2034 2847 -y FX(o\371)31 b(T)g(est)g(la)f(p)r(\351rio)r(de)h(de)g(rotation)f(de)h -(la)g(Lune)g(autour)2034 2947 y(de)d(la)f(T)-7 b(erre.)27 -b(Ainsi)h(:)2350 3166 y FC(a)23 b FL(=)2515 3109 y(32)17 -b FG(\001)h FC(d)2700 3121 y FB(t)p Fz(\000)p FB(l)p -2515 3147 289 4 v 2610 3223 a FC(T)2671 3199 y FF(2)2836 -3166 y FL(=)2934 3109 y(32)f FG(\001)i FL(3)p FC(;)14 -b FL(84404)h FG(\001)k FL(10)3507 3079 y FF(8)p 2934 -3147 610 4 v 2961 3236 a FL(\()q(30)e FG(\001)i FL(24)e -FG(\001)i FL(3600\))3478 3194 y FF(2)2417 3361 y FL(=)k(1)p -FC(;)o FL(83)18 b FG(\001)g FL(10)2796 3327 y Fz(\000)p -FF(3)2898 3361 y FL(m)q FC(=)p FL(s)3043 3327 y FF(2)2117 -3550 y FX(Cette)29 b(v)-5 b(aleur)29 b(est)g(du)g(b)r(on)g(ordre)f(de)h -(grandeur)e(puis-)2034 3650 y(qu'en)f(r\351alit\351)f +2390 y(en)j(e\033et)g(\351crire)e(:)2226 2622 y FC(h)d +FL(=)g FC(d)2428 2634 y FB(T)9 b(er)r(r)r(e)p Fz(\000)p +FB(Lune)2841 2622 y FL(=)2939 2566 y(1)p 2939 2603 42 +4 v 2939 2679 a(2)2990 2622 y FC(a)18 b FG(\001)h FC(t)3124 +2588 y FF(2)3184 2622 y FL(=)3282 2566 y(1)p 3282 2603 +V 3282 2679 a(2)3333 2622 y FC(a)g FG(\001)3437 2505 +y Fr(\022)3508 2566 y FC(T)p 3508 2603 61 4 v 3517 2679 +a FL(4)3578 2505 y Fr(\023)3639 2522 y FF(2)2034 2854 +y FY(o\371)31 b(T)g(est)g(la)f(p)r(\351rio)r(de)h(de)g(rotation)f(de)h +(la)g(Lune)g(autour)2034 2953 y(de)d(la)f(T)-7 b(erre.)27 +b(Ainsi)h(:)2350 3172 y FC(a)23 b FL(=)2515 3116 y(32)17 +b FG(\001)h FC(d)2700 3128 y FB(t)p Fz(\000)p FB(l)p +2515 3153 289 4 v 2610 3229 a FC(T)2671 3205 y FF(2)2836 +3172 y FL(=)2934 3116 y(32)f FG(\001)i FL(3)p FC(;)14 +b FL(84404)h FG(\001)k FL(10)3507 3086 y FF(8)p 2934 +3153 610 4 v 2961 3242 a FL(\()q(30)e FG(\001)i FL(24)e +FG(\001)i FL(3600\))3478 3201 y FF(2)2417 3368 y FL(=)k(1)p +FC(;)o FL(83)18 b FG(\001)g FL(10)2796 3334 y Fz(\000)p +FF(3)2898 3368 y FL(m)q FC(=)p FL(s)3043 3334 y FF(2)2117 +3557 y FY(Cette)29 b(v)-5 b(aleur)29 b(est)g(du)g(b)r(on)g(ordre)f(de)h +(grandeur)e(puis-)2034 3656 y(qu'en)f(r\351alit\351)f (l'acc\351l\351ration)g(de)h(la)f(Lune)i(v)n(ers)d(la)i(T)-7 -b(erre)2034 3749 y(v)i(aut)28 b(:)2607 3855 y FC(a)23 -b FL(=)g(2)p FC(;)p FL(7)18 b FG(\001)g FL(10)3012 3821 -y Fz(\000)p FF(3)3114 3855 y FL(m)q FC(=)p FL(s)3259 -3821 y FF(2)2117 4012 y FX(Bien)35 b(en)n(tendu,)g(ces)g(deux)g(v)-5 -b(aleurs)34 b(son)n(t)h(n\351anmoins)2034 4112 y(assez)23 +b(erre)2034 3756 y(v)i(aut)28 b(:)2607 3861 y FC(a)23 +b FL(=)g(2)p FC(;)p FL(7)18 b FG(\001)g FL(10)3012 3827 +y Fz(\000)p FF(3)3114 3861 y FL(m)q FC(=)p FL(s)3259 +3827 y FF(2)2117 4019 y FY(Bien)35 b(en)n(tendu,)g(ces)g(deux)g(v)-5 +b(aleurs)34 b(son)n(t)h(n\351anmoins)2034 4118 y(assez)23 b(di\033\351ren)n(tes.)h(Cep)r(endan)n(t,)g(\351tan)n(t)g(donn\351)g -(les)g(h)n(yp)r(o-)2034 4211 y(th\350ses)29 b(tr\350s)g(grossi\350res)e +(les)g(h)n(yp)r(o-)2034 4218 y(th\350ses)29 b(tr\350s)g(grossi\350res)e (qui)j(on)n(t)f(\351t\351)h(faites,)f(obtenir)h(un)2034 -4311 y(b)r(on)23 b(ordre)e(de)h(grandeur)f(est)i(un)g(r\351sultat)f -(remarquable.)2034 4411 y(En)40 b(e\033et,)h(on)f(a)g(consid\351r\351)f -(que)h(le)g(mouv)n(emen)n(t)g(\351tait)2034 4510 y(balistique,)g +4318 y(b)r(on)23 b(ordre)e(de)h(grandeur)f(est)i(un)g(r\351sultat)f +(remarquable.)2034 4417 y(En)40 b(e\033et,)h(on)f(a)g(consid\351r\351)f +(que)h(le)g(mouv)n(emen)n(t)g(\351tait)2034 4517 y(balistique,)g (c'est-\340-dire)e(qu'\340)h(tout)h(instan)n(t)g(la)g(direc-)2034 -4610 y(tion)29 b(dans)f(laquelle)g(la)g(Lune)h(tom)n(b)r(e)f(est)h(la)f -(m\352me.)h(Or,)2034 4710 y(\351tan)n(t)j(donn\351)f(la)g(courbure)g -(de)h(la)f(T)-7 b(erre,)30 b(sur)i(un)g(quart)2034 4809 +4617 y(tion)29 b(dans)f(laquelle)g(la)g(Lune)h(tom)n(b)r(e)f(est)h(la)f +(m\352me.)h(Or,)2034 4716 y(\351tan)n(t)j(donn\351)f(la)g(courbure)g +(de)h(la)f(T)-7 b(erre,)30 b(sur)i(un)g(quart)2034 4816 y(de)e(p)r(\351rio)r(de,)f(cette)h(direction)g(v)-5 b(arie)28 -b(de)i FL(90)3420 4779 y Fz(\016)3457 4809 y FX(.)g(En)g(r\351alit\351) -2034 4909 y(donc,)c(le)h(mouv)n(emen)n(t)f(n'est)h(pas)f(balistique,)g -(mais)g(cen-)2034 5008 y(tral,)d(c'est-\340-dire)e(que)i(la)g(c)n(h)n -(ute)g(de)g(la)g(Lune)g(se)g(fait)g(tou-)2034 5108 y(jours)f(v)n(ers)f +b(de)i FL(90)3420 4786 y Fz(\016)3457 4816 y FY(.)g(En)g(r\351alit\351) +2034 4915 y(donc,)c(le)h(mouv)n(emen)n(t)f(n'est)h(pas)f(balistique,)g +(mais)g(cen-)2034 5015 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y(Cette)g(l\351gislation)f(a)g(d\351j\340)h(cr\351\351)f(b)r -(eaucoup)g(d'emplois)h(lo-)2034 5407 y(calemen)n(t)k(p)r(our)h(sub)n(v) -n(enir)e(aux)h(b)r(esoins.)p 0 TeXcolorgray 1930 5617 +2034 5314 y(Cette)g(l\351gislation)f(a)g(d\351j\340)h(cr\351\351)f(b)r +(eaucoup)g(d'emplois)h(lo-)2034 5414 y(calemen)n(t)k(p)r(our)h(sub)n(v) +n(enir)e(aux)h(b)r(esoins.)p 0 TeXcolorgray 1930 5624 a(110)p 0 TeXcolorgray eop end %%Page: 111 111 TeXDict begin 111 110 bop 0 TeXcolorgray 0 TeXcolorgray --116 267 a FQ(CHAPITRE)27 b(7.)55 b(L'\311NER)n(GIE)1297 +-116 269 a FR(CHAPITRE)27 b(7.)55 b(L'\311NER)n(GIE)1297 b(7.9.)55 b(\311NER)n(GIES)26 b(RENOUVELABLES)p -116 -301 3753 4 v 0 TeXcolorgray 0 TeXcolorgray 0 TeXcolorgray -1219 589 a FK(Figure)j(7.9)g(\025)h FJ(Solair)l(e)e(thermique)1113 -656 y FI(Eau)d(chaude)f(sanitair)m(e)i(p)m(ar)e(solair)m(e)h(thermique) -p 0 TeXcolorgray 1760 759 a @beginspecial @setspecial +302 3753 4 v 0 TeXcolorgray 0 TeXcolorgray 0 TeXcolorgray +1219 596 a FK(Figure)j(7.9)g(\025)h FJ(Solair)l(e)e(thermique)1113 +662 y FI(Eau)d(chaude)f(sanitair)m(e)i(p)m(ar)e(solair)m(e)h(thermique) +p 0 TeXcolorgray 1760 765 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.4 SLW 0 0 0 setrgbcolor [ 0.0 -170.71649 85.35825 -170.71649 85.35825 0.0 0.0 0.0 /r 14.22636 def /Lineto { Arcto } def 0 setlinejoin false @@ -2447585,12 +2447596,12 @@ Arcto } def 0 setlinejoin false Polygon gsave 0.4 SLW 0 0 1 setrgbcolor 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end -@endspecial 1760 759 a +@endspecial 1760 765 a tx@Dict begin { 89.6264 -91.75984 } PutCoor PutBegin end 1760 -759 a 18 x Ft(Chau\033age)1760 759 y +765 a 19 x Ft(Chau\033age)1760 765 y tx@Dict begin PutEnd end - 1760 759 a @beginspecial + 1760 765 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.2 SLW 1 0 0 setrgbcolor /ArrowA { moveto } def /ArrowB { } def @@ -2447629,22 +2447640,22 @@ tx@Dict begin PutEnd end 0 setlinecap [ 2.5 2.0 ] 0 0 add DashLine grestore end @endspecial -1760 759 a +1760 765 a tx@Dict begin { 170.90013 -95.87889 } PutCoor PutBegin end - 1760 759 a 1595 784 a Ft(Sanitaires)1760 759 + 1760 765 a 1595 791 a Ft(Sanitaires)1760 765 y tx@Dict begin PutEnd end - 1760 759 a 1760 759 a + 1760 765 a 1760 765 a tx@Dict begin { 89.6264 -100.29619 } PutCoor PutBegin end - 1760 759 a 18 x Ft(d'app)r(oin)n(t)1760 -759 y + 1760 765 a 19 x Ft(d'app)r(oin)n(t)1760 +765 y tx@Dict begin PutEnd end - 1760 759 a 1760 759 a + 1760 765 a 1760 765 a tx@Dict begin { 42.67912 -42.67912 } PutCoor PutBegin end - 1760 759 a 1624 784 a Ft(\020Boiler\021) -1760 759 y + 1760 765 a 1624 791 a Ft(\020Boiler\021) +1760 765 y tx@Dict begin PutEnd end - 1760 759 a @beginspecial @setspecial + 1760 765 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.4 SLW 0 0 0 setrgbcolor 0 360 8.53569 8.53569 .5 CLW mul dup 4 -1 roll sub neg 3 1 roll sub -85.35825 -153.6451 0 true Ellipse @@ -2447696,62 +2447707,62 @@ def 0 setlinejoin false Line gsave 0.4 SLW 1 0 0 setrgbcolor 1. false Line gsave 0.4 SLW 1 0 0 setrgbcolor 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end -@endspecial 1760 759 a +@endspecial 1760 765 a tx@Dict begin { -98.16211 -170.71649 } PutCoor PutBegin end - 1760 759 a 18 x Ft(P)n(omp)r(e)h -(r\351gulatrice)1760 759 y + 1760 765 a 19 x Ft(P)n(omp)r(e)h +(r\351gulatrice)1760 765 y tx@Dict begin PutEnd end - 1760 759 a 1760 759 a + 1760 765 a 1760 765 a tx@Dict begin gsave STV CP T /ps@rot 59. def grestore end 1760 -759 a 1760 759 a +765 a 1760 765 a tx@Dict begin { -106.6978 -108.83188 } PutCoor PutBegin end - 1760 759 a 1760 759 a + 1760 765 a 1760 765 a tx@Dict begin ps@rot RotBegin end - 1760 759 a 1456 -777 a Ft(Absorban)n(t/isolan)n(t)1760 759 y + 1760 765 a 1456 +784 a Ft(Absorban)n(t/isolan)n(t)1760 765 y tx@Dict begin RotEnd end - 1760 759 -a 1760 759 a + 1760 765 +a 1760 765 a tx@Dict begin PutEnd end - 1760 759 a 1760 759 a + 1760 765 a 1760 765 a tx@Dict begin gsave STV CP T /ps@rot 59. def grestore end - 1760 759 a 1760 759 + 1760 765 a 1760 765 a tx@Dict begin { -183.52036 -149.37692 } PutCoor PutBegin end - 1760 759 a 1760 759 a + 1760 765 a 1760 765 a tx@Dict begin ps@rot RotBegin end - 1760 759 a 18 x Ft(Vitrage)1760 -759 y + 1760 765 a 19 x Ft(Vitrage)1760 +765 y tx@Dict begin RotEnd end - 1760 759 a 1760 759 a + 1760 765 a 1760 765 a tx@Dict begin PutEnd end - 1760 759 a 1760 759 a + 1760 765 a 1760 765 a tx@Dict begin gsave STV CP T /ps@rot 59. def grestore end 1760 -759 a 1760 759 a +765 a 1760 765 a tx@Dict begin { -170.71649 -156.20573 } PutCoor PutBegin end - 1760 759 a 1760 759 a + 1760 765 a 1760 765 a tx@Dict begin ps@rot RotBegin end - 1760 759 a 25 -x Ft(E\033et)g(de)f(serre)1760 759 y + 1760 765 a 26 +x Ft(E\033et)g(de)f(serre)1760 765 y tx@Dict begin RotEnd end - 1760 759 a 1760 -759 a + 1760 765 a 1760 +765 a tx@Dict begin PutEnd end - 1760 759 a 1760 759 a + 1760 765 a 1760 765 a tx@Dict begin gsave STV CP T /ps@rot 59. def grestore end - 1760 759 a 1760 759 a + 1760 765 a 1760 765 a tx@Dict begin { -98.16211 -115.23349 } PutCoor PutBegin end 1760 -759 a 1760 759 a +765 a 1760 765 a tx@Dict begin ps@rot RotBegin end - 1760 759 a 1575 777 a Ft(thermiques)1760 -759 y + 1760 765 a 1575 784 a Ft(thermiques)1760 +765 y tx@Dict begin RotEnd end - 1760 759 a 1760 759 a + 1760 765 a 1760 765 a tx@Dict begin PutEnd end - 1760 759 a @beginspecial + 1760 765 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.4 SLW 0 0 0 setrgbcolor [ -59.40079 -16.4957 -157.56291 -178.67584 @@ -2447870,12 +2447881,12 @@ stroke grestore end stroke grestore end @endspecial -1760 759 a +1760 765 a tx@Dict begin { -192.05605 0.0 } PutCoor PutBegin end - 1760 759 a 25 x Ft(Flux)g(solaire)j(inciden)n(t)1760 -759 y + 1760 765 a 26 x Ft(Flux)g(solaire)j(inciden)n(t)1760 +765 y tx@Dict begin PutEnd end - 1760 759 a @beginspecial @setspecial + 1760 765 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale 0.0 dup 0 eq { pop }{ SLW } ifelse {1 setgray true} false /DS 2.0 2. CLW mul add 2 div def EndDot EndArrow } def 0.4 @@ -2447887,10 +2447898,10 @@ false /DS 2.0 2. 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b(au)g(moins)g(une)h(fois.)f(En)g(e\033et,)h(si)f +(cette)h(nota-)116 5115 y(tion)i(est)g(relativ)n(emen)n(t)e(p)r(eu)i +(utilis\351e)g(hors)f(des)g(cercles)116 5214 y(d'ing\351nieurs,)28 b(elle)g(est)g(assez)f(souv)n(en)n(t)g(pr\351sen)n(te)h(sur)f(les)116 -5307 y(mac)n(hines)38 b(\340)g(calculer.)g(P)n(our)f(qu'elle)i(ne)g(p)r -(ose)f(pas)g(de)116 5407 y(probl\350mes,)30 b(il)h(est)g(donc)g(plus)f +5314 y(mac)n(hines)38 b(\340)g(calculer.)g(P)n(our)f(qu'elle)i(ne)g(p)r +(ose)f(pas)g(de)116 5414 y(probl\350mes,)30 b(il)h(est)g(donc)g(plus)f (n\351cessaire)g(de)h(sa)n(v)n(oir)d(ne)p 0 TeXcolorgray -0 TeXcolorgray 0 TeXcolorgray 2200 2031 1503 4 v 2200 -2137 4 106 v 2381 2107 a FW(V)-8 b(olume)390 b(\311quiv)-5 -b(alen)m(t)31 b(SI)p 3700 2137 V 2200 2140 1503 4 v 2200 -2160 V 2200 2260 4 100 v 2253 2230 a FX(Litre)c(:)h FL(1)14 -b(l)p FX(=)p FL(1)f(dm)100 b FX(=)184 b FL(1)18 b FG(\001)g -FL(10)3356 2200 y Fz(\000)p FF(3)3458 2230 y FL(m)3528 -2200 y FF(3)p 3700 2260 V 2200 2263 1503 4 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b(de)f(mesures)g(de)h(distances.)g(L'ob)r(jectif)-116 -2227 y(est)38 b(de)g(se)g(rendre)g(compte)g(\340)g(la)g(fois)g(de)g -(l'ing\351niosit\351)-116 2326 y(des)c(raisonnemen)n(ts)f(mis)h(en)g -(\367uvre)g(et)g(des)g(di\036cult\351s)-116 2426 y(tec)n(hniques)52 +2233 y(est)38 b(de)g(se)g(rendre)g(compte)g(\340)g(la)g(fois)g(de)g +(l'ing\351niosit\351)-116 2333 y(des)c(raisonnemen)n(ts)f(mis)h(en)g +(\367uvre)g(et)g(des)g(di\036cult\351s)-116 2432 y(tec)n(hniques)52 b(qui)g(se)g(son)n(t)g(pr\351sen)n(t\351es.)g(Cela)f(p)r(ermet)-116 -2525 y(de)37 b(tra)n(v)-5 b(ailler)36 b(a)n(v)n(ec)g(des)i(ordres)e(de) -h(grandeurs)f(qui)i(ne)-116 2625 y(nous)e(son)n(t)g(pas)g(familiers)g -(et)h(de)g(mieux)g(appr\351cier)e(les)-116 2725 y(connaissances)g(qui)j +2532 y(de)37 b(tra)n(v)-5 b(ailler)36 b(a)n(v)n(ec)g(des)i(ordres)e(de) +h(grandeurs)f(qui)i(ne)-116 2632 y(nous)e(son)n(t)g(pas)g(familiers)g +(et)h(de)g(mieux)g(appr\351cier)e(les)-116 2731 y(connaissances)g(qui)j 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b(\(L'astronome)f(Cl\351om\350de,)h(l'historien)g +(Stra-)-116 4514 y(b)r(on)e(et)g(le)g(naturaliste)f(romain)g(Pline)h +(l'ancien\).)g(Ces)-116 4614 y(sources,)21 b(aussi)h(\351minen)n(tes)g +(soien)n(t-elles,)g(ne)g(doiv)n(en)n(t)g(pas)-116 4713 y(\352tre)f(exemptes)g(de)h(toute)g(critique,)f(comme)g(nous)g(le)h(v)n -(er-)-116 4806 y(rons)k(par)h(la)g(suite.)-33 4909 y(Le)d(princip)r(e)h +(er-)-116 4813 y(rons)k(par)h(la)g(suite.)-33 4915 y(Le)d(princip)r(e)h (de)g(la)f(mesure)g(est)g(simple.)h(Consid\351rons)-116 -5008 y(la)31 b(\034gure)h(C.1.)f(On)h(y)g(v)n(oit)g(la)f(T)-7 -b(erre)31 b(don)n(t)h(l'axe)g(de)g(ro-)-116 5108 y(tation)f(est)h +5015 y(la)31 b(\034gure)h(C.1.)f(On)h(y)g(v)n(oit)g(la)f(T)-7 +b(erre)31 b(don)n(t)h(l'axe)g(de)g(ro-)-116 5115 y(tation)f(est)h (inclin\351)f(par)g(rapp)r(ort)g(\340)g(la)g(p)r(erp)r(endiculaire)-116 -5208 y(au)22 b(plan)h(de)f(l'\351cliptique.)h(On)g(y)f(v)n(oit)g -(l'ancienne)h(ville)g(de)-116 5307 y(Sy)n(\350ne,)g(c'est-\340-dire)g -(l'actuelle)h(Assouan,)f(qui)h(se)g(trouv)n(e)-116 5407 +5214 y(au)22 b(plan)h(de)f(l'\351cliptique.)h(On)g(y)f(v)n(oit)g +(l'ancienne)h(ville)g(de)-116 5314 y(Sy)n(\350ne,)g(c'est-\340-dire)g +(l'actuelle)h(Assouan,)f(qui)h(se)g(trouv)n(e)-116 5414 y(sur)32 b(le)g(tropique)g(du)h(Cancer,)e(au)h(momen)n(t)h(du)f (solstice)p 0 TeXcolorgray 0 TeXcolorgray 0 TeXcolorgray -0 TeXcolorgray 2179 2091 a FK(Figure)d(C.1)g(\025)h FJ(T)-6 +0 TeXcolorgray 2179 2098 a FK(Figure)d(C.1)g(\025)h FJ(T)-6 b(ail)6 b(le)26 b(de)i(la)f(terr)l(e)p 0 TeXcolorgray -2005 3208 a +2005 3215 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 2005 3208 a 2005 3208 a + 2005 3215 a 2005 3215 a tx@Dict begin { 59.75047 62.31119 } PutCoor PutBegin end - 2005 3208 a @beginspecial + 2005 3215 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.7113 SLW 0 setgray 0 360 56.90521 56.90521 0.0 0.0 0 true Ellipse closepath gsave 0.7113 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end -@endspecial 2005 3208 a +@endspecial 2005 3215 a tx@Dict begin PutEnd end - 2005 3208 a @beginspecial + 2005 3215 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.28453 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def [ @@ -2534678,12 +2534688,12 @@ setlinejoin 0 setlinecap stroke grestore end false Line gsave 0.7113 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end -@endspecial 2005 3208 a +@endspecial 2005 3215 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 2005 3208 a 2005 -3208 a + 2005 3215 a 2005 +3215 a tx@Dict begin { 70.19257 62.31119 } PutCoor PutBegin end - 2005 3208 a @beginspecial @setspecial + 2005 3215 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.28453 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def 0.0 0.0 /yOrig ED /xOrig ED 55.11267 55.11267 /ry ED /rx ED /angleA /d @@ -2534699,14 +2534709,14 @@ cos exch sin moveto exch arc mtrx setmatrix gsave 0.28453 SLW 0 setgray end @endspecial -2005 3208 a +2005 3215 a tx@Dict begin PutEnd end - 2005 3208 a 2005 3208 a + 2005 3215 a 2005 3215 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 2005 3208 a 2005 -3208 a + 2005 3215 a 2005 +3215 a tx@Dict begin { 62.22583 62.45346 } PutCoor PutBegin end - 2005 3208 a @beginspecial @setspecial + 2005 3215 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.28453 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def 0.0 0.0 /yOrig ED /xOrig ED 54.82817 54.82817 /ry ED /rx ED /angleA /d @@ -2534722,14 +2534732,14 @@ exch sin moveto exch arc mtrx setmatrix gsave 0.28453 SLW 0 setgray end @endspecial -2005 3208 a +2005 3215 a tx@Dict begin PutEnd end - 2005 3208 a 2005 3208 a + 2005 3215 a 2005 3215 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 2005 3208 a 2005 -3208 a + 2005 3215 a 2005 +3215 a tx@Dict begin { 67.68872 62.31119 } PutCoor PutBegin end - 2005 3208 a @beginspecial @setspecial + 2005 3215 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.28453 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def 0.0 0.0 /yOrig ED /xOrig ED 55.45413 55.45413 /ry ED /rx ED /angleA /d @@ -2534745,9 +2534755,9 @@ cos exch sin moveto exch arc mtrx setmatrix gsave 0.28453 SLW 0 setgray end @endspecial -2005 3208 a +2005 3215 a tx@Dict begin PutEnd end - 2005 3208 a @beginspecial @setspecial + 2005 3215 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.42676 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def [ 88.20308 91.04834 108.68893 91.04834 /Lineto /lineto load def 0 @@ -2534755,24 +2534765,24 @@ setlinejoin false Line gsave 0.42676 SLW 0 setgray 1. .setopacityalpha 2.84526 0 0 add DotLine grestore end @endspecial -2005 3208 a +2005 3215 a tx@Dict begin { 147.3845 39.5491 } PutCoor PutBegin end - 2005 3208 a 2005 3208 a + 2005 3215 a 2005 3215 a tx@Dict begin PutEnd end - 2005 3208 a 2005 -3208 a + 2005 3215 a 2005 +3215 a tx@Dict begin gsave STV CP T /ps@rot -27. def grestore end - 2005 3208 a 2005 3208 a + 2005 3215 a 2005 3215 a tx@Dict begin { 82.22801 41.54082 } PutCoor PutBegin end - 2005 3208 a 2005 3208 + 2005 3215 a 2005 3215 a tx@Dict begin ps@rot RotBegin end - 2005 3208 a 1837 3238 a FX(\311quateur)2005 3208 y + 2005 3215 a 1837 3245 a FY(\311quateur)2005 3215 y tx@Dict begin RotEnd end -2005 3208 a 2005 3208 a +2005 3215 a 2005 3215 a tx@Dict begin PutEnd end - 2005 3208 a @beginspecial @setspecial + 2005 3215 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.25 1. 