From 222e6c1f6bbcd6b491e3434d51edc53832148757 Mon Sep 17 00:00:00 2001 From: guyotv Date: Tue, 7 Jan 2025 23:26:27 +0100 Subject: [PATCH] Bibliographie avec biber et notes avec enotez --- Annexe-MRUA/Annexe-MRUA.tex | 4 +- Annexe-Maree/