2.84526 2. 1. .setopacityalpha Arrow EndArrow } def 0.42676 SLW 0 setgray /ArrowA { moveto } def /ArrowB @@ -2534794,47 +2534804,47 @@ tx@Dict begin PutEnd end grestore end @endspecial 2005 -3208 a +3215 a tx@Dict begin gsave STV CP T /ps@rot -27. def grestore end - 2005 3208 a 2005 3208 a + 2005 3215 a 2005 3215 a tx@Dict begin { 98.16148 112.38779 } PutCoor PutBegin end - 2005 3208 a 2005 3208 + 2005 3215 a 2005 3215 a tx@Dict begin ps@rot RotBegin end - 2005 3208 a 1914 3237 a FX(Nord)2005 3208 y + 2005 3215 a 1914 3243 a FY(Nord)2005 3215 y tx@Dict begin RotEnd end - 2005 3208 -a 2005 3208 a + 2005 3215 +a 2005 3215 a tx@Dict begin PutEnd end - 2005 3208 a 2005 3208 a + 2005 3215 a 2005 3215 a tx@Dict begin gsave STV CP T /ps@rot -27. def grestore end - 2005 3208 a 2005 -3208 a + 2005 3215 a 2005 +3215 a tx@Dict begin { 22.76208 10.52745 } PutCoor PutBegin end - 2005 3208 a 2005 3208 a + 2005 3215 a 2005 3215 a tx@Dict begin ps@rot RotBegin end - 2005 3208 a 1936 3237 -a FX(Sud)2005 3208 y + 2005 3215 a 1936 3243 +a FY(Sud)2005 3215 y tx@Dict begin RotEnd end - 2005 3208 a 2005 3208 a + 2005 3215 a 2005 3215 a tx@Dict begin PutEnd end - 2005 3208 -a 2005 3208 a + 2005 3215 +a 2005 3215 a tx@Dict begin { 132.02007 68.28625 } PutCoor PutBegin end - 2005 3208 a 1901 3228 a FX(Sy)n(\350ne)2005 -3208 y + 2005 3215 a 1901 3235 a FY(Sy)n(\350ne)2005 +3215 y tx@Dict begin PutEnd end - 2005 3208 a 2005 3208 a + 2005 3215 a 2005 3215 a tx@Dict begin { 140.55585 83.93518 } PutCoor PutBegin end - 2005 3208 a 1809 3237 -a FX(Alexandrie)2005 3208 y + 2005 3215 a 1809 3243 +a FY(Alexandrie)2005 3215 y tx@Dict begin PutEnd end - 2005 3208 a 2005 3208 a + 2005 3215 a 2005 3215 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end 2005 -3208 a 2005 3208 a +3215 a 2005 3215 a tx@Dict begin { 111.19278 90.59308 } PutCoor PutBegin end - 2005 3208 a @beginspecial @setspecial + 2005 3215 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.28453 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def 0.0 0.0 /yOrig ED /xOrig ED 10.78351 10.78351 /ry ED /rx ED /angleA /d @@ -2534850,16 +2534860,16 @@ cos exch sin moveto exch arc mtrx setmatrix gsave 0.28453 SLW 0 setgray end -@endspecial 2005 3208 a +@endspecial 2005 3215 a tx@Dict begin PutEnd end - 2005 3208 a 2005 3208 a + 2005 3215 a 2005 3215 a tx@Dict begin gsave STV CP T /ps@rot 90. def grestore end 2005 -3208 a 2005 3208 a +3215 a 2005 3215 a tx@Dict begin { 66.92053 64.01836 } PutCoor PutBegin end - 2005 3208 a 2005 3208 a + 2005 3215 a 2005 3215 a tx@Dict begin ps@rot RotBegin end - 2005 3208 + 2005 3215 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.28453 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def 0.0 @@ -2534875,325 +2534885,325 @@ cos exch sin moveto exch arc mtrx setmatrix gsave 0.28453 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end -@endspecial 2005 3208 a +@endspecial 2005 3215 a tx@Dict begin RotEnd end -2005 3208 a 2005 3208 a +2005 3215 a 2005 3215 a tx@Dict begin PutEnd end - 2005 3208 a 2005 3208 a + 2005 3215 a 2005 3215 a tx@Dict begin { 146.24637 97.59244 } PutCoor PutBegin end 2005 -3208 a 1710 3228 a FX(Ra)n(y)n(ons)f(du)h(soleil)2005 -3208 y +3215 a 1710 3235 a FY(Ra)n(y)n(ons)f(du)h(soleil)2005 +3215 y tx@Dict begin PutEnd end - 2005 3208 a 2005 3208 a + 2005 3215 a 2005 3215 a tx@Dict begin { 95.31622 85.64235 } PutCoor PutBegin end - 2005 3208 a 1978 3226 -a FC(\013)2005 3208 y + 2005 3215 a 1978 3232 +a FC(\013)2005 3215 y tx@Dict begin PutEnd end - 2005 3208 a 2005 3208 a + 2005 3215 a 2005 3215 a tx@Dict begin { 80.52087 67.14816 } PutCoor PutBegin end - 2005 3208 -a 1978 3226 a FC(\013)2005 3208 y + 2005 3215 +a 1978 3232 a FC(\013)2005 3215 y tx@Dict begin PutEnd end - 2005 3208 a 2005 3208 + 2005 3215 a 2005 3215 a tx@Dict begin { 135.43442 68.00171 } PutCoor PutBegin end - 2005 3208 a 2005 3208 a + 2005 3215 a 2005 3215 a tx@Dict begin PutEnd end - 2005 3208 a 2005 3208 a + 2005 3215 a 2005 3215 a tx@Dict begin { 132.30461 67.71721 } PutCoor PutBegin end 2005 -3208 a 2005 3208 a +3215 a 2005 3215 a tx@Dict begin PutEnd end - 2005 3208 a 2005 3208 a + 2005 3215 a 2005 3215 a tx@Dict begin { 21.0549 121.20811 } PutCoor PutBegin end - 2005 3208 -a 1843 3228 a FX(T)-7 b(ropique)2005 3208 y + 2005 3215 +a 1843 3235 a FY(T)-7 b(ropique)2005 3215 y tx@Dict begin PutEnd end - 2005 3208 -a 2005 3208 a + 2005 3215 +a 2005 3215 a tx@Dict begin { 158.1965 111.5342 } PutCoor PutBegin end - 2005 3208 a 2005 3208 a + 2005 3215 a 2005 3215 a tx@Dict begin PutEnd end - 2005 3208 a 2005 -3208 a + 2005 3215 a 2005 +3215 a tx@Dict begin { 136.85704 55.48257 } PutCoor PutBegin end - 2005 3208 a 1866 3237 a FX(Plan)27 b(de)2005 3208 + 2005 3215 a 1866 3243 a FY(Plan)27 b(de)2005 3215 y tx@Dict begin PutEnd end - 2005 3208 a 2005 3208 a + 2005 3215 a 2005 3215 a tx@Dict begin { 144.2547 44.38608 } PutCoor PutBegin end - 2005 3208 a 1808 3228 a FX(l'\351cliptique) -2005 3208 y + 2005 3215 a 1808 3235 a FY(l'\351cliptique) +2005 3215 y tx@Dict begin PutEnd end - 2005 3208 a 2005 3208 a + 2005 3215 a 2005 3215 a tx@Dict begin { 18.49419 111.81874 } PutCoor PutBegin end - 2005 3208 a 1959 -3237 a FX(du)2005 3208 y + 2005 3215 a 1959 +3243 a FY(du)2005 3215 y tx@Dict begin PutEnd end - 2005 3208 a 2005 3208 a + 2005 3215 a 2005 3215 a tx@Dict begin gsave STV CP T /ps@rot -27. def grestore end 2005 -3208 a 2005 3208 a +3215 a 2005 3215 a tx@Dict begin { 44.95512 93.04001 } PutCoor PutBegin end - 2005 3208 a 2005 3208 a + 2005 3215 a 2005 3215 a tx@Dict begin ps@rot RotBegin end - 2005 3208 -a 1889 3226 a FX(cancer)2005 3208 y + 2005 3215 +a 1889 3232 a FY(cancer)2005 3215 y tx@Dict begin RotEnd end - 2005 3208 a 2005 -3208 a + 2005 3215 a 2005 +3215 a tx@Dict begin PutEnd end - 2005 3208 a 2005 3208 a + 2005 3215 a 2005 3215 a tx@Dict begin { 48.36943 87.91853 } PutCoor PutBegin end - 2005 3208 a 2005 3208 + 2005 3215 a 2005 3215 a tx@Dict begin PutEnd end - 2005 3208 a 0 TeXcolorgray 1802 3502 a FX(d'\351t\351.)36 + 2005 3215 a 0 TeXcolorgray 1802 3508 a FY(d'\351t\351.)36 b(Le)h(Soleil)f(se)g(trouv)n(e)f(alors)g(au)h(z\351nith,)h(c'est-\340-) -1802 3601 y(dire)c(\340)h(la)g(p)r(erp)r(endiculaire)g(de)g(l'horizon)g -(du)g(lieu.)h(Ses)1802 3701 y(ra)n(y)n(ons)22 b(p)r(ourraien)n(t)h +1802 3608 y(dire)c(\340)h(la)g(p)r(erp)r(endiculaire)g(de)g(l'horizon)g +(du)g(lieu.)h(Ses)1802 3708 y(ra)n(y)n(ons)22 b(p)r(ourraien)n(t)h (alors)g(p)r(\351n\351trer)h(jusqu'au)h(plus)g(pro-)1802 -3801 y(fond)30 b(d'un)h(puits)g(construit)e(v)n(erticalemen)n(t.)h(A)n -(u)g(m\352me)1802 3900 y(momen)n(t,)40 b(on)h(p)r(eut)g(consid\351rer)e -(l'om)n(bre)h(au)h(sol)f(d'un)1802 4000 y(gnomon)30 b(\(un)h(b\342ton)g +3807 y(fond)30 b(d'un)h(puits)g(construit)e(v)n(erticalemen)n(t.)h(A)n +(u)g(m\352me)1802 3907 y(momen)n(t,)40 b(on)h(p)r(eut)g(consid\351rer)e +(l'om)n(bre)h(au)h(sol)f(d'un)1802 4007 y(gnomon)30 b(\(un)h(b\342ton)g (v)n(ertical\))f(plan)n(t\351)h(plus)h(au)e(nord)h(\340)1802 -4100 y(Alexandrie.)37 b(Sa)h(longueur)f(et)i(celle)f(du)h(gnomon)e(p)r -(er-)1802 4199 y(metten)n(t)f(de)g(d\351terminer)g(l'angle)f -FC(\013)i FX(de)f(la)g(\034gure)f(C.1.)1802 4299 y(Or,)17 +4106 y(Alexandrie.)37 b(Sa)h(longueur)f(et)i(celle)f(du)h(gnomon)e(p)r +(er-)1802 4206 y(metten)n(t)f(de)g(d\351terminer)g(l'angle)f +FC(\013)i FY(de)f(la)g(\034gure)f(C.1.)1802 4305 y(Or,)17 b(celui-ci)i(a)f(un)h(corresp)r(ondan)n(t)d(au)j(cen)n(tre)f(de)g(la)g -(T)-7 b(erre)1802 4398 y(qui)24 b(sous-tend)g(l'arc)f(de)i(cercle)e(en) -n(tre)h(Sy)n(\350ne)g(et)h(Alexan-)1802 4498 y(drie.)34 +(T)-7 b(erre)1802 4405 y(qui)24 b(sous-tend)g(l'arc)f(de)i(cercle)e(en) +n(tre)h(Sy)n(\350ne)g(et)h(Alexan-)1802 4505 y(drie.)34 b(Si,)i(par)e(ailleurs,)g(on)h(conna\356t)f(la)h(mesure)f(de)h(cet)1802 -4598 y(arc,)28 b(il)h(est)g(ais\351)f(de)i(d\351terminer)e(la)h -(circonf\351rence)f(de)h(la)1802 4697 y(T)-7 b(erre)26 -b(et,)i(ainsi,)f(son)g(ra)n(y)n(on.)1885 4819 y(Comme)j +4604 y(arc,)28 b(il)h(est)g(ais\351)f(de)i(d\351terminer)e(la)h +(circonf\351rence)f(de)h(la)1802 4704 y(T)-7 b(erre)26 +b(et,)i(ainsi,)f(son)g(ra)n(y)n(on.)1885 4826 y(Comme)j (\311rathosth\350ne)g(\340)g(\351v)-5 b(alu\351)31 b(la)f(distance)h -(en)n(tre)1802 4919 y(Sy)n(\350ne)23 b(et)h(Alexandrie)f(\340)h -FL(5000)12 b(stades)23 b FX(et)h(la)g(longueur)e(de)1802 -5019 y(l'om)n(bre)k(p)r(ort\351e)g(par)g(le)h(gnomon)f(\340)g -FL(1)p FC(=)p FL(8)g FX(de)h(sa)f(hauteur,)1802 5118 +(en)n(tre)1802 4926 y(Sy)n(\350ne)23 b(et)h(Alexandrie)f(\340)h +FL(5000)12 b(stades)23 b FY(et)h(la)g(longueur)e(de)1802 +5025 y(l'om)n(bre)k(p)r(ort\351e)g(par)g(le)h(gnomon)f(\340)g +FL(1)p FC(=)p FL(8)g FY(de)h(sa)f(hauteur,)1802 5125 y(on)h(p)r(eut)h(en)g(d\351duire)f(:)p 0 TeXcolorgray -1903 5307 a(1.)p 0 TeXcolorgray 41 w(que)d(l'angle)g -FC(\013)h FX(est)f(\(anac)n(hroniquemen)n(t)f(car)g(\311ra-)2009 -5407 y(thosth\350ne)33 b(l'a)f(simplemen)n(t)h(obten)n(u)f(\340)h -(partir)e(de)p 0 TeXcolorgray 1698 5617 a(169)p 0 TeXcolorgray +1903 5314 a(1.)p 0 TeXcolorgray 41 w(que)d(l'angle)g +FC(\013)h FY(est)f(\(anac)n(hroniquemen)n(t)f(car)g(\311ra-)2009 +5414 y(thosth\350ne)33 b(l'a)f(simplemen)n(t)h(obten)n(u)f(\340)h +(partir)e(de)p 0 TeXcolorgray 1698 5624 a(169)p 0 TeXcolorgray eop end %%Page: 170 170 TeXDict begin 170 169 bop 0 TeXcolorgray 0 TeXcolorgray -116 262 a FQ(C.1.)55 b(LA)28 b(T)-7 b(AILLE)27 b(DE)h(LA)g(TERRE)901 +116 269 a FR(C.1.)55 b(LA)28 b(T)-7 b(AILLE)27 b(DE)h(LA)g(TERRE)901 b(ANNEXE)28 b(C.)55 b(MESURES)28 b(DE)f(DIST)-7 b(ANCES)p -116 296 3753 4 v 0 TeXcolorgray 324 525 a FX(mesures)27 -b(faites)g(a)n(v)n(ec)f(un)i(scaph\351)1414 495 y FV(a)1452 -525 y FX(\))g(donn\351)f(par)g(:)376 760 y FL(tan\()p -FC(\013)p FL(\))d(=)735 704 y(1)p FC(=)p FL(8)p 735 741 -125 4 v 777 817 a(1)893 760 y(=)e(1)p FC(=)p FL(8)45 +116 302 3753 4 v 0 TeXcolorgray 324 532 a FY(mesures)27 +b(faites)g(a)n(v)n(ec)f(un)i(scaph\351)1414 502 y FW(a)1452 +532 y FY(\))g(donn\351)f(par)g(:)376 766 y FL(tan\()p +FC(\013)p FL(\))d(=)735 710 y(1)p FC(=)p FL(8)p 735 747 +125 4 v 777 823 a(1)893 766 y(=)e(1)p FC(=)p FL(8)45 b FG(\))h FC(\013)24 b FL(=)e(7)p FC(;)14 b FL(13)1607 -726 y Fz(\016)1667 760 y FL(=)22 b(7)1796 726 y Fz(\016)1834 -760 y FL(8)1876 726 y Fz(0)p 0 TeXcolorgray 218 985 a -FX(2.)p 0 TeXcolorgray 41 w(que)27 b(la)h(circonf\351rence)e(de)i(la)f -(T)-7 b(erre)26 b(v)-5 b(aut)28 b(:)534 1205 y FC(C)h -FL(=)23 b(5000)16 b FG(\001)964 1149 y FL(360)p 946 1186 -162 4 v 946 1262 a(7)p FC(;)e FL(13)1140 1205 y(=)23 -b(252)j(631)13 b(stades)p 0 TeXcolorgray 218 1447 a FX(3.)p +732 y Fz(\016)1667 766 y FL(=)22 b(7)1796 732 y Fz(\016)1834 +766 y FL(8)1876 732 y Fz(0)p 0 TeXcolorgray 218 992 a +FY(2.)p 0 TeXcolorgray 41 w(que)27 b(la)h(circonf\351rence)e(de)i(la)f +(T)-7 b(erre)26 b(v)-5 b(aut)28 b(:)534 1212 y FC(C)h +FL(=)23 b(5000)16 b FG(\001)964 1156 y FL(360)p 946 1193 +162 4 v 946 1269 a(7)p FC(;)e FL(13)1140 1212 y(=)23 +b(252)j(631)13 b(stades)p 0 TeXcolorgray 218 1454 a FY(3.)p 0 TeXcolorgray 41 w(et)28 b(que)f(son)g(ra)n(y)n(on)f(v)-5 -b(aut)28 b(alors,)324 1677 y FC(C)h FL(=)23 b(2)9 b FG(\001)g +b(aut)28 b(alors,)324 1684 y FC(C)h FL(=)23 b(2)9 b FG(\001)g FC(\031)j FG(\001)d FC(R)36 b FG(\))46 b FC(R)24 b FL(=)1087 -1621 y(252)1213 1591 y Fz(0)1234 1621 y FL(631)p 1087 -1658 273 4 v 1147 1734 a(2)18 b FG(\001)g FC(\031)1392 -1677 y FL(=)23 b(40)j(208)13 b(stades)116 1922 y FX(\311videmmen)n(t,) +1628 y(252)1213 1598 y Fz(0)1234 1628 y FL(631)p 1087 +1665 273 4 v 1147 1741 a(2)18 b FG(\001)g FC(\031)1392 +1684 y FL(=)23 b(40)j(208)13 b(stades)116 1929 y FY(\311videmmen)n(t,) 36 b(il)g(faut)g(sa)n(v)n(oir)e(ce)h(que)h(v)-5 b(aut)36 -b(un)g(stade.)116 2022 y(Et)j(l\340)f(appara\356t)g(le)h(premier)f -(probl\350me.)g(En)h(e\033et,)g(les)116 2121 y(estimations)34 +b(un)g(stade.)116 2028 y(Et)j(l\340)f(appara\356t)g(le)h(premier)f +(probl\350me.)g(En)h(e\033et,)g(les)116 2128 y(estimations)34 b(v)-5 b(arien)n(t)33 b(en)n(tre)h(157,5)e(et)j FL(192)p -FC(;)n FL(27)13 b(m)q FX(.)34 b(Si)g(on)116 2221 y(utilise)28 +FC(;)n FL(27)13 b(m)q FY(.)34 b(Si)g(on)116 2228 y(utilise)28 b(la)f(premi\350re)g(v)-5 b(aleur,)27 b(on)h(a)f(:)497 -2408 y FC(R)d FL(=)f(40)756 2373 y Fz(0)778 2408 y FL(208)17 +2414 y FC(R)d FL(=)f(40)756 2380 y Fz(0)778 2414 y FL(208)17 b FG(\001)i FL(157)p FC(;)14 b FL(5)21 b(=)h(6333)12 -b(km)116 2594 y FX(Ce)27 b(qui)g(repr\351sen)n(te,)e(par)h(rapp)r(ort)g -(\340)g(la)g(v)-5 b(aleur)26 b(actuelle,)116 2694 y(une)i(erreur)e(de)i -(:)467 2908 y FC(e)22 b FL(=)626 2852 y(6)668 2822 y -Fz(0)691 2852 y FL(378)17 b FG(\000)h FL(6)959 2822 y -Fz(0)982 2852 y FL(333)p 626 2889 481 4 v 771 2965 a(6)813 -2941 y Fz(0)836 2965 y FL(378)1135 2908 y FG(\001)g FL(100)k(=)g(0)p -FC(;)14 b FL(7\045)116 3117 y FX(alors)26 b(qu'a)n(v)n(ec)g(la)i -(seconde)f(v)-5 b(aleur,)27 b(on)g(a)g(:)477 3304 y FC(R)c -FL(=)g(40)735 3270 y Fz(0)757 3304 y FL(208)17 b FG(\001)i -FL(192)p FC(;)14 b FL(27)20 b(=)j(7730)12 b(km)116 3491 -y FX(Ce)28 b(qui)f(repr\351sen)n(te)g(une)h(erreur)e(de)h(:)458 -3721 y FC(e)22 b FL(=)617 3665 y(7)659 3635 y Fz(0)682 -3665 y FL(730)17 b FG(\000)h FL(6378)p 617 3702 457 4 -v 762 3778 a(6378)1102 3721 y FG(\001)h FL(100)i(=)i(21)p -FC(;)14 b FL(2\045)116 3981 y FY(C.1.2)113 b(T)-9 b(ec)m(hniquemen)m(t) -199 4138 y FX(On)21 b(loue)f(souv)n(en)n(t)f(la)h(m\351tho)r(de)h -(d'\311rathosth\350ne)e(p)r(our)116 4238 y(la)52 b(pr\351cision)f(de)i -(sa)e(mesure.)h(Mais)g(comme)g(on)g(ne)116 4337 y(conna\356t)25 +b(km)116 2601 y FY(Ce)27 b(qui)g(repr\351sen)n(te,)e(par)h(rapp)r(ort)g +(\340)g(la)g(v)-5 b(aleur)26 b(actuelle,)116 2701 y(une)i(erreur)e(de)i +(:)467 2915 y FC(e)22 b FL(=)626 2858 y(6)668 2828 y +Fz(0)691 2858 y FL(378)17 b FG(\000)h FL(6)959 2828 y +Fz(0)982 2858 y FL(333)p 626 2895 481 4 v 771 2971 a(6)813 +2947 y Fz(0)836 2971 y FL(378)1135 2915 y FG(\001)g FL(100)k(=)g(0)p +FC(;)14 b FL(7\045)116 3124 y FY(alors)26 b(qu'a)n(v)n(ec)g(la)i +(seconde)f(v)-5 b(aleur,)27 b(on)g(a)g(:)477 3311 y FC(R)c +FL(=)g(40)735 3276 y Fz(0)757 3311 y FL(208)17 b FG(\001)i +FL(192)p FC(;)14 b FL(27)20 b(=)j(7730)12 b(km)116 3497 +y FY(Ce)28 b(qui)f(repr\351sen)n(te)g(une)h(erreur)e(de)h(:)458 +3728 y FC(e)22 b FL(=)617 3671 y(7)659 3641 y Fz(0)682 +3671 y FL(730)17 b FG(\000)h FL(6378)p 617 3708 457 4 +v 762 3785 a(6378)1102 3728 y FG(\001)h FL(100)i(=)i(21)p +FC(;)14 b FL(2\045)116 3988 y FM(C.1.2)113 b(T)-9 b(ec)m(hniquemen)m(t) +199 4145 y FY(On)21 b(loue)f(souv)n(en)n(t)f(la)h(m\351tho)r(de)h +(d'\311rathosth\350ne)e(p)r(our)116 4245 y(la)52 b(pr\351cision)f(de)i +(sa)e(mesure.)h(Mais)g(comme)g(on)g(ne)116 4344 y(conna\356t)25 b(pas)g(de)g(mani\350re)g(certaine)f(la)h(v)-5 b(aleur)25 -b(du)g(stade,)116 4437 y(il)j(faut)g(\352tre)f(tr\350s)g(pruden)n(t.) -199 4539 y(D'autan)n(t)38 b(plus)h(pruden)n(t)f(que)f(ce)h(n'est)h(pas) -e(le)h(seul)116 4638 y(probl\350me)55 b(p)r(os\351)f(par)g(la)h(mesure) -g(d'\311rathosth\350ne)1887 4608 y FV(b)1928 4638 y FX(.)116 -4738 y(Jean-Baptiste)42 b(Joseph)h(Delam)n(bre)f(dans)h(\(Delam)n(bre,) -116 4838 y(1821,)34 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FL(=)e FC(d)502 1108 y FB(T)9 b(er)r(r)r(e)p Fz(\000)p -FB(Lune)915 1096 y FL(=)1052 1040 y(3618)p 1013 1077 -245 4 v 1013 1153 a(0)p FC(;)14 b FL(0087)1290 1096 y(=)23 -b(415)j(862)13 b(km)116 1336 y FX(Ce)24 b(qui)g(repr\351sen)n(te)e(en)n +116 302 3753 4 v 0 TeXcolorgray 116 532 a FY(en)28 b(radian)e(et)i(au)g +(ra)n(y)n(on)d FC(R)k FY(du)e(cercle,)g(on)h(tire)f(:)292 +727 y FC(L)c FL(=)f FC(\013)d FG(\001)g FC(R)47 b FG(\))285 +904 y FC(R)24 b FL(=)469 848 y FC(L)p 469 885 57 4 v +471 961 a(\013)559 904 y FL(=)656 848 y FC(\036)705 860 +y FB(lune)p 656 885 187 4 v 723 961 a FC(\013)285 1103 +y(R)g FL(=)e FC(d)502 1115 y FB(T)9 b(er)r(r)r(e)p Fz(\000)p +FB(Lune)915 1103 y FL(=)1052 1047 y(3618)p 1013 1084 +245 4 v 1013 1160 a(0)p FC(;)14 b FL(0087)1290 1103 y(=)23 +b(415)j(862)13 b(km)116 1343 y FY(Ce)24 b(qui)g(repr\351sen)n(te)e(en)n (viron)h(8\045)h(d'\351cart)f(a)n(v)n(ec)f(la)i(v)-5 -b(aleur)116 1436 y(d'aujourd'h)n(ui.)199 1604 y(De)35 +b(aleur)116 1442 y(d'aujourd'h)n(ui.)199 1611 y(De)35 b(nos)f(jours,)f(la)h(distance)g(de)g(la)g(T)-7 b(erre)33 -b(\340)h(la)g(Lune)116 1704 y(est)20 b(mesur\351)g(par)f(la)h +b(\340)h(la)g(Lune)116 1711 y(est)20 b(mesur\351)g(par)f(la)h (r\351\035exion)f(de)i(faisceaux)e(laser)g(sur)g(des)116 -1804 y(miroirs)h(d\351p)r(os\351s)g(par)g(les)h(missions)f(Ap)r(ollo.)g -(Elle)h(attein)n(t)116 1903 y(une)28 b(pr\351cision)f(de)g(l'ordre)g -(de)g(quelques)h(millim\350tres.)116 2212 y FM(C.4)135 -b(La)45 b(distance)h(T)-11 b(erre-Soleil)199 2406 y FX(La)47 +1810 y(miroirs)h(d\351p)r(os\351s)g(par)g(les)h(missions)f(Ap)r(ollo.)g +(Elle)h(attein)n(t)116 1910 y(une)28 b(pr\351cision)f(de)g(l'ordre)g +(de)g(quelques)h(millim\350tres.)116 2219 y FN(C.4)135 +b(La)45 b(distance)h(T)-11 b(erre-Soleil)199 2413 y FY(La)47 b(mesure)f(de)i(distances)e(plus)i(imp)r(ortan)n(tes)e(que)116 -2506 y(celle)24 b(de)g(la)f(T)-7 b(erre)23 b(\340)g(la)h(Lune)g(fut)h -(r\351alis\351e)d(par)h(la)g(suite)i(\340)116 2605 y(l'aide)k(de)g(la)f +2512 y(celle)24 b(de)g(la)f(T)-7 b(erre)23 b(\340)g(la)h(Lune)g(fut)h +(r\351alis\351e)d(par)h(la)g(suite)i(\340)116 2612 y(l'aide)k(de)g(la)f (m\351tho)r(de)h(de)g(la)f(parallaxe.)f(On)i(p)r(eut)g(\351v)n(o-)116 -2705 y(quer)19 b(ici)g(cette)h(m\351tho)r(de)g(qui)f(n\351cessite)g -(une)h(observ)-5 b(ation)116 2805 y(en)28 b(deux)h(p)r(oin)n(ts)f +2712 y(quer)19 b(ici)g(cette)h(m\351tho)r(de)g(qui)f(n\351cessite)g +(une)h(observ)-5 b(ation)116 2811 y(en)28 b(deux)h(p)r(oin)n(ts)f (di\033\351ren)n(ts)g(de)g(la)g(T)-7 b(erre.)27 b(Une)h(v)-5 -b(arian)n(te)116 2904 y(de)33 b(cette)h(m\351tho)r(de)f(sera)f -(utilis\351e)h(p)r(our)f(la)h(mesure)f(des)116 3004 y(distances)27 -b(aux)g(\351toiles.)199 3110 y(La)33 b(mesure)g(de)g(la)g(parallaxe)f -(rep)r(ose)g(sur)h(l'id\351e)g(sui-)116 3210 y(v)-5 b(an)n(te.)27 +b(arian)n(te)116 2911 y(de)33 b(cette)h(m\351tho)r(de)f(sera)f +(utilis\351e)h(p)r(our)f(la)h(mesure)f(des)116 3010 y(distances)27 +b(aux)g(\351toiles.)199 3117 y(La)33 b(mesure)g(de)g(la)g(parallaxe)f +(rep)r(ose)g(sur)h(l'id\351e)g(sui-)116 3216 y(v)-5 b(an)n(te.)27 b(Quand)e(on)i(observ)n(e)d(son)i(p)r(ouce)h(lev)n(\351)e(dev)-5 -b(an)n(t)27 b(soi)116 3309 y(\340)f(b)r(out)g(de)g(bras)e(a)n(v)n(ec)h +b(an)n(t)27 b(soi)116 3316 y(\340)f(b)r(out)g(de)g(bras)e(a)n(v)n(ec)h (l'\367il)g(droit)h(puis)g(l'\367il)f(gauc)n(he)g(al-)116 -3409 y(ternativ)n(emen)n(t,)i(on)f(v)n(oit)h(qu'il)g(se)f(d\351place)h -(par)f(rapp)r(ort)116 3508 y(aux)21 b(ob)r(jets)h(\351loign\351s.)e(Si) +3415 y(ternativ)n(emen)n(t,)i(on)f(v)n(oit)h(qu'il)g(se)f(d\351place)h +(par)f(rapp)r(ort)116 3515 y(aux)21 b(ob)r(jets)h(\351loign\351s.)e(Si) i(le)f(p)r(ouce)g(est)h(pro)r(c)n(he)e(des)i(y)n(eux,)116 -3608 y(il)33 b(se)g(d\351place)f(fortemen)n(t)h(et)g(s'il)g(est)g -(\351loign\351,)f(il)h(se)f(d\351-)116 3708 y(place)c(faiblemen)n(t.)g +3615 y(il)33 b(se)g(d\351place)f(fortemen)n(t)h(et)g(s'il)g(est)g +(\351loign\351,)f(il)h(se)f(d\351-)116 3714 y(place)c(faiblemen)n(t.)g (L'observ)-5 b(ation)26 b(de)i(son)g(mouv)n(emen)n(t)116 -3807 y(p)r(ermet)20 b(donc)g(de)g(se)f(faire)g(une)h(id\351e)g(de)g(la) -f(distance)h(en)n(tre)116 3907 y(les)28 b(y)n(eux)f(et)h(le)f(p)r -(ouce.)199 4013 y(En)37 b(termes)g(astronomiques,)e(on)i(v)n(oit)f(sur) -h(la)g(\034gure)116 4113 y(C.3)h(que)g(l'angle)g FC(\013)g -FX(en)n(tre)g(une)g(\351toile)g(loin)n(taine)g(et)g(la)116 -4212 y(P)n(olaire)21 b(est)i(le)g(m\352me)h(p)r(our)e(deux)h(p)r(oin)n -(ts)g(d'observ)-5 b(ation)116 4312 y FC(C)35 b FX(et)28 -b FC(P)40 b FX(sur)27 b(la)h(T)-7 b(erre.)27 b(P)n(our)f(un)j(astre)e -(p)r(eu)h(\351loign\351)f FC(M)9 b FX(,)116 4412 y(ces)32 -b(deux)h(angles)e FC(\014)37 b FX(et)c FC(\015)k FX(son)n(t)31 -b(di\033\351ren)n(ts.)i(On)f(app)r(elle)116 4511 y(parallaxe)26 -b(de)i(l'astre)e FC(M)37 b FX(l'angle)27 b FC(\016)j -FX(qui)e(v)-5 b(aut)28 b(:)858 4707 y FC(\016)e FL(=)d -FC(\015)g FG(\000)18 b FC(\014)116 4902 y FX(en)36 b(raison)f(du)h +3814 y(p)r(ermet)20 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b(aur)l(ait)g(\351t\351)f(attribu\351)l(e)h(\340) +g(la)g(p)l(ar)l(al)6 b(laxe)s FY(\021)2200 2624 y(J.)22 b(D.)h(Cassini,)f(dans)g(\020M\351moires)g(de)h(l'A)n(cad\351-)2200 -2717 y(mie)e(Ro)n(y)n(ale)f(des)g(Sciences\021,)h(v)n(olume)g(8,)f -(ann\351e)2200 2817 y(1730.)2391 2787 y FV(91)p 0 TeXcolorgray -0 TeXcolorgray 2386 3112 a FK(Figure)29 b(C.3)g(\025)h -FJ(Par)l(al)6 b(laxe)28 b(de)g(Mars)2104 3179 y FI(Pr)m(emi\350r)m(e)23 +2724 y(mie)e(Ro)n(y)n(ale)f(des)g(Sciences\021,)h(v)n(olume)g(8,)f +(ann\351e)2200 2823 y(1730.)2391 2793 y FW(91)p 0 TeXcolorgray +0 TeXcolorgray 2386 3119 a FK(Figure)29 b(C.3)g(\025)h +FJ(Par)l(al)6 b(laxe)28 b(de)g(Mars)2104 3186 y FI(Pr)m(emi\350r)m(e)23 b(\351tap)m(e)h(p)m(our)g(d\351terminer)h(la)g(distanc)m(e)g(T)-5 -b(err)m(e-Soleil.)p 0 TeXcolorgray 2179 4300 a +b(err)m(e-Soleil.)p 0 TeXcolorgray 2179 4307 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 2179 4300 -a 2179 4300 a + 2179 4307 +a 2179 4307 a tx@Dict begin { 28.6233 35.1105 } PutCoor PutBegin end - 2179 4300 a @beginspecial @setspecial + 2179 4307 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.42676 SLW 0 setgray 0 360 26.06259 26.06259 0.0 0.0 0 true Ellipse closepath gsave 0.42676 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end @endspecial -2179 4300 a +2179 4307 a tx@Dict begin PutEnd end - 2179 4300 a 2179 4300 a + 2179 4307 a 2179 4307 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 2179 4300 a 2179 -4300 a + 2179 4307 a 2179 +4307 a tx@Dict begin { 137.42609 79.95183 } PutCoor PutBegin end - 2179 4300 a @beginspecial @setspecial + 2179 4307 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.28453 SLW 0 setgray 0 360 4.12561 4.12561 0.0 0.0 0 true Ellipse closepath gsave 0.28453 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end @endspecial -2179 4300 a +2179 4307 a tx@Dict begin PutEnd end - 2179 4300 a @beginspecial @setspecial + 2179 4307 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.28453 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def [ 137.71059 79.95183 48.65396 51.78372 /Lineto /lineto load def 0 @@ -2548945,11 +2548955,11 @@ def 0 setlinejoin false Polygon gsave 0.28453 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end @endspecial -2179 4300 a +2179 4307 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 2179 4300 a 2179 4300 a + 2179 4307 a 2179 4307 a tx@Dict begin { 49.16609 51.5561 } PutCoor PutBegin end - 2179 4300 a @beginspecial + 2179 4307 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.28453 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def 0.0 @@ -2548964,55 +2548974,55 @@ CM def xOrig yOrig T rx ry scale 0 0 moveto exch dup dup cos exch sin moveto exch arc mtrx setmatrix gsave 0.28453 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end -@endspecial 2179 4300 a +@endspecial 2179 4307 a tx@Dict begin PutEnd end - 2179 4300 a 2179 -4300 a + 2179 4307 a 2179 +4307 a tx@Dict begin { 102.42938 41.54082 } PutCoor PutBegin end - 2179 4300 a 2179 4300 a + 2179 4307 a 2179 4307 a tx@Dict begin PutEnd end - 2179 4300 a 2179 4300 + 2179 4307 a 2179 4307 a tx@Dict begin { 17.3561 19.34778 } PutCoor PutBegin end - 2179 4300 a 2179 4300 a + 2179 4307 a 2179 4307 a tx@Dict begin PutEnd end - 2179 4300 a 2179 4300 a + 2179 4307 a 2179 4307 a tx@Dict begin { 66.29457 57.47424 } PutCoor PutBegin end 2179 -4300 a 2179 4300 a +4307 a 2179 4307 a tx@Dict begin PutEnd end - 2179 4300 a 2179 4300 a + 2179 4307 a 2179 4307 a tx@Dict begin { 72.55414 21.0549 } PutCoor PutBegin end - 2179 4300 -a 2179 4300 a + 2179 4307 +a 2179 4307 a tx@Dict begin PutEnd end - 2179 4300 a 2179 4300 a + 2179 4307 a 2179 4307 a tx@Dict begin { 95.88527 4.26788 } PutCoor PutBegin end - 2179 4300 a 2179 -4300 a + 2179 4307 a 2179 +4307 a tx@Dict begin PutEnd end - 2179 4300 a 2179 4300 a + 2179 4307 a 2179 4307 a tx@Dict begin { 182.66571 97.30789 } PutCoor PutBegin end - 2179 4300 a 2151 4329 -a FX(E)2179 4300 y + 2179 4307 a 2151 4335 +a FY(E)2179 4307 y tx@Dict begin PutEnd end - 2179 4300 a 2179 4300 a + 2179 4307 a 2179 4307 a tx@Dict begin { 73.69223 53.4909 } PutCoor PutBegin end - 2179 4300 -a 2153 4321 a FC(\014)2179 4300 y + 2179 4307 +a 2153 4327 a FC(\014)2179 4307 y tx@Dict begin PutEnd end - 2179 4300 a 2179 4300 + 2179 4307 a 2179 4307 a tx@Dict begin { 41.82532 50.93015 } PutCoor PutBegin end - 2179 4300 a 2151 4329 a FX(P)2179 4300 y + 2179 4307 a 2151 4335 a FY(P)2179 4307 y tx@Dict begin PutEnd end - 2179 4300 -a 2179 4300 a + 2179 4307 +a 2179 4307 a tx@Dict begin { 48.65396 29.87523 } PutCoor PutBegin end - 2179 4300 a 2149 4329 a FX(C)2179 4300 + 2179 4307 a 2149 4335 a FY(C)2179 4307 y tx@Dict begin PutEnd end - 2179 4300 a @beginspecial @setspecial + 2179 4307 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.28453 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def [ 54.62898 36.70384 48.65396 51.78372 /Lineto /lineto load def 0 setlinejoin @@ -2549020,12 +2549030,12 @@ false Line gsave 0.28453 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end @endspecial -2179 4300 a +2179 4307 a tx@Dict begin { 23.61566 40.40268 } PutCoor PutBegin end - 2179 4300 a 2149 4329 a FX(T)2179 4300 y + 2179 4307 a 2149 4335 a FY(T)2179 4307 y tx@Dict begin PutEnd end -2179 4300 a @beginspecial @setspecial +2179 4307 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.28453 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def [ 29.02164 104.9901 29.02164 34.9967 /Lineto /lineto load def 0 setlinejoin @@ -2549063,12 +2549073,12 @@ setlinejoin false Line gsave 0.28453 SLW 0 setgray 1. .setopacityalpha false Line gsave 0.28453 SLW 0 setgray 1. .setopacityalpha 0 setlinecap [ 2.84526 2.84526 ] 0 0 add DashLine grestore end -@endspecial 2179 4300 a +@endspecial 2179 4307 a tx@Dict begin { 42.67891 112.10324 } PutCoor PutBegin end - 2179 4300 a 2053 -4329 a FX(P)n(olaire)2179 4300 y + 2179 4307 a 2053 +4335 a FY(P)n(olaire)2179 4307 y tx@Dict begin PutEnd end - 2179 4300 a @beginspecial + 2179 4307 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.14226 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def [ @@ -2549076,12 +2549086,12 @@ tx@Dict begin PutEnd end false Line gsave 0.14226 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end -@endspecial 2179 4300 a +@endspecial 2179 4307 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 2179 4300 a 2179 -4300 a + 2179 4307 a 2179 +4307 a tx@Dict begin { 49.36528 50.98706 } PutCoor PutBegin end - 2179 4300 a @beginspecial @setspecial + 2179 4307 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { BeginArrow 1. 1. scale false 0.25 1. 2.84526 2. 1. .setopacityalpha Arrow EndArrow moveto } def /ArrowB { } def 0.28453 SLW 0 setgray /ArrowA { BeginArrow 1. @@ -2549100,14 +2549110,14 @@ cos exch sin moveto exch arc mtrx setmatrix gsave 0.28453 SLW 0 setgray end @endspecial -2179 4300 a +2179 4307 a tx@Dict begin PutEnd end - 2179 4300 a 2179 4300 a + 2179 4307 a 2179 4307 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 2179 4300 a 2179 -4300 a + 2179 4307 a 2179 +4307 a tx@Dict begin { 54.74283 37.27292 } PutCoor PutBegin end - 2179 4300 a @beginspecial @setspecial + 2179 4307 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { BeginArrow 1. 1. scale false 0.25 1. 2.84526 2. 1. .setopacityalpha Arrow EndArrow moveto } def /ArrowB { } def 0.28453 SLW 0 setgray /ArrowA { BeginArrow 1. @@ -2549126,14 +2549136,14 @@ cos exch sin moveto exch arc mtrx setmatrix gsave 0.28453 SLW 0 setgray end @endspecial -2179 4300 a +2179 4307 a tx@Dict begin PutEnd end - 2179 4300 a 2179 4300 a + 2179 4307 a 2179 4307 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 2179 4300 a 2179 -4300 a + 2179 4307 a 2179 +4307 a tx@Dict begin { 54.62898 36.36243 } PutCoor PutBegin end - 2179 4300 a @beginspecial @setspecial + 2179 4307 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.28453 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def 0.0 0.0 /yOrig ED /xOrig ED 12.91745 12.91745 /ry ED /rx ED /angleA /d @@ -2549148,44 +2549158,44 @@ moveto exch arc mtrx setmatrix gsave 0.28453 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end @endspecial -2179 4300 a +2179 4307 a tx@Dict begin PutEnd end - 2179 4300 a 2179 4300 a + 2179 4307 a 2179 4307 a tx@Dict begin { 63.44931 71.70055 } PutCoor PutBegin end - 2179 4300 a 2155 -4310 a FC(\015)2179 4300 y + 2179 4307 a 2155 +4317 a FC(\015)2179 4307 y tx@Dict begin PutEnd end - 2179 4300 a 2179 4300 a + 2179 4307 a 2179 4307 a tx@Dict begin { 147.669 84.78877 } PutCoor PutBegin end 2179 -4300 a 2141 4329 a FX(M)2179 4300 y +4307 a 2141 4335 a FY(M)2179 4307 y tx@Dict begin PutEnd end - 2179 4300 a 2179 -4300 a + 2179 4307 a 2179 +4307 a tx@Dict begin { 61.1731 76.25299 } PutCoor PutBegin end - 2179 4300 a 2179 4300 a + 2179 4307 a 2179 4307 a tx@Dict begin PutEnd end - 2179 4300 a 2179 4300 + 2179 4307 a 2179 4307 a tx@Dict begin { 59.18143 74.83035 } PutCoor PutBegin end - 2179 4300 a 2179 4300 a + 2179 4307 a 2179 4307 a tx@Dict begin PutEnd end - 2179 4300 a 2179 4300 a + 2179 4307 a 2179 4307 a tx@Dict begin { 109.82707 70.84697 } PutCoor PutBegin end 2179 -4300 a 2179 4300 a +4307 a 2179 4307 a tx@Dict begin PutEnd end - 2179 4300 a 2179 4300 a + 2179 4307 a 2179 4307 a tx@Dict begin { 62.02669 34.42766 } PutCoor PutBegin end - 2179 4300 -a 2152 4318 a FC(\013)2179 4300 y + 2179 4307 +a 2152 4324 a FC(\013)2179 4307 y tx@Dict begin PutEnd end - 2179 4300 a 2179 4300 + 2179 4307 a 2179 4307 a tx@Dict begin { 43.53249 63.73381 } PutCoor PutBegin end - 2179 4300 a 2152 4318 a FC(\013)2179 4300 y + 2179 4307 a 2152 4324 a FC(\013)2179 4307 y tx@Dict begin PutEnd end - 2179 4300 + 2179 4307 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.14226 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def [ @@ -2549193,18 +2549203,18 @@ a @beginspecial @setspecial false Line gsave 0.14226 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end -@endspecial 2179 4300 a +@endspecial 2179 4307 a tx@Dict begin { 25.0383 66.57907 } PutCoor PutBegin end -2179 4300 a 2148 4329 a FX(N)2179 4300 y +2179 4307 a 2148 4335 a FY(N)2179 4307 y tx@Dict begin PutEnd end - 2179 4300 a -2179 4300 a + 2179 4307 a +2179 4307 a tx@Dict begin { 32.72049 4.26788 } PutCoor PutBegin end - 2179 4300 a 2156 4329 a FX(S)2179 4300 y + 2179 4307 a 2156 4335 a FY(S)2179 4307 y tx@Dict begin PutEnd end -2179 4300 a @beginspecial @setspecial +2179 4307 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.28453 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def [ 137.71059 79.95183 29.02164 34.9967 /Lineto /lineto load def 0 setlinejoin @@ -2549212,11 +2549222,11 @@ false Line gsave 0.28453 SLW 0 setgray 1. .setopacityalpha 0 setlinecap [ 2.84526 2.84526 ] 0 0 add DashLine grestore end @endspecial 2179 -4300 a +4307 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 2179 4300 a 2179 4300 a + 2179 4307 a 2179 4307 a tx@Dict begin { 116.37114 71.13152 } PutCoor PutBegin end - 2179 4300 a @beginspecial + 2179 4307 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.28453 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def 0.0 @@ -2549232,443 +2549242,443 @@ cos exch sin moveto exch arc mtrx setmatrix gsave 0.28453 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end -@endspecial 2179 4300 a +@endspecial 2179 4307 a tx@Dict begin PutEnd end - 2179 4300 a 2179 -4300 a + 2179 4307 a 2179 +4307 a tx@Dict begin { 120.35452 79.38275 } PutCoor PutBegin end - 2179 4300 a 2159 4329 a FC(\016)2179 4300 y + 2179 4307 a 2159 4335 a FC(\016)2179 4307 y tx@Dict begin PutEnd end 2179 -4300 a 2179 4300 a +4307 a 2179 4307 a tx@Dict begin { 46.66225 43.24794 } PutCoor PutBegin end - 2179 4300 a 2147 4329 a FX(O)2179 -4300 y + 2179 4307 a 2147 4335 a FY(O)2179 +4307 y tx@Dict begin PutEnd end - 2179 4300 a 0 TeXcolorgray 2117 4510 a FX(L'application)46 + 2179 4307 a 0 TeXcolorgray 2117 4517 a FY(L'application)46 b(de)g(cette)h(m\351tho)r(de)g(p)r(our)f(d\351termi-)2034 -4610 y(ner)34 b(la)g(p)r(osition)g(d'un)g(astre)f(comme)h(Mars,)f -FC(M)43 b FX(sur)34 b(le)2034 4710 y(sc)n(h\351ma)39 +4617 y(ner)34 b(la)g(p)r(osition)g(d'un)g(astre)f(comme)h(Mars,)f +FC(M)43 b FY(sur)34 b(le)2034 4716 y(sc)n(h\351ma)39 b(C.3,)h(consiste)f(\340)g(observ)n(er)f(cette)i(plan\350te)g(si-)2034 -4809 y(m)n(ultan\351men)n(t)27 b(depuis)g(deux)g(endroits)f -(\351loign\351s)g(l'un)h(de)2034 4909 y(l'autre)32 b(\340)g(la)f +4816 y(m)n(ultan\351men)n(t)27 b(depuis)g(deux)g(endroits)f +(\351loign\351s)g(l'un)h(de)2034 4915 y(l'autre)32 b(\340)g(la)f (surface)h(de)g(la)g(terre.)f(Deux)i(observ)-5 b(ateurs)2034 -5008 y FC(P)47 b FX(et)35 b FC(C)41 b FX(\(les)35 b(astronomes)e -(Cassini)i(\340)f(P)n(aris)f(et)j(Ric)n(her)2034 5108 +5015 y FC(P)47 b FY(et)35 b FC(C)41 b FY(\(les)35 b(astronomes)e +(Cassini)i(\340)f(P)n(aris)f(et)j(Ric)n(her)2034 5115 y(\340)h(Ca)n(y)n(enne,)e(en)i(1672\))f(mesuren)n(t)g(au)h(m\352me)g -(momen)n(t)2034 5208 y(l'\351cart)c(angulaire)f(en)n(tre)h(Mars)g(M)g -(et)h(une)g(\351toile)g(E)f(en)2034 5307 y(arri\350re)38 +(momen)n(t)2034 5214 y(l'\351cart)c(angulaire)f(en)n(tre)h(Mars)g(M)g +(et)h(une)g(\351toile)g(E)f(en)2034 5314 y(arri\350re)38 b(plan.)h(La)h(somme)f(des)g(deux)h(angles)f(mesur\351s)2034 -5407 y(constitue)d(l'angle)f FC(\016)j FX(au)e(sommet)f(du)h(triangle)f -FC(P)12 b(M)d(C)d FX(,)p 0 TeXcolorgray 1930 5617 a(172)p +5414 y(constitue)d(l'angle)f FC(\016)j FY(au)e(sommet)f(du)h(triangle)f +FC(P)12 b(M)d(C)d FY(,)p 0 TeXcolorgray 1930 5624 a(172)p 0 TeXcolorgray eop end %%Page: 173 173 TeXDict begin 173 172 bop 0 TeXcolorgray 0 TeXcolorgray --116 262 a FQ(ANNEXE)28 b(C.)55 b(MESURES)27 b(DE)h(DIST)-7 +-116 269 a FR(ANNEXE)28 b(C.)55 b(MESURES)27 b(DE)h(DIST)-7 b(ANCES)736 b(C.4.)54 b(LA)28 b(DIST)-7 b(ANCE)29 b(TERRE-SOLEIL)p --116 296 3753 4 v 0 TeXcolorgray -116 525 a FX(soit)f(la)f(parallaxe.)f +-116 302 3753 4 v 0 TeXcolorgray -116 532 a FY(soit)f(la)f(parallaxe.)f (En)i(raison)f(de)h(l'imp)r(ortan)n(t)g(\351loigne-)-116 -625 y(men)n(t)c(de)g(Mars)f(par)g(rapp)r(ort)g(\340)g(la)h(distance)f -FC(P)12 b(C)31 b FX(\(P)n(aris-)-116 725 y(Ca)n(y)n(enne\),)37 +632 y(men)n(t)c(de)g(Mars)f(par)g(rapp)r(ort)g(\340)g(la)h(distance)f +FC(P)12 b(C)31 b FY(\(P)n(aris-)-116 731 y(Ca)n(y)n(enne\),)37 b(on)h(p)r(eut)h(p)r(oser)f(gr\342ce)e(\340)i(la)g(relation)g(A.2,)-116 -824 y(page)26 b(163)h(:)343 1045 y FC(\016)f FL(=)516 -989 y FC(P)12 b(C)p 503 1026 156 4 v 503 1102 a(M)d(O)715 -1045 y FG(\))46 b FC(M)9 b(O)25 b FL(=)1120 989 y FC(P)12 -b(C)p 1120 1026 131 4 v 1165 1102 a(\016)-116 1250 y -FX(La)46 b(distance)g FC(P)12 b(C)6 b FX(,)47 b(appro)n(ximativ)n(emen) -n(t)e(la)h(distance)-116 1350 y(en)n(tre)41 b(P)n(aris)g(et)h(Ca)n(y)n -(enne,)f(p)r(ermet)h(alors)f(de)h(trouv)n(er)-116 1450 -y FC(M)9 b(O)r FX(.)28 b(La)f(distance)g(de)h(la)f(T)-7 +831 y(page)26 b(163)h(:)343 1051 y FC(\016)f FL(=)516 +995 y FC(P)12 b(C)p 503 1032 156 4 v 503 1108 a(M)d(O)715 +1051 y FG(\))46 b FC(M)9 b(O)25 b FL(=)1120 995 y FC(P)12 +b(C)p 1120 1032 131 4 v 1165 1108 a(\016)-116 1257 y +FY(La)46 b(distance)g FC(P)12 b(C)6 b FY(,)47 b(appro)n(ximativ)n(emen) +n(t)e(la)h(distance)-116 1357 y(en)n(tre)41 b(P)n(aris)g(et)h(Ca)n(y)n +(enne,)f(p)r(ermet)h(alors)f(de)h(trouv)n(er)-116 1456 +y FC(M)9 b(O)r FY(.)28 b(La)f(distance)g(de)h(la)f(T)-7 b(erre)27 b(\340)g(Mars)f(v)-5 b(aut)28 b(alors)e(:)110 -1632 y FC(d)153 1644 y FB(T)9 b Fz(\000)p FB(M)350 1632 +1639 y FC(d)153 1651 y FB(T)9 b Fz(\000)p FB(M)350 1639 y FL(=)23 b FC(M)9 b(O)21 b FL(+)d FC(O)r(T)34 b FL(=)23 -b FC(M)9 b(O)21 b FL(+)d FC(R)1251 1644 y FB(T)1529 1632 -y FX(\(C.1\))-116 1815 y(o\371)27 b FC(R)62 1827 y FB(T)142 -1815 y FX(est)h(le)f(ra)n(y)n(on)f(de)i(la)f(T)-7 b(erre.)-33 -1940 y(Le)27 b(r\351sultat)g(est)h(donn\351)f(par)g(Cassini)g +b FC(M)9 b(O)21 b FL(+)d FC(R)1251 1651 y FB(T)1529 1639 +y FY(\(C.1\))-116 1822 y(o\371)27 b FC(R)62 1834 y FB(T)142 +1822 y FY(est)h(le)f(ra)n(y)n(on)f(de)i(la)f(T)-7 b(erre.)-33 +1947 y(Le)27 b(r\351sultat)g(est)h(donn\351)f(par)g(Cassini)g (lui-m\352me)h(:)p 0 TeXcolorgray 0 TeXcolorgray 174 -2069 a(\020)p FU(L)l(e)64 b(5)g(septembr)l(e)g(1672,)i(tr)l(ois)e -(jours)50 2168 y(avant)31 b(l'opp)l(osition)k(du)c(Soleil)h(\340)g -(Mars,)h(nous)50 2268 y(observ\342mes)59 b(\340)f(Paris)h(tr)l(ois)e -(Etoiles)i(dans)50 2367 y(l'Eau)33 b(A)l(quarius)f(mar)l(qu\351)l(es)h -(p)l(ar)g(Bayerus)g FL(\011)p FU(,)50 2467 y(vers)25 +2075 a(\020)p FV(L)l(e)64 b(5)g(septembr)l(e)g(1672,)i(tr)l(ois)e +(jours)50 2175 y(avant)31 b(l'opp)l(osition)k(du)c(Soleil)h(\340)g +(Mars,)h(nous)50 2274 y(observ\342mes)59 b(\340)f(Paris)h(tr)l(ois)e +(Etoiles)i(dans)50 2374 y(l'Eau)33 b(A)l(quarius)f(mar)l(qu\351)l(es)h +(p)l(ar)g(Bayerus)g FL(\011)p FV(,)50 2474 y(vers)25 b(lesquel)6 b(les)26 b(Mars)g(al)6 b(loit)27 b(p)l(ar)e(son)h(mouve-)50 -2567 y(ment)37 b(p)l(articulier)i(r)l(\351tr)l(o)l(gr)l(ade,)g(de)g -(sorte)f(que)50 2666 y(l'on)30 b(juge)l(oit)g(qu'il)g(en)f(aur)l(oit)g -(pu)g(c)l(acher)i(une.)50 2766 y(Il)24 b(\351toit)h(alors)g(un)f(p)l -(eu)g(plus)g(septentrional)i(que)50 2866 y(la)h(plus)g(septentrionale)g -(des)h(tr)l(ois.)f(On)f(prit)h(la)50 2965 y(hauteur)f(M\351ridienne)i -(de)f(c)l(el)6 b(le-ci)28 b(qui)f(p)l(assoit)50 3065 +2573 y(ment)37 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+5414 y(Pythagore)h(et)i(la)g(g\351om\351trie)f(\351viden)n(te)i(du)f (probl\350me)p 0 TeXcolorgray 0 TeXcolorgray 0 TeXcolorgray -0 TeXcolorgray 2183 2091 a FK(Figure)h(G.1)h(\025)f FJ(Chute)g(de)f(la) -f(lune)p 0 TeXcolorgray 2238 3451 a +0 TeXcolorgray 2183 2098 a FK(Figure)h(G.1)h(\025)f FJ(Chute)g(de)f(la) +f(lune)p 0 TeXcolorgray 2238 3458 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 2238 3451 a 2238 -3451 a + 2238 3458 a 2238 +3458 a tx@Dict begin { 20.74193 28.42416 } PutCoor PutBegin end - 2238 3451 a @beginspecial @setspecial + 2238 3458 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.85358 SLW 0 setgray 0 360 18.32347 18.32347 0.0 0.0 0 true Ellipse closepath gsave 0.85358 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end @endspecial -2238 3451 a +2238 3458 a tx@Dict begin PutEnd end - 2238 3451 a 2238 3451 a + 2238 3458 a 2238 3458 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 2238 3451 a 2238 -3451 a + 2238 3458 a 2238 +3458 a tx@Dict begin { 20.79884 159.47685 } PutCoor PutBegin end - 2238 3451 a @beginspecial @setspecial + 2238 3458 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.85358 SLW 0 setgray 0 360 4.63779 4.63779 0.0 0.0 0 true Ellipse closepath gsave 0.85358 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end @endspecial -2238 3451 a +2238 3458 a tx@Dict begin PutEnd end - 2238 3451 a @beginspecial @setspecial + 2238 3458 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.85358 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def [ 21.0549 155.63574 21.0549 46.9468 /Lineto /lineto load def 0 setlinejoin @@ -2657204,49 +2657214,49 @@ false Line gsave 0.85358 SLW 0 setgray 1. .setopacityalpha 2.84526 end @endspecial -2238 3451 a +2238 3458 a tx@Dict begin { 20.7704 23.90016 } PutCoor PutBegin end - 2238 3451 a 2142 3480 a FX(T)-7 b(erre)2238 -3451 y + 2238 3458 a 2142 3486 a FY(T)-7 b(erre)2238 +3458 y tx@Dict begin PutEnd end - 2238 3451 a 2238 3451 a + 2238 3458 a 2238 3458 a tx@Dict begin { 35.8503 149.66072 } PutCoor PutBegin end - 2238 3451 a 2147 3480 -a FX(Lune)2238 3451 y + 2238 3458 a 2147 3486 +a FY(Lune)2238 3458 y tx@Dict begin PutEnd end - 2238 3451 a 2238 3451 a + 2238 3458 a 2238 3458 a tx@Dict begin { 69.13983 114.9485 } PutCoor PutBegin end - 2238 3451 -a 1877 3472 a FX(temps)28 b(de)f(c)n(h)n(ute)h(:)f FL(1)14 -b FC(s)2238 3451 y + 2238 3458 +a 1877 3478 a FY(temps)28 b(de)f(c)n(h)n(ute)h(:)f FL(1)14 +b FC(s)2238 3458 y tx@Dict begin PutEnd end - 2238 3451 a 2238 3451 a + 2238 3458 a 2238 3458 a tx@Dict begin { 9.67386 159.90363 } PutCoor PutBegin end - 2238 3451 -a 2207 3480 a FX(A)2238 3451 y + 2238 3458 +a 2207 3486 a FY(A)2238 3458 y tx@Dict begin PutEnd end - 2238 3451 a 2238 3451 + 2238 3458 a 2238 3458 a tx@Dict begin { 109.25798 159.90363 } PutCoor PutBegin end - 2238 3451 a 2209 3480 a FX(B)2238 3451 y + 2238 3458 a 2209 3486 a FY(B)2238 3458 y tx@Dict begin PutEnd end - 2238 3451 -a 2238 3451 a + 2238 3458 +a 2238 3458 a tx@Dict begin { 78.8137 137.14154 } PutCoor PutBegin end - 2238 3451 a 2208 3480 a FX(C)2238 3451 + 2238 3458 a 2208 3486 a FY(C)2238 3458 y tx@Dict begin PutEnd end - 2238 3451 a 2238 3451 a + 2238 3458 a 2238 3458 a tx@Dict begin { 21.624 34.14313 } PutCoor PutBegin end - 2238 3451 a 2206 3480 a FX(D)2238 -3451 y + 2238 3458 a 2206 3486 a FY(D)2238 +3458 y tx@Dict begin PutEnd end - 2238 3451 a 2238 3451 a + 2238 3458 a 2238 3458 a tx@Dict begin { 34.14313 72.26959 } PutCoor PutBegin end - 2238 3451 a 2211 3469 -a FC(\013)2238 3451 y + 2238 3458 a 2211 3476 +a FC(\013)2238 3458 y tx@Dict begin PutEnd end - 2238 3451 a @beginspecial @setspecial + 2238 3458 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.25 1. 2.84526 2. 1. .setopacityalpha Arrow EndArrow } def 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FK(Figure)29 b(J.2)g(\025)h FJ(Syst\350me)f(T)-6 +b(err)l(e-Lune)p 0 TeXcolorgray 337 1400 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 337 1393 a -337 1393 a + 337 1400 a +337 1400 a tx@Dict begin { 43.3333 43.19102 } PutCoor PutBegin end - 337 1393 a @beginspecial @setspecial + 337 1400 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.85358 SLW 0 setgray 0 360 40.34576 40.34576 0.0 0.0 0 true Ellipse closepath gsave 0.85358 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end @endspecial -337 1393 a +337 1400 a tx@Dict begin PutEnd end - 337 1393 a 337 1393 a + 337 1400 a 337 1400 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 337 1393 a 337 1393 + 337 1400 a 337 1400 a tx@Dict begin { 155.63574 42.10986 } PutCoor PutBegin end - 337 1393 a @beginspecial @setspecial + 337 1400 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.85358 SLW 0 setgray 0 360 8.82031 8.82031 0.0 0.0 0 true Ellipse closepath gsave 0.85358 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end @endspecial 337 -1393 a +1400 a tx@Dict begin PutEnd end - 337 1393 a @beginspecial @setspecial + 337 1400 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { BeginArrow 1. 1. scale false 0.25 1. 2.84526 2. 1. .setopacityalpha Arrow EndArrow moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.25 1. 2.84526 2. @@ -2677396,11 +2677405,11 @@ load def 0 setlinejoin false Line gsave 0.42676 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end @endspecial -337 1393 a +337 1400 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 337 1393 a 337 1393 a + 337 1400 a 337 1400 a tx@Dict begin { 67.71721 41.71152 } PutCoor PutBegin end - 337 1393 a @beginspecial + 337 1400 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.85358 SLW 0 setgray 0 360 1.02429 1.02429 0.0 0.0 0 true Ellipse @@ -2677408,51 +2677417,51 @@ tx@Dict begin { 67.71721 41.71152 } PutCoor PutBegin end 0.85358 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end -@endspecial 337 1393 a +@endspecial 337 1400 a tx@Dict begin PutEnd end - 337 1393 a 337 1393 + 337 1400 a 337 1400 a tx@Dict begin { 42.96344 11.38104 } PutCoor PutBegin end - 337 1393 a 271 1415 a FC(M)352 1427 y FB(T)337 1393 + 337 1400 a 271 1422 a FC(M)352 1434 y FB(T)337 1400 y tx@Dict begin PutEnd end - 337 1393 a 337 1393 a + 337 1400 a 337 1400 a tx@Dict begin { 57.47424 47.80038 } PutCoor PutBegin end - 337 1393 a 272 1422 a FC(C)6 -b(G)337 1393 y + 337 1400 a 272 1428 a FC(C)6 +b(G)337 1400 y tx@Dict begin PutEnd end - 337 1393 a 337 1393 a + 337 1400 a 337 1400 a tx@Dict begin { 55.48257 28.16806 } PutCoor PutBegin end - 337 1393 a 317 1411 -a FC(r)337 1393 y + 337 1400 a 317 1418 +a FC(r)337 1400 y tx@Dict begin PutEnd end - 337 1393 a 337 1393 a + 337 1400 a 337 1400 a tx@Dict begin { 108.1199 46.66225 } PutCoor PutBegin end - 337 1393 a 241 -1412 a FC(d)284 1424 y FB(T)j Fz(\000)p FB(L)337 1393 + 337 1400 a 241 +1419 a FC(d)284 1431 y FB(T)j Fz(\000)p FB(L)337 1400 y tx@Dict begin PutEnd end - 337 1393 a 337 1393 a + 337 1400 a 337 1400 a tx@Dict begin { 154.2131 26.74542 } PutCoor PutBegin end - 337 1393 a 272 1415 a FC(M)353 -1427 y FB(L)337 1393 y + 337 1400 a 272 1422 a FC(M)353 +1434 y FB(L)337 1400 y tx@Dict begin PutEnd end - 337 1393 a 337 1393 a + 337 1400 a 337 1400 a tx@Dict begin { 36.98839 69.99342 } PutCoor PutBegin end - 337 1393 -a 210 1422 a FX(Axe)28 b(de)337 1393 y + 337 1400 +a 210 1428 a FY(Axe)28 b(de)337 1400 y tx@Dict begin PutEnd end - 337 1393 a 337 -1393 a + 337 1400 a 337 +1400 a tx@Dict begin { 42.39436 61.45764 } PutCoor PutBegin end - 337 1393 a 192 1419 a FX(rotation)337 1393 y + 337 1400 a 192 1426 a FY(rotation)337 1400 y tx@Dict begin PutEnd end 337 -1393 a 337 1393 a +1400 a 337 1400 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 337 1393 a 337 1393 a + 337 1400 a 337 1400 a tx@Dict begin { 67.71721 68.00171 } PutCoor PutBegin end - 337 1393 a @beginspecial + 337 1400 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.42676 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def 0.0 @@ -2677468,15 +2677477,15 @@ cos exch sin moveto exch arc mtrx setmatrix gsave 0.42676 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end -@endspecial 337 1393 a +@endspecial 337 1400 a tx@Dict begin PutEnd end - 337 1393 a 337 1393 + 337 1400 a 337 1400 a tx@Dict begin { 21.9085 33.00504 } PutCoor PutBegin end - 337 1393 a 279 1415 a FC(R)342 1427 y FB(T)337 1393 + 337 1400 a 279 1422 a FC(R)342 1434 y FB(T)337 1400 y tx@Dict begin PutEnd end - 337 1393 a @beginspecial @setspecial + 337 1400 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.25 1. 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-2246 y(en)35 b(rempla\347an)n(t)f(le)g FC(m)h FX(du)g(n)n(um\351rateur) -f(de)g(la)h(fraction)116 2345 y(par)27 b FC(M)9 b FX(\).)116 -2619 y FM(J.3)136 b(F)-11 b(orce)44 b(d'inertie)199 2801 -y FX(En)36 b(substance,)g(le)h(probl\350me)f(des)g(mar\351es)f(est)h(p) -r(os\351)116 2901 y(par)20 b(la)h(rotation)e(d'une)i(masse)f -FC(m)h FX(d'eau)f(non)h(pas)f(autour)116 3000 y(du)i(cen)n(tre)f(de)h +2252 y(en)35 b(rempla\347an)n(t)f(le)g FC(m)h FY(du)g(n)n(um\351rateur) +f(de)g(la)h(fraction)116 2352 y(par)27 b FC(M)9 b FY(\).)116 +2626 y FN(J.3)136 b(F)-11 b(orce)44 b(d'inertie)199 2808 +y FY(En)36 b(substance,)g(le)h(probl\350me)f(des)g(mar\351es)f(est)h(p) +r(os\351)116 2907 y(par)20 b(la)h(rotation)e(d'une)i(masse)f +FC(m)h FY(d'eau)f(non)h(pas)f(autour)116 3007 y(du)i(cen)n(tre)f(de)h (la)f(T)-7 b(erre,)20 b(mais)i(autour)e(du)i(cen)n(tre)f(de)h(gra-)116 -3100 y(vit\351)k(du)f(syst\350me)h(T)-7 b(erre-Lune.)24 -b(Il)h(s'agit)g(d'un)h(mouv)n(en)n(t)116 3200 y(circulaire)k(uniforme)g -(et)h(l'une)g(des)g(comp)r(osan)n(tes)f(de)g(la)116 3299 +3107 y(vit\351)k(du)f(syst\350me)h(T)-7 b(erre-Lune.)24 +b(Il)h(s'agit)g(d'un)h(mouv)n(en)n(t)116 3206 y(circulaire)k(uniforme)g +(et)h(l'une)g(des)g(comp)r(osan)n(tes)f(de)g(la)116 3306 y(seconde)e(loi)g(de)g(Newton)h(est)f(l'acc\351l\351ration)f(cen)n -(trip)r(\350te)116 3399 y FC(a)160 3411 y FB(c)230 3399 -y FX(de)35 b(cette)h(masse.)f(On)h(p)r(eut)g(l'exprimer)f(sous)g -(di\033\351-)116 3498 y(ren)n(tes)27 b(formes)g(pr\351sen)n(t\351es)f -(dans)i(l'\351quation)f(I.2)g(:)726 3725 y FC(a)770 3737 -y FB(c)827 3725 y FL(=)924 3669 y FC(v)967 3639 y FF(2)p -924 3706 81 4 v 932 3782 a FC(R)1038 3725 y FL(=)c FC(!)1181 -3691 y FF(2)1236 3725 y FG(\001)18 b FC(R)439 b FX(\(J.2\))116 -3926 y(o\371)21 b FC(v)k FX(est)c(la)g(vitesse)g(lin\351aire)g(de)g(la) -g(masse)g FC(m)g FX(d'eau,)g FC(R)h FX(la)116 4026 y(distance)28 +(trip)r(\350te)116 3405 y FC(a)160 3417 y FB(c)230 3405 +y FY(de)35 b(cette)h(masse.)f(On)h(p)r(eut)g(l'exprimer)f(sous)g +(di\033\351-)116 3505 y(ren)n(tes)27 b(formes)g(pr\351sen)n(t\351es)f +(dans)i(l'\351quation)f(J.2)g(:)726 3732 y FC(a)770 3744 +y FB(c)827 3732 y FL(=)924 3676 y FC(v)967 3646 y FF(2)p +924 3713 81 4 v 932 3789 a FC(R)1038 3732 y FL(=)c FC(!)1181 +3698 y FF(2)1236 3732 y FG(\001)18 b FC(R)439 b FY(\(J.2\))116 +3933 y(o\371)21 b FC(v)k FY(est)c(la)g(vitesse)g(lin\351aire)g(de)g(la) +g(masse)g FC(m)g FY(d'eau,)g FC(R)h FY(la)116 4032 y(distance)28 b(du)g(cen)n(tre)f(de)g(gra)n(vit\351)f(\340)i(la)f(masse)g -FC(m)g FX(et)h FC(!)j FX(sa)116 4125 y(vitesse)26 b(angulaire.)f(En)g -(e\033et,)i(l'\351quation)f(2.13,)f(page)g(47)116 4225 +FC(m)g FY(et)h FC(!)j FY(sa)116 4132 y(vitesse)26 b(angulaire.)f(En)g +(e\033et,)i(l'\351quation)f(2.13,)f(page)g(47)116 4232 y(mon)n(tre)31 b(que)g(la)f(vitesse)h(lin\351aire)f(d'un)i(corps)e -(tournan)n(t)116 4325 y(en)j(mouv)n(emen)n(t)g(circulaire)e(uniforme)i +(tournan)n(t)116 4331 y(en)j(mouv)n(emen)n(t)g(circulaire)e(uniforme)i (v)-5 b(aut)33 b FC(v)i FL(=)d FC(!)24 b FG(\001)e FC(R)116 -4424 y FX(a)n(v)n(ec)k(p)r(our)i(unit\351)g FL([)p FC(!)s -FL(])23 b(=)g(rad)p FC(=)p FL(s)n FX(.)116 4656 y FY(J.3.1)113 -b(Vitesse)37 b(angulaire)199 4809 y FX(Or,)24 b(la)g(vitesse)g +4431 y FY(a)n(v)n(ec)k(p)r(our)i(unit\351)g FL([)p FC(!)s +FL(])23 b(=)g(rad)p FC(=)p FL(s)n FY(.)116 4663 y FM(J.3.1)113 +b(Vitesse)37 b(angulaire)199 4816 y FY(Or,)24 b(la)g(vitesse)g (lin\351aire)f(de)i(la)f(masse)f(d'eau)h(n'est)h(pas)116 -4909 y(celle)39 b(qui)g(r\351sulte)g(de)g(sa)g(rotation)f(diurne)h -(autour)f(du)116 5008 y(cen)n(tre)27 b(de)g(la)g(T)-7 +4915 y(celle)39 b(qui)g(r\351sulte)g(de)g(sa)g(rotation)f(diurne)h +(autour)f(du)116 5015 y(cen)n(tre)27 b(de)g(la)g(T)-7 b(erre,)26 b(mais)h(celle)g(corresp)r(ondan)n(t)e(au)i(d\351-)116 -5108 y(placemen)n(t)32 b(de)f FC(m)h FX(sous)f(l'in\035uence)h(de)f(la) -h(Lune,)f(c'est-)116 5208 y(\340-dire)f(celle)h(corresp)r(ondan)n(t)e -(\340)i(sa)f(rotation)h(autour)f(du)116 5307 y(cen)n(tre)h(de)h(gra)n +5115 y(placemen)n(t)32 b(de)f FC(m)h FY(sous)f(l'in\035uence)h(de)f(la) +h(Lune,)f(c'est-)116 5214 y(\340-dire)f(celle)h(corresp)r(ondan)n(t)e +(\340)i(sa)f(rotation)h(autour)f(du)116 5314 y(cen)n(tre)h(de)h(gra)n (vit\351)e(du)i(syst\350me)f(T)-7 b(erre-Lune.)30 b(A)-9 -b(v)n(ec)31 b(les)116 5407 y(grandeurs)19 b(pr\351sen)n(t\351es)g(\340) -h(la)g(\034gure)f(I.2)h(et)h(l'\351quation)e(I.1,)p 0 -TeXcolorgray 0 TeXcolorgray 0 TeXcolorgray 0 TeXcolorgray -2296 589 a FK(Figure)29 b(J.3)g(\025)h FJ(Syst\350me)f(T)-6 -b(err)l(e-Lune-e)l(au)p 0 TeXcolorgray 2255 1393 a +b(v)n(ec)31 b(les)116 5414 y(grandeurs)37 b(pr\351sen)n(t\351es)g(\340) +g(la)h(\034gure)g(J.2)f(et)i(l'\351quation)p 0 TeXcolorgray +0 TeXcolorgray 0 TeXcolorgray 0 TeXcolorgray 2296 596 +a FK(Figure)29 b(J.3)g(\025)h FJ(Syst\350me)f(T)-6 b(err)l(e-Lune-e)l +(au)p 0 TeXcolorgray 2255 1400 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 2255 -1393 a 2255 1393 a + 2255 1400 a 2255 1400 +a tx@Dict begin { 43.3333 43.19102 } PutCoor PutBegin end - 2255 1393 a @beginspecial @setspecial + 2255 1400 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.85358 SLW 0 setgray 0 360 40.34576 40.34576 0.0 0.0 0 true Ellipse closepath gsave 0.85358 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end - - -@endspecial 2255 1393 a + +@endspecial +2255 1400 a tx@Dict begin PutEnd end - 2255 1393 a 2255 1393 a + 2255 1400 a 2255 1400 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 2255 -1393 a 2255 1393 a + 2255 1400 a 2255 +1400 a tx@Dict begin { 155.63574 42.10986 } PutCoor PutBegin end - 2255 1393 a @beginspecial @setspecial + 2255 1400 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.85358 SLW 0 setgray 0 360 8.82031 8.82031 0.0 0.0 0 true Ellipse closepath gsave 0.85358 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end - - -@endspecial 2255 1393 a + +@endspecial +2255 1400 a tx@Dict begin PutEnd end - 2255 1393 a @beginspecial @setspecial + 2255 1400 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { BeginArrow 1. 1. scale false 0.25 1. 2.84526 2. 1. .setopacityalpha Arrow EndArrow moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.25 1. 2.84526 2. @@ -2677575,9 +2677584,9 @@ def /ArrowB { BeginArrow 1. 1. scale false 0.25 1. 2.84526 2. /lineto load def 0 setlinejoin false Line gsave 0.42676 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end - - -@endspecial @beginspecial @setspecial + +@endspecial +@beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.56903 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def [ 67.71721 2.84526 67.71721 82.79709 /Lineto /lineto load def 0 setlinejoin @@ -2677610,11 +2677619,11 @@ load def 0 setlinejoin false Line gsave 0.42676 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end @endspecial -2255 1393 a +2255 1400 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 2255 1393 a 2255 1393 a + 2255 1400 a 2255 1400 a tx@Dict begin { 67.71721 41.71152 } PutCoor PutBegin end - 2255 1393 a @beginspecial + 2255 1400 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.85358 SLW 0 setgray 0 360 1.02429 1.02429 0.0 0.0 0 true Ellipse @@ -2677622,36 +2677631,36 @@ tx@Dict begin { 67.71721 41.71152 } PutCoor PutBegin end 0.85358 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end -@endspecial 2255 1393 a +@endspecial 2255 1400 a tx@Dict begin PutEnd end - 2255 1393 a 2255 -1393 a + 2255 1400 a 2255 +1400 a tx@Dict begin { 31.5824 65.15645 } PutCoor PutBegin end - 2255 1393 a 2189 1415 a FC(M)2270 1427 y FB(T)2255 -1393 y + 2255 1400 a 2189 1422 a FC(M)2270 1434 y FB(T)2255 +1400 y tx@Dict begin PutEnd end - 2255 1393 a 2255 1393 a + 2255 1400 a 2255 1400 a tx@Dict begin { 55.19803 37.84196 } PutCoor PutBegin end - 2255 1393 a 2235 1411 -a FC(r)2255 1393 y + 2255 1400 a 2235 1418 +a FC(r)2255 1400 y tx@Dict begin PutEnd end - 2255 1393 a 2255 1393 a + 2255 1400 a 2255 1400 a tx@Dict begin { 116.65569 64.01836 } PutCoor PutBegin end - 2255 1393 -a 2158 1412 a FC(d)2201 1424 y FB(T)9 b Fz(\000)p FB(L)2255 -1393 y + 2255 1400 +a 2158 1419 a FC(d)2201 1431 y FB(T)9 b Fz(\000)p FB(L)2255 +1400 y tx@Dict begin PutEnd end - 2255 1393 a 2255 1393 a + 2255 1400 a 2255 1400 a tx@Dict begin { 155.63574 25.89188 } PutCoor PutBegin end - 2255 1393 a 2190 1415 -a FC(M)2271 1427 y FB(L)2255 1393 y + 2255 1400 a 2190 1422 +a FC(M)2271 1434 y FB(L)2255 1400 y tx@Dict begin PutEnd end - 2255 1393 a 2255 -1393 a + 2255 1400 a 2255 +1400 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end - 2255 1393 a 2255 1393 a + 2255 1400 a 2255 1400 a tx@Dict begin { 67.94482 68.34317 } PutCoor PutBegin end - 2255 1393 a @beginspecial + 2255 1400 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.42676 SLW 0 setgray /ArrowA { moveto } def /ArrowB { } def 0.0 @@ -2677667,15 +2677676,15 @@ cos exch sin moveto exch arc mtrx setmatrix gsave 0.42676 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end -@endspecial 2255 1393 a +@endspecial 2255 1400 a tx@Dict begin PutEnd end - 2255 1393 a 2255 -1393 a + 2255 1400 a 2255 +1400 a tx@Dict begin { 21.9085 33.00504 } PutCoor PutBegin end - 2255 1393 a 2197 1415 a FC(R)2260 1427 y FB(T)2255 -1393 y + 2255 1400 a 2197 1422 a FC(R)2260 1434 y FB(T)2255 +1400 y tx@Dict begin PutEnd end - 2255 1393 a @beginspecial @setspecial + 2255 1400 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.25 1. 2.84526 2. 1. .setopacityalpha Arrow EndArrow } def 0.42676 SLW 0 setgray /ArrowA { moveto } def /ArrowB @@ -2677693,21 +2677702,21 @@ end false Polygon gsave 0.85358 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end -@endspecial 2255 1393 a +@endspecial 2255 1400 a tx@Dict begin gsave STV CP T /ps@rot 0 def grestore end 2255 -1393 a 2255 1393 a +1400 a 2255 1400 a tx@Dict begin { 90.7638 41.82532 } PutCoor PutBegin end - 2255 1393 a @beginspecial @setspecial + 2255 1400 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { } def 0.85358 SLW 0 setgray 0 360 4.55243 4.55243 0.0 0.0 0 true Ellipse closepath gsave 0.85358 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end -@endspecial 2255 1393 a +@endspecial 2255 1400 a tx@Dict begin PutEnd end - 2255 1393 a @beginspecial @setspecial + 2255 1400 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { moveto } def /ArrowB { BeginArrow 1. 1. scale false 0.25 1. 2.84526 2. 1. .setopacityalpha Arrow EndArrow } def 0.85358 SLW 0 setgray /ArrowA { moveto } def /ArrowB @@ -2677739,24 +2677748,24 @@ end 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end -@endspecial 2255 1393 a +@endspecial 2255 1400 a tx@Dict begin { 106.98181 47.23134 } PutCoor PutBegin end - 2255 1393 a 2213 -1380 a FG(\000)-65 b(!)2223 1437 y FC(R)2255 1393 y + 2255 1400 a 2213 +1387 a FG(\000)-65 b(!)2223 1443 y FC(R)2255 1400 y tx@Dict begin PutEnd end 2255 -1393 a 2255 1393 a +1400 a 2255 1400 a tx@Dict begin { 126.04504 40.40268 } PutCoor PutBegin end - 2255 1393 a 2203 1374 a FG(\000)-44 -b(!)2203 1431 y FC(F)2256 1443 y FB(L)2255 1393 y + 2255 1400 a 2203 1380 a FG(\000)-44 +b(!)2203 1437 y FC(F)2256 1449 y FB(L)2255 1400 y tx@Dict begin PutEnd end 2255 -1393 a 2255 1393 a +1400 a 2255 1400 a tx@Dict begin { 75.96844 49.5075 } PutCoor PutBegin end - 2255 1393 a 2213 1380 a FG(\000)-65 -b(!)2223 1437 y FC(P)2255 1393 y + 2255 1400 a 2213 1387 a FG(\000)-65 +b(!)2223 1443 y FC(P)2255 1400 y tx@Dict begin PutEnd end - 2255 1393 a @beginspecial + 2255 1400 a @beginspecial @setspecial tx@Dict begin STP newpath /ArrowA { BeginArrow 1. 1. scale false 0.25 1. 2.84526 2. 1. .setopacityalpha Arrow EndArrow moveto } @@ -2677769,253 +2677778,252 @@ def /ArrowB { BeginArrow 1. 1. scale false 0.25 1. 2.84526 2. load def 0 setlinejoin false Line gsave 0.42676 SLW 0 setgray 1. .setopacityalpha 0 setlinejoin 0 setlinecap stroke grestore end -@endspecial 2255 1393 a +@endspecial 2255 1400 a tx@Dict begin { 83.93518 24.18471 } PutCoor PutBegin end - 2255 1393 a 2223 -1422 a FC(R)2255 1393 y + 2255 1400 a 2223 +1428 a FC(R)2255 1400 y tx@Dict begin PutEnd end - 2255 1393 a 0 TeXcolorgray 2034 -1645 a FX(le)28 b(calcul)g(de)g(la)g(vitesse)f(angulaire)g -FC(!)k FX(de)d(ce)g(dernier)f(est)2034 1745 y(le)h(suiv)-5 -b(an)n(t)27 b(:)2513 1930 y FC(F)35 b FL(=)23 b FC(M)2770 -1942 y FB(L)2838 1930 y FG(\001)18 b FC(!)2934 1896 y -FF(2)2989 1930 y FG(\001)h FC(R)2110 2106 y(G)g FG(\001)2245 -2050 y FC(M)2326 2062 y FB(T)2396 2050 y FG(\001)g FC(M)2519 -2062 y 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FC(\033)f FL(=)2055 4440 y Fr(v)2055 4487 y(u)2055 -4537 y(u)2055 4586 y(u)2055 4636 y(t)p 2143 4440 597 -4 v 2153 4462 a(P)2185 4597 y FB(i)2254 4524 y FC(n)2304 -4536 y FB(i)2350 4524 y FG(\001)19 b FL(\()p FC(L)2481 -4536 y FB(i)2527 4524 y FG(\000)f FC(\026)p FL(\))2692 -4500 y FF(2)p 2153 4619 577 4 v 2280 4633 a Fr(P)2312 -4768 y FB(i)2381 4695 y FC(n)2431 4707 y FB(i)2477 4695 -y FG(\000)g FL(1)2762 4638 y(=)2850 4506 y Fr(r)p 2933 -4506 274 4 v 2943 4582 a FL(3)2985 4558 y Fz(0)3008 4582 -y FL(777)p FC(:)p FL(1)p 2943 4619 254 4 v 3007 4695 -a(789)3230 4638 y(=)k(2)p FC(;)p FL(2)13 b(cm)p 0 TeXcolorgray -1802 4857 734 4 v 1891 4934 a FE(a.)35 b(Le)26 b(-1)f(apparaissan)n(t)h +(celle)1802 4324 y(d'\351cart)27 b(t)n(yp)r(e)2252 4294 +y FW(a)2316 4324 y FY(d\351\034nie)h(par)f(:)1894 4645 +y FC(\033)f FL(=)2055 4447 y Fr(v)2055 4493 y(u)2055 +4543 y(u)2055 4593 y(u)2055 4643 y(t)p 2143 4447 597 +4 v 2153 4469 a(P)2185 4604 y FB(i)2254 4531 y FC(n)2304 +4543 y FB(i)2350 4531 y FG(\001)19 b FL(\()p FC(L)2481 +4543 y FB(i)2527 4531 y FG(\000)f FC(\026)p FL(\))2692 +4507 y FF(2)p 2153 4626 577 4 v 2280 4639 a Fr(P)2312 +4775 y FB(i)2381 4702 y FC(n)2431 4714 y FB(i)2477 4702 +y FG(\000)g FL(1)2762 4645 y(=)2850 4513 y Fr(r)p 2933 +4513 274 4 v 2943 4588 a FL(3)2985 4564 y Fz(0)3008 4588 +y FL(777)p FC(:)p FL(1)p 2943 4626 254 4 v 3007 4702 +a(789)3230 4645 y(=)k(2)p FC(;)p FL(2)13 b(cm)p 0 TeXcolorgray +1802 4864 734 4 v 1891 4940 a FE(a.)35 b(Le)26 b(-1)f(apparaissan)n(t)h (au)g(d\351nominateur)h(de)f(la)f(fraction)h(de)1802 -5013 y(l'\351cart)k(t)n(yp)r(e)h(vien)n(t)h(d'une)e(estimation)h(de)g -(l'\351cart)g(t)n(yp)r(e)g(\(ou)g(v)l(a-)1802 5091 y(riance\))h(de)h +5019 y(l'\351cart)k(t)n(yp)r(e)h(vien)n(t)h(d'une)e(estimation)h(de)g +(l'\351cart)g(t)n(yp)r(e)g(\(ou)g(v)l(a-)1802 5098 y(riance\))h(de)h (la)f(p)r(opulation)h(des)f(mesures)g(bas\351e)h(sur)f(un)g(\351c)n -(han-)1802 5170 y(tillon)d(de)h(celle-ci.)f(P)n(our)g(bien)h(le)g -(comprendre,)f(il)g(faut)h(\351v)n(o)r(quer)1802 5249 +(han-)1802 5177 y(tillon)d(de)h(celle-ci.)f(P)n(our)g(bien)h(le)g +(comprendre,)f(il)g(faut)h(\351v)n(o)r(quer)1802 5256 y(le)d(calcul)g(des)h(probabilit\351s)f(et)h(la)f(notion)h(de)g(v)l -(ariable)f(al\351atoire,)1802 5328 y(ce)d(qui)g(d\351passe)h(le)f +(ariable)f(al\351atoire,)1802 5335 y(ce)d(qui)g(d\351passe)h(le)f (cadre)h(de)f(ce)h(do)r(cumen)n(t.)g(V)-6 b(ous)25 b(trouv)n(erez)g -(des)1802 5407 y(informations)e(sur)g(in)n(ternet.)p -0 TeXcolorgray 1698 5617 a FX(247)p eop end +(des)1802 5414 y(informations)e(sur)g(in)n(ternet.)p +0 TeXcolorgray 1698 5624 a FY(247)p eop end %%Page: 248 248 -TeXDict begin 248 247 bop 0 TeXcolorgray 116 262 a FQ(M.3.)55 +TeXDict begin 248 247 bop 0 TeXcolorgray 116 269 a FR(M.3.)55 b(INCER)-7 b(TITUDE)196 b(ANNEXE)28 b(M.)55 b(ORDRE)28 b(DE)f(GRANDEUR,)i(ERREUR)f(ET)f(INCER)-7 b(TITUDES)p -116 296 3753 4 v 0 TeXcolorgray 0 TeXcolorgray 390 589 +116 302 3753 4 v 0 TeXcolorgray 0 TeXcolorgray 390 596 a FK(Figure)29 b(M.1)g(\025)h FJ(Baguettes)g(d'une)d(ann\351)l(e)p -0 TeXcolorgray 117 1780 a +0 TeXcolorgray 117 1786 a currentpoint currentpoint translate 0.6 0.6 scale neg exch neg exch translate - 117 1780 a 447 1519 40 4 v -365 1544 a FL(0)p 2983 1519 V 447 1311 V 324 1336 a(20)p -2983 1311 V 447 1103 V 324 1128 a(40)p 2983 1103 V 447 -895 V 324 920 a(60)p 2983 895 V 447 687 V 324 712 a(80)p -2983 687 V 447 479 V 282 504 a(100)p 2983 479 V 447 271 -V 282 296 a(120)p 2983 271 V 447 63 V 282 88 a(140)p -2983 63 V 447 1519 4 40 v 405 1626 a(36)p 447 103 V 877 -1519 V 346 w(38)p 877 103 V 1305 1519 V 344 w(40)p 1305 -103 V 1735 1519 V 346 w(42)p 1735 103 V 2165 1519 V 346 -w(44)p 2165 103 V 2593 1519 V 344 w(46)p 2593 103 V 3023 -1519 V 346 w(48)p 3023 103 V 447 1519 4 1456 v 447 1519 -2576 4 v 3023 1519 4 1456 v 447 63 2576 4 v 1177 478 + 117 1786 a 447 1526 40 4 v +365 1550 a FL(0)p 2983 1526 V 447 1318 V 324 1342 a(20)p +2983 1318 V 447 1110 V 324 1134 a(40)p 2983 1110 V 447 +902 V 324 926 a(60)p 2983 902 V 447 694 V 324 718 a(80)p +2983 694 V 447 486 V 282 510 a(100)p 2983 486 V 447 278 +V 282 302 a(120)p 2983 278 V 447 70 V 282 94 a(140)p +2983 70 V 447 1526 4 40 v 405 1632 a(36)p 447 110 V 877 +1526 V 346 w(38)p 877 110 V 1305 1526 V 344 w(40)p 1305 +110 V 1735 1526 V 346 w(42)p 1735 110 V 2165 1526 V 346 +w(44)p 2165 110 V 2593 1526 V 344 w(46)p 2593 110 V 3023 +1526 V 346 w(48)p 3023 110 V 447 1526 4 1456 v 447 1526 +2576 4 v 3023 1526 4 1456 v 447 70 2576 4 v 1177 484 a gsave currentpoint currentpoint translate 90 neg rotate neg exch neg exch translate - 1177 478 a 30 x FX(\311cart)f(t)n(yp)r(e)1177 478 y + 1177 484 a 30 x FY(\311cart)f(t)n(yp)r(e)1177 484 y currentpoint grestore moveto -1177 478 a 2251 82 a +1177 484 a 2251 88 a gsave currentpoint currentpoint translate -90 neg rotate neg exch neg exch translate - 2251 82 a 30 x FX(\311cart)g(t)n(yp)r(e)2251 -82 y + 2251 88 a 30 x FY(\311cart)g(t)n(yp)r(e)2251 +88 y currentpoint grestore moveto - 2251 82 a 1777 686 a + 2251 88 a 1777 692 a gsave currentpoint currentpoint translate -90 neg rotate neg exch neg exch translate - 1777 686 a 20 x FX(Mo)n(y)n(enne)1777 -686 y + 1777 692 a 21 x FY(Mo)n(y)n(enne)1777 +692 y currentpoint grestore moveto - 1777 686 a 1239 1518 4 1249 v 1241 1518 a Fb(?)p -2183 1518 V 861 w(?)p 1711 1518 V -555 w(?)205 790 y + 1777 692 a 1239 1524 4 1249 v 1241 1524 a Fb(?)p +2183 1524 V 861 w(?)p 1711 1524 V -555 w(?)205 796 y gsave currentpoint currentpoint translate 90 neg rotate neg exch neg exch translate -205 790 a -181 810 a FX(Nom)n(bre)h(de)h(baguettes)205 -790 y +205 796 a -181 817 a FY(Nom)n(bre)h(de)h(baguettes)205 +796 y currentpoint grestore moveto - 205 790 a 1150 1742 a FX(Longueur)e(des)i(baguettes)f(\(en)h -(cm\))p 769 1519 4 552 v 769 967 214 4 v 983 1519 4 552 -v 769 1519 214 4 v 983 1519 4 749 v 983 771 216 4 v 1199 -1519 4 749 v 983 1519 216 4 v 1199 1519 4 989 v 1199 -531 214 4 v 1413 1519 4 989 v 1199 1519 214 4 v 1413 -1519 4 1258 v 1413 261 214 4 v 1627 1519 4 1258 v 1413 -1519 214 4 v 1627 1519 4 1352 v 1627 167 216 4 v 1843 -1519 4 1352 v 1627 1519 216 4 v 1843 1519 4 1229 v 1843 -291 214 4 v 2057 1519 4 1229 v 1843 1519 214 4 v 2057 -1519 4 936 v 2057 583 214 4 v 2271 1519 4 936 v 2057 -1519 214 4 v 2271 1519 4 696 v 2271 823 216 4 v 2487 -1519 4 696 v 2271 1519 216 4 v 2487 1519 4 458 v 2487 -1061 214 4 v 2701 1519 4 458 v 2487 1519 214 4 v 447 -1519 4 1456 v 447 1519 2576 4 v 3023 1519 4 1456 v 447 -63 2576 4 v 117 1780 a + 205 796 a 1150 1749 a FY(Longueur)e(des)i(baguettes)f(\(en)h +(cm\))p 769 1526 4 552 v 769 974 214 4 v 983 1526 4 552 +v 769 1526 214 4 v 983 1526 4 749 v 983 778 216 4 v 1199 +1526 4 749 v 983 1526 216 4 v 1199 1526 4 989 v 1199 +538 214 4 v 1413 1526 4 989 v 1199 1526 214 4 v 1413 +1526 4 1258 v 1413 268 214 4 v 1627 1526 4 1258 v 1413 +1526 214 4 v 1627 1526 4 1352 v 1627 174 216 4 v 1843 +1526 4 1352 v 1627 1526 216 4 v 1843 1526 4 1229 v 1843 +298 214 4 v 2057 1526 4 1229 v 1843 1526 214 4 v 2057 +1526 4 936 v 2057 590 214 4 v 2271 1526 4 936 v 2057 +1526 214 4 v 2271 1526 4 696 v 2271 830 216 4 v 2487 +1526 4 696 v 2271 1526 216 4 v 2487 1526 4 458 v 2487 +1068 214 4 v 2701 1526 4 458 v 2487 1526 214 4 v 447 +1526 4 1456 v 447 1526 2576 4 v 3023 1526 4 1456 v 447 +70 2576 4 v 117 1786 a currentpoint currentpoint translate 1 0.6 div 1 0.6 div scale neg exch neg exch translate - 117 1780 a 0 TeXcolorgray 116 -2146 a FX(Il)22 b(s'agit)f(de)i(la)e(mo)n(y)n(enne)g(des)h(\351carts)f -(quadratiques,)f(soit)116 2245 y(de)40 b(la)f(racine)f(de)h(la)g(mo)n -(y)n(enne)g(des)g(\351carts)f(au)h(carr\351s.)116 2345 + 117 1786 a 0 TeXcolorgray 116 +2152 a FY(Il)22 b(s'agit)f(de)i(la)e(mo)n(y)n(enne)g(des)h(\351carts)f +(quadratiques,)f(soit)116 2252 y(de)40 b(la)f(racine)f(de)h(la)g(mo)n +(y)n(enne)g(des)g(\351carts)f(au)h(carr\351s.)116 2352 y(L'\351l\351v)-5 b(ation)24 b(au)g(carr\351)f(p)r(ermet)h(de)h(ne)f -(pas)g(tenir)g(compte)116 2445 y(du)k(signe)f(des)h(\351carts.)199 -2553 y(On)21 b(p)r(eut)g(alors)e(a\036rmer)h(qu'une)g(forte)h(prop)r -(ortion)e(de)116 2653 y(la)31 b(longueur)g(L)g(des)g(baguettes)g(se)h +(pas)g(tenir)g(compte)116 2451 y(du)k(signe)f(des)h(\351carts.)199 +2560 y(On)21 b(p)r(eut)g(alors)e(a\036rmer)h(qu'une)g(forte)h(prop)r +(ortion)e(de)116 2659 y(la)31 b(longueur)g(L)g(des)g(baguettes)g(se)h (trouv)n(e)e(en)n(tre)h FC(\026)21 b FG(\000)g FC(\033)116 -2752 y FX(et)28 b FC(\026)19 b FL(+)f FC(\033)s FX(,)28 -b(soit)f(en)n(tre)g FL(39)p FC(;)o FL(7)g FX(et)h FL(44)p -FC(;)o FL(1)14 b(cm)p FX(.)199 2995 y(P)n(our)28 b(aller)h(plus)h +2759 y FY(et)28 b FC(\026)19 b FL(+)f FC(\033)s FY(,)28 +b(soit)f(en)n(tre)g FL(39)p FC(;)o FL(7)g FY(et)h FL(44)p +FC(;)o FL(1)14 b(cm)p FY(.)199 3002 y(P)n(our)28 b(aller)h(plus)h (loin,)g(il)g(faut)g(v)n(oir)e(l'ensem)n(ble)i(com-)116 -3095 y(plet)44 b(des)f(mesures)g(qui)h(p)r(ourraien)n(t)e(\352tre)h -(faites)h(dans)116 3194 y(le)49 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y(troisi\350me)g(loi,)g(171)-116 -4710 y(Kepler,)g(48,)f(49)50 4809 y(Johanes,)g(49)50 -4909 y(premi\350re)h(loi,)g(48)50 5008 y(seconde)g(loi,)g(48)50 -5108 y(troisi\350me)g(loi,)g(48)-116 5208 y(kilo)n(w)n(attheure,)f(103) --116 5307 y(kin\352ma,)h(37)-116 5407 y(k)-7 b(Wh,)28 -b(103)p 0 TeXcolorgray 0 TeXcolorgray 1802 525 a FW(L)p -1886 500 V 1802 654 a FX(latitude,)g(166)1802 754 y(latitude,)g(22)1802 -855 y(Leibnitz,)g(59)1802 956 y(L\351onides,)f(26)1802 -1056 y(lepton,)g(35)1802 1157 y(liaison,)f(111)1802 1257 -y(liaison)1968 1358 y(in)n(teratomique,)g(70)1802 1458 -y(licence)1968 1559 y(GFDL,)i(2)1802 1660 y(lieu)f(naturel)h(de)f(rep)r -(os,)g(52)1802 1760 y(ligne)g(des)g(n\367uds,)h(28)1802 -1861 y(limite)1968 1961 y(de)f(la)h(deuxi\350me)f(loi,)h(61)1802 -2062 y(limite)g(de)g(Betz,)f(107,)f(205)1802 2162 y(limite)i(de)g(Ro)r -(c)n(he,)f(199)1802 2263 y(liqu\351faction,)g(139)1802 -2364 y(lithium,)h(33)1802 2464 y(Lo)r(cal)e(Standard)h(of)h(Rest,)g -(184)1802 2565 y(loi)1968 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d'une page (par défaut 1) diff --git a/CoursMecaniqueOSDF.tex.bak b/CoursMecaniqueOSDF.tex.bak index 29acabd..3368ee9 100644 --- a/CoursMecaniqueOSDF.tex.bak +++ b/CoursMecaniqueOSDF.tex.bak @@ -22,7 +22,7 @@ \newtheorem{exosc}{Exercice OS} \newenvironment{exos}{\begin{exosc}\normalfont}{\end{exosc}} -\setlength{\headheight}{12.2pt} % spécifie la hauteur de l'entête pour qu'elle ne couvre pas le titre +\setlength{\headheight}{13pt} % spécifie la hauteur de l'entête pour qu'elle ne couvre pas le titre \setcounter{topnumber}{3} % nombre maximal de flottant en haut d'une page (par défaut 2) \setcounter{bottomnumber}{2} % nombre maximal de flottant en bas d'une page (par défaut 1) diff --git a/Dynamique/Dynamique.tex b/Dynamique/Dynamique.tex index 3735fd1..315ca6b 100644 --- a/Dynamique/Dynamique.tex +++ b/Dynamique/Dynamique.tex @@ -664,8 +664,10 @@ Le résultat correspond au graphe du champ vectoriel\index{maree@marée!champ ve On peut montrer sur la base de la deuxième loi de Newton et de la loi de la gravitation universelle (voir \cite[p. 416]{GC88}) que le vecteur \(\overrightarrow F_{mar\acute ee}\) correspondant à la force de marée s'exerçant sur une masse \(m\) d'eau située au point de coordonnées \((x,y)\) d'un référentiel cartésien lié au centre de la Terre (dans le plan d'un méridien) vaut~: \begin{equation}\label{eqmareevect} -\overrightarrow F_{mar\acute ee}=G\cdot \frac{M_L\cdot m}{d_{T-L}^3}\cdot {2\cdot x \choose -y} +\overrightarrow F_{mar\acute ee}=G\cdot \frac{M_L\cdot m}{d_{T-L}^3}\cdot \binom{2\cdot x}{-y} \end{equation} +% Attention, dans l'équation ci-dessus, il ne faut pas remplacer \binom{2\cdot x}{-y} par 2\cdot x \choose -y +% car cela produit un warning de foreign command \atopwithdemims. Où \(M_L\) est la masse de la Lune et \(d_{T-L}\) la distance Terre-Lune. L'expression de la force \(\overrightarrow F_{mar\acute ee}\) donnée par \ref{eqmareevect} trouve sa représentation graphique dans le champ de vecteurs représenté à la figure \ref{mareechampforce}. On y voit l'attraction de la Lune sur les masses d'eau qui se trouvent de son côté et, de l'autre côté, l'effet de la force d'inertie (pseudo-force centrifuge). Deux marées hautes se trouvent donc aux antipodes l'une de l'autre. La Terre tournant sur elle-même bien plus rapidement que la Lune tourne autour d'elle, l'existence de deux marées par jour trouve donc ici une explication à travers l'application de la deuxième loi de Newton. diff --git a/Dynamique/Dynamique.tex.bak b/Dynamique/Dynamique.tex.bak index 3735fd1..64a0c88 100644 --- a/Dynamique/Dynamique.tex.bak +++ b/Dynamique/Dynamique.tex.bak @@ -666,6 +666,8 @@ On peut montrer sur la base de la deuxième loi de Newton et de la loi de la gra \begin{equation}\label{eqmareevect} \overrightarrow F_{mar\acute ee}=G\cdot \frac{M_L\cdot m}{d_{T-L}^3}\cdot {2\cdot x \choose -y} \end{equation} +% Attention, dans l'équation ci-dessus, il ne faut pas remplacer \binom{x}{-y} par x \choose -y +% car cela produit un warning Où \(M_L\) est la masse de la Lune et \(d_{T-L}\) la distance Terre-Lune. L'expression de la force \(\overrightarrow F_{mar\acute ee}\) donnée par \ref{eqmareevect} trouve sa représentation graphique dans le champ de vecteurs représenté à la figure \ref{mareechampforce}. On y voit l'attraction de la Lune sur les masses d'eau qui se trouvent de son côté et, de l'autre côté, l'effet de la force d'inertie (pseudo-force centrifuge). Deux marées hautes se trouvent donc aux antipodes l'une de l'autre. La Terre tournant sur elle-même bien plus rapidement que la Lune tourne autour d'elle, l'existence de deux marées par jour trouve donc ici une explication à travers l'application de la deuxième loi de Newton. diff --git a/EnergieOS/EnergieOS.aux b/EnergieOS/EnergieOS.aux index d106e2e..8c50b71 100644 --- a/EnergieOS/EnergieOS.aux +++ b/EnergieOS/EnergieOS.aux @@ -27,7 +27,7 @@ \newlabel{enpotdef}{{8.2}{122}} \newlabel{\IeC {\'e}nergie cin\IeC {\'e}tique}{{8.3.3}{122}} \@writefile{toc}{\contentsline {subsection}{\numberline {8.3.3}\IeC {\'E}nergie cin\IeC {\'e}tique}{122}} -\newlabel{encindef}{{8.3}{122}} +\newlabel{eqencindef}{{8.3}{122}} \@writefile{toc}{\contentsline {subsection}{\numberline {8.3.4}\IeC {\'E}nergie m\IeC {\'e}canique}{122}} \newlabel{enmec}{{8.4}{122}} \@writefile{toc}{\contentsline {subsection}{\numberline {8.3.5}Exemple}{122}} diff --git a/EnergieOS/EnergieOS.tex b/EnergieOS/EnergieOS.tex index ece5931..9340bba 100644 --- a/EnergieOS/EnergieOS.tex +++ b/EnergieOS/EnergieOS.tex @@ -162,7 +162,7 @@ On remarque que ce travail se compose de deux parties. Chacune d'elle ne dépend l'objet. On peut donc appeler chacun de ces termes "énergie cinétique\index{energie@énergie!cinétique}" pour la vitesse considérée. Ainsi, le travail se traduit par une différence d'énergie cinétique. Et sa définition prend la forme suivante~: -\begin{equation}\label{encindef} +\begin{equation}\label{eqencindef} \fbox{\(\displaystyle E_{cin}=\frac{1}{2}\cdot m\cdot v^{2}\)} \end{equation} diff --git a/EnergieOS/EnergieOS.tex.bak b/EnergieOS/EnergieOS.tex.bak index ece5931..9340bba 100644 --- a/EnergieOS/EnergieOS.tex.bak +++ b/EnergieOS/EnergieOS.tex.bak @@ -162,7 +162,7 @@ On remarque que ce travail se compose de deux parties. Chacune d'elle ne dépend l'objet. On peut donc appeler chacun de ces termes "énergie cinétique\index{energie@énergie!cinétique}" pour la vitesse considérée. Ainsi, le travail se traduit par une différence d'énergie cinétique. 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copyright de l'image. Remerciements à la NASA.}}} -\includegraphics[width=7cm]{UniversProfond.eps} +\includegraphics[width=7cm]{universprofond.eps} \end{figure} La plus grande structure connue est l'univers. La taille de l'univers observable est estimée à environ \SI{43}{\mega\lightyear}, soit \num{43} milliards d'années lumière. Sa composition est analogue à une sorte de gaz dont les particules seraient réparties uniformément dans le volume qui le contient. Sauf que de contenant il n'y a pas et que les particules sont des super-amas\index{super@super!amas} de galaxies dont la taille ne dépasse pas \numrange{200}{300} millions d'années lumière. Leur nombre dans l'univers est estimé à \num{10} millions. @@ -325,7 +325,7 @@ Puis, comme précédemment, les éléments plus lourds sont aussi formés par d \multicolumn{5}{|c|}{\includegraphics[width=13.635cm]{StructuresAtomiques.eps}}\\ \multicolumn{1}{|c}{Atome} & \multicolumn{1}{c}{Noyau} & \multicolumn{1}{c}{Nucléon} & \multicolumn{1}{c}{Quarks} & \multicolumn{1}{c|}{Cordes}\\ \hhline{|=#==#==|} - \multirow{2}{2.6cm}[-3mm]{\textbf{\textsc{Fermions}}\\Ce sont les particules qui constituent la matière ordinaire} & \multicolumn{2}{>{\columncolor[gray]{0.8}}c||}{\textbf{\textsc{Leptons}}} & \multicolumn{2}{>{\columncolor[gray]{0.8}}c|}{\textbf{\textsc{Quarks}}}\\ + \multirow{2}{2.6cm}[-3mm]{\textsc{Fermions}\\Ce sont les particules qui constituent la matière ordinaire} & \multicolumn{2}{>{\columncolor[gray]{0.8}}c||}{\textsc{Leptons}} & \multicolumn{2}{>{\columncolor[gray]{0.8}}c|}{\textsc{Quarks}}\\ \cline{2-5} & \color{black}\textsc{Électron (\(e^-\))} & \color{black}\textsc{Neutrino (\(\nu_e\)) électronique} & \color{black}\textsc{Bas (d)} & \color{black}\textsc{Haut (u)}\\ & Il détermine les propriétés chimiques. Chargé négativement. & Très faible interaction avec la matière. Sans charge. & 1x dans le proton, 2x dans le neutron. & 2x dans le proton, 1x dans le neutron\\ @@ -337,7 +337,7 @@ Puis, comme précédemment, les éléments plus lourds sont aussi formés par d & Un muon plus massif & Un autre neutrino & Un étrange plus massif & Un haut encore plus massif\\ \hhline{|=#==#==|} %\hline\hline - \multirow{2}{2.6cm}[-3mm]{\textbf{\textsc{Bosons}}\\Particules représentant les forces élémentaires} & \color{black}\textsc{Photon (\(\gamma\))} & \color{black}\textsc{Gluon (g)} & \color{black}\textsc{Bosons (W Z) intermédiaires} & \color{black}\textsc{Graviton} \\ + \multirow{2}{2.6cm}[-3mm]{\textsc{Bosons}\\Particules représentant les forces élémentaires} & \color{black}\textsc{Photon (\(\gamma\))} & \color{black}\textsc{Gluon (g)} & \color{black}\textsc{Bosons (W Z) intermédiaires} & \color{black}\textsc{Graviton} \\ & Grain de lumière ; vecteur de la force électromagnétique & Cohésion du noyau et des nucléons ; vecteur de la force forte & Radioactivité ; vecteur de la force faible & Poids~: vecteur de la force de gravitation \\ \hline \end{tabular} diff --git a/Introduction/Introduction.tex.bak b/Introduction/Introduction.tex.bak index 1bad9df..fe80d5f 100644 --- a/Introduction/Introduction.tex.bak +++ b/Introduction/Introduction.tex.bak @@ -18,7 +18,7 @@ Qui dit périodes dit donc mouvement et, plus précisément, mouvement répétit \begin{figure}[t] \centering \caption[L'univers profond]{L'univers profond\label{universprofond} \par \scriptsize{Image du télescope spatial Hubble\endnote{Voir le site du télescope spatial Hubble~: \url=http://hubble.nasa.gov/multimedia/astronomy.php= notamment pour le copyright de l'image. Remerciements à la NASA.}}} -\includegraphics[width=7cm]{UniversProfond.eps} +\includegraphics[width=7cm]{universprofond.eps} \end{figure} La plus grande structure connue est l'univers. La taille de l'univers observable est estimée à environ \SI{43}{\mega\lightyear}, soit \num{43} milliards d'années lumière. Sa composition est analogue à une sorte de gaz dont les particules seraient réparties uniformément dans le volume qui le contient. Sauf que de contenant il n'y a pas et que les particules sont des super-amas\index{super@super!amas} de galaxies dont la taille ne dépasse pas \numrange{200}{300} millions d'années lumière. Leur nombre dans l'univers est estimé à \num{10} millions. @@ -101,7 +101,7 @@ Les mouvements locaux des galaxies entre elles donnent lieu à des \og chocs\fg{ Les galaxies sont donc composées d'étoiles. Plus de 100 milliards pour la Voie Lactée\index{Voie@Voie!Lactée}, la galaxie\index{galaxie@galaxie} dans laquelle nous nous trouvons. Environ \num{30000} milliards de milliards pour l'univers en entier. Ces étoiles sont plus ou moins grandes. Les plus grosses ont une masse d'une centaine de fois la masse de notre étoile, celle autour de laquelle nous nous déplaçons qui se nomme le Soleil\index{Soleil@Soleil}. C'est une étoile de taille petite à moyenne. Le destin de notre étoile (voir figure \ref{evosol}) est d'enfler considérablement pour devenir une géante rouge\index{geante@géante!rouge} et ensuite de s'effondrer en laissant ses couches extérieures en périphérie et en concentrant ses couches intérieures en une naine blanche\index{naine@naine!blanche}, puis une naine noire\index{naine@naine!noire}. Le résultat présente l'allure spectaculaire (voir figure \ref{planetaire}) de la \og nébuleuse planétaire\index{nebuleuse@nébuleuse!planétaire}\fg{}. -Pour les étoiles bien plus grosses que le Soleil, dont la masse m est telle que \(1,4\cdot m_{soleil}5\cdot m_{soleil}\), l'évolution est la même que précédemment jusqu'à la supernovae. Après les restes sont si denses qu'il se crée un trou noir\index{trou@trou!noir}. +Pour les étoiles bien plus grosses que le Soleil, dont la masse m est telle que \(1,4\cdot m_{soleil}5\cdot m_{soleil}\), l'évolution est la même que précédemment jusqu'à la supernov\ae. Après les restes sont si denses qu'il se crée un trou noir\index{trou@trou!noir}. Le destin et l'évolution des étoiles est donc une chose complexe, d'autant plus que les différents éléments répertoriés dans le tableau périodique\index{tableau@tableau!périodique} de Mendeleïev\index{Mendeleiev@Mendeleïev} ont été créés au sein des étoiles. Si la physique de ces constructions dépasse le propos de ce cours, il en sera dit quelques mots au paragraphe \ref{subsectionsubatomique}. @@ -127,7 +127,7 @@ La première exoplanète découverte l'a été en 1995 par l'observatoire de Gen En 2005, soit dix ans après, la première image d'une exoplanète (voir figure \ref{2M1207}) a été réalisée par le VLT (Very Large Telescope). Il s'agit de la naine brune 2M1207, une étoile avortée faiblement lumineuse, autour de laquelle tourne une exoplanète d'environ cinq fois la masse de Jupiter, à une distance deux fois plus importante que celle de Neptune autour de notre étoile, le Soleil. -Le 13 novembre 2008, une seconde planète a été observée en lumière visible dans la constellation australe du Poisson autour de l'étoile Fomalhaut. C'est une planète d'environ trois fois la masse de jupiter et elle se trouve à environ dix fois la distance entre le soleil et saturne de son étoile Fomalhaut. +Le 13 novembre 2008, une seconde planète a été observée en lumière visible dans la constellation australe du Poisson autour de l'étoile Fomalhaut. C'est une planète d'environ trois fois la masse de Jupiter et elle se trouve à environ dix fois la distance entre le soleil et saturne de son étoile Fomalhaut. \smallskip Autour de notre étoile, le Soleil\index{Soleil@Soleil} tournent huit planètes (MVTMJSUN \dots) et d'autres corps plus petits parmis lesquels se trouvent des planètes dites naines. Cérès (dans la ceinture d'astéroïde\index{ceinture@ceinture!d'astéroïde}), Éris (un tout petit peu plus grande que Pluton et qui fait partie de la ceinture de Kuiper\index{ceinture@ceinture!de Kuiper}, au-delà de l'orbite de Neptune) et Pluton en font partie. La figure \ref{systemesolaire} présente le système solaire sans respecter les ordres de grandeurs. @@ -158,7 +158,7 @@ En passant elles laissent sur leur orbite\index{orbite@orbite} une traînée de \includegraphics[width=6cm]{Billet10FrsComete.eps} \end{figure} -Ce sont ces traînées de poussières que la Terre rencontre sur son orbite\index{orbite@orbite} en donnant lieu aux fameuses pluies d'étoiles filantes\index{etoile@étoile!filante} (voir la figure \ref{Leonides} qui montre une observation des Léonides. \og Les léonides sont causées par le passage d'une comète, la comète Tempel-Tuttle qui a une période de 33 ans. À chaque passage, la comète laisse une trainée de débris rocheux qui forme un essaim que la Terre traverse tous les ans aux environs du mois de novembre. Le radian\index{radian@radian} étant situé dans la constellation du Lion, on appelle donc les météores\index{meteor@météore} « léonides »\index{Leonides@Léonides}.\fg{}\endnote{Voir \url=http://fr.wikipedia.org/wiki/Leonides=}). Il s'agit de petites météorites qui se consument en entrant dans l'atmosphère en produisant une trace lumineuse, \emph{les étoiles filantes}. Elles ne sont donc ni des étoiles, ni des planètes ou des comètes\index{comete@comète}. Dans le cas des pluies d'étoiles filantes crées par la rencontre de la terre avec les poussières de l'orbite d'une comète, elles semblent provenir d'un point bien précis dans le ciel, comme la neige qui tombe sur le pare-brise d'une voiture semble venir d'un point situé dans la direction du déplacement de la voiture. Ce point se nomme le radian\index{radian@radian}. +Ce sont ces traînées de poussières que la Terre rencontre sur son orbite\index{orbite@orbite} en donnant lieu aux fameuses pluies d'étoiles filantes\index{etoile@étoile!filante} (voir la figure \ref{Leonides} qui montre une observation des Léonides. \og Les léonides sont causées par le passage d'une comète, la comète Tempel-Tuttle qui a une période de 33 ans. À chaque passage, la comète laisse une trainée de débris rocheux qui forme un essaim que la Terre traverse tous les ans aux environs du mois de novembre. Le radian\index{radian@radian} étant situé dans la constellation du Lion, on appelle donc les météores\index{meteor@météore} « Léonides »\index{Leonides@Léonides}.\fg{}\endnote{Voir \url=http://fr.wikipedia.org/wiki/Leonides=}). Il s'agit de petites météorites qui se consument en entrant dans l'atmosphère en produisant une trace lumineuse, \emph{les étoiles filantes}. Elles ne sont donc ni des étoiles, ni des planètes ou des comètes\index{comete@comète}. Dans le cas des pluies d'étoiles filantes crées par la rencontre de la terre avec les poussières de l'orbite d'une comète, elles semblent provenir d'un point bien précis dans le ciel, comme la neige qui tombe sur le pare-brise d'une voiture semble venir d'un point situé dans la direction du déplacement de la voiture. Ce point se nomme le radian\index{radian@radian}. \begin{figure}[h!t] \centering @@ -236,7 +236,7 @@ La question se pose alors de la différence entre éclipse de Soleil\index{eclip \includegraphics[width=6cm]{Orbite-lune-soleil.eps} \end{figure} -Comme ces plans ne coïncident pas, tant que la Lune n'est pas dans le plan de l'Écliptique\index{ecliptique@écliptique}, c'est-à-dire sur la ligne des n\oe uds\index{ligne@ligne des n\oe uds} présentée dans la figure \ref{Orbite-lune-soleil}, il ne peut y avoir d'éclipse. Or, la Lune coupe le plan de l'Écliptique deux fois par mois. Mais encore faut-il que la ligne des noeuds soit alors alignée avec le Soleil. Il faut dire aussi que le plan de rotation de la Lune tourne sur lui-même entraînant la ligne des noeuds avec lui. Sa période de rotation est de \SI{18,61}{\year}. Ainsi, la ligne des noeuds tourne sur elle-même d'un angle de \(\sim\) \ang{19,6} par an. Finalement donc, on peut calculer que l'alignement de la ligne des noeuds et du Soleil se fait tout les \SI{173}{\day} environ\endnote{Voir aux sujet des éclipses l'excellent site de l'institut de mécanique céleste~: http://www.imcce.fr/}. Cette durée constitue ce qu'on appelle une saison d'éclipses\index{saison@saison!d'éclipse}. +Comme ces plans ne coïncident pas, tant que la Lune n'est pas dans le plan de l'Écliptique\index{ecliptique@écliptique}, c'est-à-dire sur la ligne des n\oe uds\index{ligne@ligne des n\oe uds} présentée dans la figure \ref{Orbite-lune-soleil}, il ne peut y avoir d'éclipse. Or, la Lune coupe le plan de l'Écliptique deux fois par mois. Mais encore faut-il que la ligne des n\oe uds soit alors alignée avec le Soleil. Il faut dire aussi que le plan de rotation de la Lune tourne sur lui-même entraînant la ligne des n\oe uds avec lui. Sa période de rotation est de \SI{18,61}{\year}. Ainsi, la ligne des n\oe uds tourne sur elle-même d'un angle de \(\sim\) \ang{19,6} par an. Finalement donc, on peut calculer que l'alignement de la ligne des n\oe uds et du Soleil se fait tout les \SI{173}{\day} environ\endnote{Voir aux sujet des éclipses l'excellent site de l'institut de mécanique céleste~: http://www.imcce.fr/}. Cette durée constitue ce qu'on appelle une saison d'éclipses\index{saison@saison!d'éclipse}. Mais, tout cela est encore compliqué, pour les éclipses de Soleil notamment, par le fait que l'ombre de la Lune ne couvre pas la totalité de la Terre. Si bien qu'en un lieu donné de sa surface, au moment où des éclipses de Soleil et de Lune sont possibles, il se peut que seule une éclipse de Lune soit visible, alors que celle de Soleil ne l'est pas à cet endroit. @@ -325,7 +325,7 @@ Puis, comme précédemment, les éléments plus lourds sont aussi formés par d \multicolumn{5}{|c|}{\includegraphics[width=13.635cm]{StructuresAtomiques.eps}}\\ \multicolumn{1}{|c}{Atome} & \multicolumn{1}{c}{Noyau} & \multicolumn{1}{c}{Nucléon} & \multicolumn{1}{c}{Quarks} & \multicolumn{1}{c|}{Cordes}\\ \hhline{|=#==#==|} - \multirow{2}{2.6cm}[-3mm]{\textbf{\textsc{Fermions}}\\Ce sont les particules qui constituent la matière ordinaire} & \multicolumn{2}{>{\columncolor[gray]{0.8}}c||}{\textbf{\textsc{Leptons}}} & \multicolumn{2}{>{\columncolor[gray]{0.8}}c|}{\textbf{\textsc{Quarks}}}\\ + \multirow{2}{2.6cm}[-3mm]{\textsc{Fermions}\\Ce sont les particules qui constituent la matière ordinaire} & \multicolumn{2}{>{\columncolor[gray]{0.8}}c||}{\textsc{Leptons}} & \multicolumn{2}{>{\columncolor[gray]{0.8}}c|}{\textsc{Quarks}}\\ \cline{2-5} & \color{black}\textsc{Électron (\(e^-\))} & \color{black}\textsc{Neutrino (\(\nu_e\)) électronique} & \color{black}\textsc{Bas (d)} & \color{black}\textsc{Haut (u)}\\ & Il détermine les propriétés chimiques. Chargé négativement. & Très faible interaction avec la matière. Sans charge. & 1x dans le proton, 2x dans le neutron. & 2x dans le proton, 1x dans le neutron\\ @@ -337,7 +337,7 @@ Puis, comme précédemment, les éléments plus lourds sont aussi formés par d & Un muon plus massif & Un autre neutrino & Un étrange plus massif & Un haut encore plus massif\\ \hhline{|=#==#==|} %\hline\hline - \multirow{2}{2.6cm}[-3mm]{\textbf{\textsc{Bosons}}\\Particules représentant les forces élémentaires} & \color{black}\textsc{Photon (\(\gamma\))} & \color{black}\textsc{Gluon (g)} & \color{black}\textsc{Bosons (W Z) intermédiaires} & \color{black}\textsc{Graviton} \\ + \multirow{2}{2.6cm}[-3mm]{\textsc{Bosons}\\Particules représentant les forces élémentaires} & \color{black}\textsc{Photon (\(\gamma\))} & \color{black}\textsc{Gluon (g)} & \color{black}\textsc{Bosons (W Z) intermédiaires} & \color{black}\textsc{Graviton} \\ & Grain de lumière ; vecteur de la force électromagnétique & Cohésion du noyau et des nucléons ; vecteur de la force forte & Radioactivité ; vecteur de la force faible & Poids~: vecteur de la force de gravitation \\ \hline \end{tabular} diff --git a/MecaniqueDim/MecaniqueDim.aux b/MecaniqueDim/MecaniqueDim.aux index c11ee3d..27b7bd1 100644 --- a/MecaniqueDim/MecaniqueDim.aux +++ b/MecaniqueDim/MecaniqueDim.aux @@ -50,7 +50,7 @@ \@writefile{toc}{\contentsline {subsubsection}{Cin\IeC {\'e}matique}{80}} \@writefile{toc}{\contentsline {subsubsection}{Relation importante}{81}} \@writefile{lof}{\contentsline {figure}{\numberline {4.7}{\ignorespaces Mouvement circulaire uniforme\relax }}{81}} -\newlabel{MCU}{{4.7}{81}} +\newlabel{dimMCU}{{4.7}{81}} \@writefile{toc}{\contentsline {subsubsection}{Dynamique}{81}} \@writefile{toc}{\contentsline {subsubsection}{Virages inclin\IeC {\'e}s}{81}} \@writefile{toc}{\contentsline {paragraph}{Vitesses minimales}{82}} @@ -63,7 +63,7 @@ \newlabel{viragesvmaxfinie}{{4.10}{83}} \citation{GC88} \@writefile{toc}{\contentsline {subsection}{\numberline {4.4.5}Satellite en orbite g\IeC {\'e}ostationnaire}{84}} -\newlabel{geostat}{{4.4.5}{84}} +\newlabel{dimgeostat}{{4.4.5}{84}} \@writefile{toc}{\contentsline {subsubsection}{Introduction}{84}} \@writefile{toc}{\contentsline {subsubsection}{Th\IeC {\'e}oriquement}{84}} \@writefile{toc}{\contentsline {subsubsection}{Num\IeC {\'e}riquement}{84}} diff --git a/MecaniqueDim/MecaniqueDim.tex b/MecaniqueDim/MecaniqueDim.tex index efd41b6..aaf245d 100644 --- a/MecaniqueDim/MecaniqueDim.tex +++ b/MecaniqueDim/MecaniqueDim.tex @@ -447,11 +447,11 @@ implique par dérivation~: \[\frac{dL}{dt}=v=\omega\cdot R=\frac{d\theta}{dt}\cdot R\;\Rightarrow\; v=\omega\cdot R\] \subsubsection{Relation importante} -La complexité de la dynamique de ce mouvement tient dans son caractère bidimensionnel. En d'autres termes, il est nécessaire de tenir compte du caractère vectoriel de la vitesse (voir figure~: \ref{MCU}) +La complexité de la dynamique de ce mouvement tient dans son caractère bidimensionnel. En d'autres termes, il est nécessaire de tenir compte du caractère vectoriel de la vitesse (voir figure~: \ref{dimMCU}) \begin{figure}[htbp] \centering -\caption{Mouvement circulaire uniforme\label{MCU}} +\caption{Mouvement circulaire uniforme\label{dimMCU}} \includegraphics[width=4cm]{MCU.eps} \end{figure} @@ -471,7 +471,7 @@ De plus, on montre que la valeur de l'accélération\index{acceleration@accélé où v est la vitesse scalaire et R le rayon du cercle. \bigskip -En effet, selon la figure \ref{MCU}, on a~: +En effet, selon la figure \ref{dimMCU}, on a~: \[\Delta x=\alpha\cdot R \mbox{ et } \Delta v=\alpha\cdot v\] où \(\Delta x\) est la longueur de l'arc de cercle entre les deux instants où on considère la vitesse. Si \(\Delta t\) est le temps entre ces @@ -589,8 +589,7 @@ La situation est alors la suivante~: \[v_{min}=v_1\;\mbox{ et }\;v_{max}=\infty\] \end{enumerate} -\subsection{Satellite en orbite géostationnaire} -\label{geostat} +\subsection{Satellite en orbite géostationnaire}\label{dimgeostat} \subsubsection{Introduction} Un exemple intéressant de l'utilisation de la seconde loi de Newton\index{loi@loi!seconde loi}, du mouvement circulaire uniforme\index{mouvement@mouvement!circulaire uniforme} et de la loi de la gravitation universelle\index{loi@loi!de la gravitation universelle}, est donné par le calcul de l'altitude\index{altitude@altitude} nécessaire pour qu'un satellite\index{satellite@satellite} soit en orbite géostationnaire\index{orbite@orbite!géostationnaire}. diff --git a/MecaniqueDim/MecaniqueDim.tex.bak b/MecaniqueDim/MecaniqueDim.tex.bak index efd41b6..aaf245d 100644 --- a/MecaniqueDim/MecaniqueDim.tex.bak +++ b/MecaniqueDim/MecaniqueDim.tex.bak @@ -447,11 +447,11 @@ implique par dérivation~: \[\frac{dL}{dt}=v=\omega\cdot R=\frac{d\theta}{dt}\cdot R\;\Rightarrow\; v=\omega\cdot R\] \subsubsection{Relation importante} -La complexité de la dynamique de ce mouvement tient dans son caractère bidimensionnel. En d'autres termes, il est nécessaire de tenir compte du caractère vectoriel de la vitesse (voir figure~: \ref{MCU}) +La complexité de la dynamique de ce mouvement tient dans son caractère bidimensionnel. En d'autres termes, il est nécessaire de tenir compte du caractère vectoriel de la vitesse (voir figure~: \ref{dimMCU}) \begin{figure}[htbp] \centering -\caption{Mouvement circulaire uniforme\label{MCU}} +\caption{Mouvement circulaire uniforme\label{dimMCU}} \includegraphics[width=4cm]{MCU.eps} \end{figure} @@ -471,7 +471,7 @@ De plus, on montre que la valeur de l'accélération\index{acceleration@accélé où v est la vitesse scalaire et R le rayon du cercle. \bigskip -En effet, selon la figure \ref{MCU}, on a~: +En effet, selon la figure \ref{dimMCU}, on a~: \[\Delta x=\alpha\cdot R \mbox{ et } \Delta v=\alpha\cdot v\] où \(\Delta x\) est la longueur de l'arc de cercle entre les deux instants où on considère la vitesse. Si \(\Delta t\) est le temps entre ces @@ -589,8 +589,7 @@ La situation est alors la suivante~: \[v_{min}=v_1\;\mbox{ et }\;v_{max}=\infty\] \end{enumerate} -\subsection{Satellite en orbite géostationnaire} -\label{geostat} +\subsection{Satellite en orbite géostationnaire}\label{dimgeostat} \subsubsection{Introduction} Un exemple intéressant de l'utilisation de la seconde loi de Newton\index{loi@loi!seconde loi}, du mouvement circulaire uniforme\index{mouvement@mouvement!circulaire uniforme} et de la loi de la gravitation universelle\index{loi@loi!de la gravitation universelle}, est donné par le calcul de l'altitude\index{altitude@altitude} nécessaire pour qu'un satellite\index{satellite@satellite} soit en orbite géostationnaire\index{orbite@orbite!géostationnaire}. diff --git a/Prefaces/Prefaces.tex b/Prefaces/Prefaces.tex index a75bb8d..4aa7562 100644 --- a/Prefaces/Prefaces.tex +++ b/Prefaces/Prefaces.tex @@ -7,14 +7,14 @@ \AddToShipoutPicture*{\BackgroundPic} % pour mettre une image en fond de première page \vspace*{2.5cm} -\begin{center}\textbf{\textsc{\fontsize{36}{12}\selectfont Physique \opt{OS}{OS}}}\end{center}{\Huge \par} +\begin{center}{\textsc{\fontsize{36}{12}\selectfont Physique \opt{OS}{OS}}}\end{center}{\Huge \par} \vspace*{3cm} -\begin{center}\textbf{\textsc{\huge \textcolor{white}{Mécanique}}}\end{center}{\large \par} +\begin{center}{\textsc{\huge \textcolor{white}{Mécanique}}}\end{center}{\large \par} -\begin{center}\textbf{\textsc{\large \textcolor{white}{\&}}}\end{center}{\large \par} +\begin{center}{\textsc{\large \textcolor{white}{\&}}}\end{center}{\large \par} -\begin{center}\textbf{\textsc{\huge \textcolor{white}{Énergie}}}\end{center}{\large \par} +\begin{center}{\textsc{\huge \textcolor{white}{Énergie}}}\end{center}{\large \par} \vfill{} %\begin{flushright}vg \end{flushright} diff --git a/Prefaces/Prefaces.tex.bak b/Prefaces/Prefaces.tex.bak new file mode 100644 index 0000000..d0063ce --- /dev/null +++ b/Prefaces/Prefaces.tex.bak @@ -0,0 +1,108 @@ +\pagestyle{fancy} +%\lhead{Lycée Blaise Cendrars\\La Chaux-de-Fonds} +\onecolumn +%\pagenumbering{arabic} + +\titlepage +\AddToShipoutPicture*{\BackgroundPic} % pour mettre une image en fond de première page + +\vspace*{2.5cm} +\begin{center}{\textsc{\fontsize{36}{12}\selectfont Physique \opt{OS}{OS}}}\end{center}{\Huge \par} + +\vspace*{3cm} +\begin{center}\textbf{\textsc{\huge \textcolor{white}{Mécanique}}}\end{center}{\large \par} + +\begin{center}\textbf{\textsc{\large \textcolor{white}{\&}}}\end{center}{\large \par} + +\begin{center}\textbf{\textsc{\huge \textcolor{white}{Énergie}}}\end{center}{\large \par} + +\vfill{} +%\begin{flushright}vg \end{flushright} + +\begin{flushright}\textcolor{white}{\today} + +\onecolumn\end{flushright} +\thispagestyle{empty} % pas de numéro de page et d'entête pour cette page. + +\begin{center}\textbf{Préambule}~:\end{center} +\medskip + +\medskip +Ce cours de mécanique et énergie a été écrit au début avec le logiciel de PAO Lyx, une interface graphique au célèbre Latex et aujourd'hui directement en latex. Il a donc été créé dans un environnement (ces deux logiciels tournant sous GNU-Linux) libre dont l'objectif est de contribuer au progrès en mettant à disposition de chacun, pour un coût moindre, le travail de milliers de programmeurs bénévoles. Dans ce cadre, il était naturel de permettre à chaque étudiant d'avoir accès à ce cours librement. C'est pourquoi, à l'instar des logiciels, il est distribué sous licence GFDL, licence de documentation libre. Attention cependant aux images qui ne sont pas toutes sous licence GFDL, mais peuvent être soumises à une autre licence libre ou être dans le domaine publique. Cela peut avoir une importance dans certains cas. + +Normalement la licence GFDL\index{licence@licence!GFDL} doit figurer avec le cours. Ce n'est pas le cas et ce pour ne pas allonger trop le texte. Mais le texte de la GFDL se trouve partout sur internet et il suffit d'un moteur de recherche pour le trouver. Par ailleurs, le texte de ce cours et ses sources \LaTeX sont disponibles en téléchargement à l'adresse + +\begin{center}https://framagit.org/users/guyotv/projects\end{center} + +Pour tout renseignement complémentaire s'adresser à~: + +\medskip +\begin{center}Vincent Guyot\end{center} + +\begin{center}Chapeau-Râblé 37\end{center} + +\begin{center}2300 La Chaux-de-Fonds\end{center} + +\begin{center}vincent@cvgg.org\end{center} + +\bigskip{} +\begin{center}\textbf{Copyright 2007 Guyot Vincent}\end{center} + +\begin{center}Permission vous est donnée de copier, distribuer et/ou modifier ce document selon les termes de la Licence GNU Free Documentation License, Version 1.1 ou ultérieure publiée par la Free Software Fundation ; avec les sections inaltérables suivantes~:\end{center} + +\begin{center}\emph{Pas de section inaltérable}\end{center} + +\begin{center}avec le texte de première page de couverture suivant~:\end{center} + +\begin{center}\emph{Physique Mécanique \& Énergie}\end{center} + +\begin{center}avec le texte de dernière page de couverture suivant~:\end{center} + +\begin{center}\emph{Pas de texte de dernière page de couverture}\end{center} + +\begin{center}Une copie transparente de ce document se trouve à l'adresse +suivante~:\end{center} + +\begin{center}https://framagit.org/users/guyotv/projects\end{center} +\vfill{} + +%\newpage + +\myclearpage + +\textsc{Remerciements} + +\bigskip + +Je tiens ici à remercier tout particulièrement l'encyclopédie Wikipedia et la NASA, pour les nombreuses illustrations dont ce cours à pu bénéficier. Toutes deux rendent accessibles gratuitement à tous des savoirs importants. + +\medskip +En particulier, je remercie Alain Riazuelo, cosmologue à l'Institut d'Astrophysique de Paris, chercheur au CNRS, pour la magnifique représentation (sous licence libre) d'un trou noir qui fait la couverture de cet ouvrage et qu'il est possible de consulter à l'adresse suivante~: + +\smallskip +\url=http://commons.wikimedia.org/wiki/Image:FY221c15.png= + +\smallskip +Il faut aussi évoquer dans ce cadre le magnifique ouvrage de Hans-Peter Nollert et Hanns Ruder \cite{HNHR08} qui présente des images relativistes au voisinage de trous noirs dans l'esprit de celles d'Alain Riazuello. C'est un ouvrage d'abord pour les yeux, dans l'esprit de découverte de George Gamow, et pour l'esprit par les interrogations qu'il suscite. + +\smallskip +L'image de couverture d'Alain Riazuelo est particulièrement adaptée à ce cours. En effet, on verra que l'accent est mis sur la notion de gravitation\index{gravitation@gravitation} à travers la chute libre\index{chute@chute!libre}, les satellites\index{satellite@satellite} et les marées\index{maree@marée}. Évidemment, il s'agit de physique classique. Pas question d'aborder ici la relativité générale\index{relativite@relativité!générale}, au c\oe ur de la description des trous noirs\index{trous@trous!noir}. Cependant, comme ils sont issus de la plus moderne des théories de la gravitation et qu'aujourd'hui ils sont autant vus à travers la relativité que sous l'angle de la physique quantique\index{physique@physique!quantique}, ils sont la conclusion provisoire presque naturelle de notre compréhension de la gravitation dans cette incroyable courbure de l'espace qui les enveloppe. + +\smallskip +Il faut aussi remercier les archives visuelles Émilio Segrè pour l'image de la chute de la lune des Principia de Newton, reproduite deux fois dans ce cours (pages \pageref{chutelunenewton} et \pageref{chuteprincipia}). L'image est dans le domaine publique et c'est avec leur accord que je la publie, mais comme toujours, c'est le genre d'image qu'il est difficile d'obtenir. Merci à eux de nous la fournir comme illustration centrale de ce cours. + +\bigskip + +Je tiens enfin à remercier mes collègues MM. Michel Augsburger et surtout Marcel Fiechter pour leur travail, ingrat mais nécessaire, de relecture attentive, de corrections et de suggestions pertinentes qui ont grandement augmenté la qualité de ce cours. + +\bigskip +Le chapitre d'introduction est un résumé d'une présentation d'introduction à la physique réalisée avec le logiciel \emph{\textsc{BEAMER}}. Cette présentation est publiée en licence GFDL à la même adresse (www.cvgg.org) que ce cours. Toutes les images utilisées sont libres (dans le domaine publique ou en GFDL) et référencées. Elle constitue un complément à ce cours. + +\bigskip +\textsc{Avertissements} + +\bigskip + +A l'instar des logiciels libres, je décline toute responsabilité relative à l'utilisation de ce cours. Comme je tiens à le mettre aussi vite que possible à disposition de tous, je mets clairement l'accent sur la réalisation de son contenu, plutôt que sur les nombreuses relectures qu'il nécessite assurément. Si la nécessité est claire, le temps manque et il faut faire des choix. J'encourage donc toute personne intéressée à collaborer avec moi à la création de ce cours, sous toute ses formes, à me contacter à l'adresse mail ci-dessus. Reste que si toutes les suggestions de corrections sont les bienvenues, cela ne veut pas dire qu'elles seront prises en considération immédiatement, pour des raisons de temps. Si cela vous semble insuffisant, n'hésitez pas à me faire parvenir vos modifications, corrections, ajouts déjà rédigés sous une forme directement intégrable au cours, en licence GFDL naturellement. Cela me permettra de les reporter plus rapidement dans le cours. Si cela est encore insuffisant, le mieux est de participer directement à la rédaction en prenant contact avec moi. + +\myclearpage \ No newline at end of file diff --git a/SolutionsOS.tex b/SolutionsOS.tex index 446eff5..4197747 100644 --- a/SolutionsOS.tex +++ b/SolutionsOS.tex @@ -2,7 +2,7 @@ La masse m constitue évidemment le système. On choisit un système d'axes vertical et horizontal dirigé vers le haut et dans le sens de l'accélération. Les forces extérieures exercées sur la masse sont au nombre de trois~: son poids P, la réaction du plan R et la force F. - \begin{figure}[h] + \begin{figure}[ht] \caption[Force inclinée]{Une force inclinée}\label{forceinclinee} \smallskip \begin{center} @@ -38,7 +38,7 @@ \end{Solution OS} \begin{Solution OS}{2} Commençons par trouver les forces exercées par les câbles sur la lampe. Considérons donc la lampe comme système. Pour des câbles souples la force est exercée le long du câble. La situation est donc celle de la figure \ref{lampe}. - \begin{figure}[h] + \begin{figure}[ht] \caption[Lampe suspendue]{Une lampe suspendue}\label{lampe} \smallskip \begin{center} @@ -119,7 +119,7 @@ \medskip Une autre manière de résoudre le problème est de procéder avec méthode. Le système qu'on doit choisir est bien évidemment la masse m, puisque c'est de celle-ci qu'on cherche l'accélération pour en trouver la vitesse au bout de \SI{2}{\second}. - \begin{figure}[h] + \begin{figure}[ht] \centering \caption[Plan incliné]{Le plan incliné}\label{incline} \medskip @@ -276,7 +276,7 @@ \medskip Imaginons une poulie suspendue à une corde qui dépasse de celle-ci des deux côtés d'une longueur L, comme présenté sur la figure \ref{cordepoulie}. La demi-circonférence de la poulie vaut aussi L. - \begin{figure}[h] + \begin{figure}[ht] \centering \caption[Corde poulie]{Corde et poulie}\label{cordepoulie} \medskip @@ -290,7 +290,7 @@ \smallskip Pour le déterminer, il faut considérer qu'en tirant sur la corde pour la faire monter d'une hauteur L, on amène le point A qui est à l'origine au contact de la poulie à la place du point B du haut de la corde (voir figure \ref{cordepoulie}). Si la poulie restait à sa place, on aurait la situation de la figure \ref{cordepoulietiree}). Mais, elle est en réalité libre de monter. Ce qui reste fixe est le point C de la figure \ref{cordepoulie}. - \begin{figure}[h] + \begin{figure}[ht] \centering \caption[Corde tirée poulie]{Corde tirée et poulie}\label{cordepoulietiree} \medskip @@ -298,7 +298,7 @@ \input{Annexe-Exercices/Images/cordepoulietiree.eps_tex} \end{figure} On a donc a répartir une longueur 2L de corde entre le point A de la figure \ref{cordepoulietiree} et le point C de la figure \ref{cordepoulie}. Comme la demi-circonférence de la poulie vaut L, il reste une longueur L à répartir des deux côtés de la poulie, soit L/2 de chaque côté, comme le montre la figure \ref{cordepoulietireejuste}. - \begin{figure}[h] + \begin{figure}[ht] \centering \caption[Corde tirée poulie juste]{Corde tirée et poulie montée}\label{cordepoulietireejuste} \medskip @@ -458,7 +458,7 @@ \end{Solution OS} \begin{Solution OS}{13} La situation est celle de la figure \ref{inclinefrottement}. - \begin{figure}[h] + \begin{figure}[ht] \centering \caption[Frottements]{Frottements sur plan incliné}\label{inclinefrottement} \medskip @@ -551,7 +551,7 @@ Le poids du bloc de masse m vaut~: \[P_m=m\cdot g=3\cdot 9,81=\SI{29,43}{\newton}\] Pour que ce bloc ne tombe pas, il faut qu'une force verticale s'exerce vers le haut et compense le poids calculé ci-dessus, soit \(F_{fr}=P\). L'origine de cette force est évidemment le frottement entre les deux blocs. Or, celle-ci dépend de la force exercée par la masse M sur m, notée \(\overrightarrow{N}\), qui joue le rôle de la réaction R du sol pour un objet glissant horizontalement. La figure \ref{blocsuspenduforces} présente la situation qui permet d'exprimer la force de frottement et de déterminer la valeur N de la réaction. - \begin{figure}[h] + \begin{figure}[ht] \centering \caption[Forces sur bloc suspendu]{Forces sur le bloc suspendu}\label{blocsuspenduforces} \medskip diff --git a/ThermodynamiqueOS/ThermodynamiqueOS.tex b/ThermodynamiqueOS/ThermodynamiqueOS.tex index 67528fb..114bc14 100644 --- a/ThermodynamiqueOS/ThermodynamiqueOS.tex +++ b/ThermodynamiqueOS/ThermodynamiqueOS.tex @@ -7,7 +7,7 @@ \subsection{Température} \lettrine{L}{a notion} de température n'est pas facile à cerner sans avoir recours à un modèle atomique de la matière. En effet, celle-ci est liée à l'agitation des molécules et plus particulièrement à leur énergie cinétique. Nous verrons par la suite au paragraphe \ref{thermostat} une définition statistique de la température qui précisera cette remarque. Provisoirement, on peut définir deux échelles de température. -La première se base sur la stabilité constatée expérimentalement du palier de fusion de la glace et du palier d’ébullition de l'eau. Elle est dite de Celsius et attribue la température de \SI{0}{\celsius} (zéro degré celsius) à la température de la glace fondante et la température de \SI{100}{\celsius} à la température de l'eau en ébullition. Ces deux points fixes permettent alors de définir une échelle linéaire comportant des nombres négatifs. +La première se base sur la stabilité constatée expérimentalement du palier de fusion de la glace et du palier d’ébullition de l'eau. Elle est dite de Celsius et attribue la température de \SI{0}{\celsius} (zéro degré Celsius) à la température de la glace fondante et la température de \SI{100}{\celsius} à la température de l'eau en ébullition. Ces deux points fixes permettent alors de définir une échelle linéaire comportant des nombres négatifs. La seconde se base sur l'énergie cinétique des molécules. Elle est dite de Kelvin ou échelle de température absolue et fait correspondre la température de \SI{0}{\kelvin} (zéro Kelvin) à un état où les molécules sont supposées être totalement figées. On y reviendra au paragraphe \ref{thermostat}. Cette température peut être définie en \si{\celsius} et vaut \SI{-273,15}{\celsius}. Ainsi \[\SI{0}{\kelvin}=\SI{-273,15}{\celsius}\] @@ -591,7 +591,7 @@ En d'autres termes, un système qui reçoit de la chaleur réagit par une variat Nous avons déjà vu des changements d'état entre solide et liquides et entre liquides et gaz. En réalité, on devrait plutôt parler de transformation d'état pour réserver le terme de changement d'état à un changement des grandeurs qui caractérisent l'état d'un solide, d'un liquide ou d'un gaz. Par exemple, quand de la glace fond et devient de l'eau, on parle devrait parler de transformation de l'état de l'eau qui de glace devient de l'eau liquide. Par contre, quand on élève la température de l'eau en lui fournissant de la chaleur, on devrait parler de changement de l'état de l'eau, état défini au début par une température initiale et à la fin par une autre température. Dans la pratique, on considère ces deux termes comme synonymes et, par la suite, on utilisera indifféremment l'un ou l'autre. \smallskip -Ainsi, pour un gaz, on parlera de changement d'état quand les grandeurs qui définissent l'état d'un gaz, selon par exemple la loi des gaz parfaits, changent. Ces grandeurs sont la pression, le volume et la température. L'évolution de ces grandeurs lors d'un changement d'état peut être partiellement représenté graphiquement à l'aide de ce qu'on nomme un \emph{diagramme P-V}. Il s'agit de la représentation graphique de la pression d'un gaz en fonction de son volume. Chaque point de ce diagramme constitue un état thermodynamique du gaz défini pour un gaz parfait par la loi des gaz parfaits. Un changement de l'état du gaz se traduit par un déplacement d'un point à un autre du diagramme. Sur la figure \ref{diagrammepv}, on voit l'évolution d'un gaz entre quatre états thermodynamiques A, B, C et D. Chaque courbe représentant l'évolution du gaz représente un changement d'état caractéristique comme on va le voir plus loin. +Ainsi, pour un gaz, on parlera de changement d'état quand les grandeurs qui définissent l'état d'un gaz, selon par exemple la loi des gaz parfaits, changent. Ces grandeurs sont la pression, le volume et la température. L'évolution de ces grandeurs lors d'un changement d'état peut être partiellement représenté graphiquement à l'aide de ce qu'on nomme un \emph{diagramme P-V}. Il s'agit de la représentation graphique de la pression d'un gaz en fonction de son volume. Chaque point de ce diagramme constitue un état thermodynamique du gaz défini pour un gaz parfait par la loi des gaz parfaits. Un changement de l'état du gaz se traduit par un déplacement d'un point à un autre du diagramme. Sur la figure \ref{diagpvmotsimple}, page \pageref{diagpvmotsimple}, on voit l'évolution d'un gaz entre quatre états thermodynamiques. Chaque courbe liant deux états traduisant l'évolution du gaz représente un changement d'état caractéristique comme on va le voir plus loin. \subsubsection{Transformation isobare} Une transformation isobare est une transformation qui se fait à pression constante. @@ -1310,10 +1310,10 @@ Fondamentalement, c'est le même que celui d'un climatiseur. \subsection{Cycle de Carnot} Il s'agit d'un cycle très important, car il possède un rendement maximum qu'aucun moteur ne peut dépasser. Ce rendement n'est pas de 100\%, pour des raisons dues au second principe que nous verrons au paragraphe \ref{secondprincipe}. Comme il dépend de la température des sources chaude et froide, une comparaison des rendements n'est pas significative. En effet, la différence de température entre les deux sources implique des rendements maximum différents. C'est pourquoi on utilise le rendement de Carnot pour comparer l'efficacité des moteurs. -Voyons maintenant sur quelles transformations repose le cycle de Carnot. Pour cela examinons la figure \ref{diagpvcarnot} qui donne son diagramme PV. +Voyons maintenant sur quelles transformations repose le cycle de Carnot. Pour cela examinons la figure \ref{diagpvcarnot} ... qui donne son diagramme PV. \section{Thermodynamique statistique}\label{thermostat} -Au paragraphe \ref{apprmolecul}, nous avons considéré un gaz parfait du point de vue de ses éléments constitutifs. Reprenons cette approche pour déterminer comment un état donné est réalisé microscopiquement par un gaz. Pour cela, partons d'un volume divisé en trois parties et qui contient trois molécules sans interactions mutuelles. Nous ne prendrons pas en compte les différentes manières de répartir l'énergie interne entre les quatre molécules. Dénombrons le nombre d'états possibles, c'est-à-dire le nombre de manières différentes de placer les trois molécules dans les trois parties. On suppose que les molécules sont identiques. La figure \ref{} montre qu'il existe dix états microscopique différent, dont un comporte une seule molécule dans chaque partie, six comportent deux molécules dans l'une et/ou l'autre des parties et trois comportent trois molécules dans l'une des parties. Visiblement, sur la base du seul critère de la position des molécules, la probabilité de réalisation d'un état avec une, deux ou trois molécules dans une partie est très différente. Certains états sont réalisés plus souvent que d'autres, comme ici celui avec deux molécules dans l'une des parties. Visuellement cet état est aussi le plus désordonné. +Au paragraphe \ref{apprmolecul}, nous avons considéré un gaz parfait du point de vue de ses éléments constitutifs. Reprenons cette approche pour déterminer comment un état donné est réalisé microscopiquement par un gaz. Pour cela, partons d'un volume divisé en trois parties et qui contient trois molécules sans interactions mutuelles. Nous ne prendrons pas en compte les différentes manières de répartir l'énergie interne entre les quatre molécules. Dénombrons le nombre d'états possibles, c'est-à-dire le nombre de manières différentes de placer les trois molécules dans les trois parties. On suppose que les molécules sont identiques. La figure \ref{} ... montre qu'il existe dix états microscopique différent, dont un comporte une seule molécule dans chaque partie, six comportent deux molécules dans l'une et/ou l'autre des parties et trois comportent trois molécules dans l'une des parties. Visiblement, sur la base du seul critère de la position des molécules, la probabilité de réalisation d'un état avec une, deux ou trois molécules dans une partie est très différente. Certains états sont réalisés plus souvent que d'autres, comme ici celui avec deux molécules dans l'une des parties. Visuellement cet état est aussi le plus désordonné. De manière plus générale, considérons un volume \(V\) décomposé en \(n\) parties de volume \(v=V/n\) contenant \(N\) particules différentes. On peut mettre la première particule dans l'une ou l'autre des \(n\) parties. De la même manière, on peut placer les \(N\) particules suivantes de \(n\) manières différentes. Au total, on a donc \(n^N\) manières de peupler notre volume \(V\). Or, comme \(n=V/v\), on a~: \[n^N=(\frac{V}{v})^N\sim V^N\] diff --git a/ThermodynamiqueOS/ThermodynamiqueOS.tex.bak b/ThermodynamiqueOS/ThermodynamiqueOS.tex.bak index 67528fb..42fa2fa 100644 --- a/ThermodynamiqueOS/ThermodynamiqueOS.tex.bak +++ b/ThermodynamiqueOS/ThermodynamiqueOS.tex.bak @@ -7,7 +7,7 @@ \subsection{Température} \lettrine{L}{a notion} de température n'est pas facile à cerner sans avoir recours à un modèle atomique de la matière. En effet, celle-ci est liée à l'agitation des molécules et plus particulièrement à leur énergie cinétique. Nous verrons par la suite au paragraphe \ref{thermostat} une définition statistique de la température qui précisera cette remarque. Provisoirement, on peut définir deux échelles de température. -La première se base sur la stabilité constatée expérimentalement du palier de fusion de la glace et du palier d’ébullition de l'eau. Elle est dite de Celsius et attribue la température de \SI{0}{\celsius} (zéro degré celsius) à la température de la glace fondante et la température de \SI{100}{\celsius} à la température de l'eau en ébullition. Ces deux points fixes permettent alors de définir une échelle linéaire comportant des nombres négatifs. +La première se base sur la stabilité constatée expérimentalement du palier de fusion de la glace et du palier d’ébullition de l'eau. Elle est dite de Celsius et attribue la température de \SI{0}{\celsius} (zéro degré Celsius) à la température de la glace fondante et la température de \SI{100}{\celsius} à la température de l'eau en ébullition. Ces deux points fixes permettent alors de définir une échelle linéaire comportant des nombres négatifs. La seconde se base sur l'énergie cinétique des molécules. Elle est dite de Kelvin ou échelle de température absolue et fait correspondre la température de \SI{0}{\kelvin} (zéro Kelvin) à un état où les molécules sont supposées être totalement figées. On y reviendra au paragraphe \ref{thermostat}. Cette température peut être définie en \si{\celsius} et vaut \SI{-273,15}{\celsius}. Ainsi \[\SI{0}{\kelvin}=\SI{-273,15}{\celsius}\] @@ -591,7 +591,7 @@ En d'autres termes, un système qui reçoit de la chaleur réagit par une variat Nous avons déjà vu des changements d'état entre solide et liquides et entre liquides et gaz. En réalité, on devrait plutôt parler de transformation d'état pour réserver le terme de changement d'état à un changement des grandeurs qui caractérisent l'état d'un solide, d'un liquide ou d'un gaz. Par exemple, quand de la glace fond et devient de l'eau, on parle devrait parler de transformation de l'état de l'eau qui de glace devient de l'eau liquide. Par contre, quand on élève la température de l'eau en lui fournissant de la chaleur, on devrait parler de changement de l'état de l'eau, état défini au début par une température initiale et à la fin par une autre température. Dans la pratique, on considère ces deux termes comme synonymes et, par la suite, on utilisera indifféremment l'un ou l'autre. \smallskip -Ainsi, pour un gaz, on parlera de changement d'état quand les grandeurs qui définissent l'état d'un gaz, selon par exemple la loi des gaz parfaits, changent. Ces grandeurs sont la pression, le volume et la température. L'évolution de ces grandeurs lors d'un changement d'état peut être partiellement représenté graphiquement à l'aide de ce qu'on nomme un \emph{diagramme P-V}. Il s'agit de la représentation graphique de la pression d'un gaz en fonction de son volume. Chaque point de ce diagramme constitue un état thermodynamique du gaz défini pour un gaz parfait par la loi des gaz parfaits. Un changement de l'état du gaz se traduit par un déplacement d'un point à un autre du diagramme. Sur la figure \ref{diagrammepv}, on voit l'évolution d'un gaz entre quatre états thermodynamiques A, B, C et D. Chaque courbe représentant l'évolution du gaz représente un changement d'état caractéristique comme on va le voir plus loin. +Ainsi, pour un gaz, on parlera de changement d'état quand les grandeurs qui définissent l'état d'un gaz, selon par exemple la loi des gaz parfaits, changent. Ces grandeurs sont la pression, le volume et la température. L'évolution de ces grandeurs lors d'un changement d'état peut être partiellement représenté graphiquement à l'aide de ce qu'on nomme un \emph{diagramme P-V}. Il s'agit de la représentation graphique de la pression d'un gaz en fonction de son volume. Chaque point de ce diagramme constitue un état thermodynamique du gaz défini pour un gaz parfait par la loi des gaz parfaits. Un changement de l'état du gaz se traduit par un déplacement d'un point à un autre du diagramme. Sur la figure \ref{diagpvmotsimple}, page \pageref{diagpvmotsimple}, on voit l'évolution d'un gaz entre quatre états thermodynamiques. Chaque courbe liant deux états traduisant l'évolution du gaz représente un changement d'état caractéristique comme on va le voir plus loin. \subsubsection{Transformation isobare} Une transformation isobare est une transformation qui se fait à pression constante. @@ -1313,7 +1313,7 @@ Il s'agit d'un cycle très important, car il possède un rendement maximum qu'au Voyons maintenant sur quelles transformations repose le cycle de Carnot. Pour cela examinons la figure \ref{diagpvcarnot} qui donne son diagramme PV. \section{Thermodynamique statistique}\label{thermostat} -Au paragraphe \ref{apprmolecul}, nous avons considéré un gaz parfait du point de vue de ses éléments constitutifs. Reprenons cette approche pour déterminer comment un état donné est réalisé microscopiquement par un gaz. Pour cela, partons d'un volume divisé en trois parties et qui contient trois molécules sans interactions mutuelles. Nous ne prendrons pas en compte les différentes manières de répartir l'énergie interne entre les quatre molécules. Dénombrons le nombre d'états possibles, c'est-à-dire le nombre de manières différentes de placer les trois molécules dans les trois parties. On suppose que les molécules sont identiques. La figure \ref{} montre qu'il existe dix états microscopique différent, dont un comporte une seule molécule dans chaque partie, six comportent deux molécules dans l'une et/ou l'autre des parties et trois comportent trois molécules dans l'une des parties. Visiblement, sur la base du seul critère de la position des molécules, la probabilité de réalisation d'un état avec une, deux ou trois molécules dans une partie est très différente. Certains états sont réalisés plus souvent que d'autres, comme ici celui avec deux molécules dans l'une des parties. Visuellement cet état est aussi le plus désordonné. +Au paragraphe \ref{apprmolecul}, nous avons considéré un gaz parfait du point de vue de ses éléments constitutifs. Reprenons cette approche pour déterminer comment un état donné est réalisé microscopiquement par un gaz. Pour cela, partons d'un volume divisé en trois parties et qui contient trois molécules sans interactions mutuelles. Nous ne prendrons pas en compte les différentes manières de répartir l'énergie interne entre les quatre molécules. Dénombrons le nombre d'états possibles, c'est-à-dire le nombre de manières différentes de placer les trois molécules dans les trois parties. On suppose que les molécules sont identiques. La figure \ref{} ... montre qu'il existe dix états microscopique différent, dont un comporte une seule molécule dans chaque partie, six comportent deux molécules dans l'une et/ou l'autre des parties et trois comportent trois molécules dans l'une des parties. Visiblement, sur la base du seul critère de la position des molécules, la probabilité de réalisation d'un état avec une, deux ou trois molécules dans une partie est très différente. Certains états sont réalisés plus souvent que d'autres, comme ici celui avec deux molécules dans l'une des parties. Visuellement cet état est aussi le plus désordonné. De manière plus générale, considérons un volume \(V\) décomposé en \(n\) parties de volume \(v=V/n\) contenant \(N\) particules différentes. On peut mettre la première particule dans l'une ou l'autre des \(n\) parties. De la même manière, on peut placer les \(N\) particules suivantes de \(n\) manières différentes. Au total, on a donc \(n^N\) manières de peupler notre volume \(V\). Or, comme \(n=V/v\), on a~: \[n^N=(\frac{V}{v})^N\sim V^N\]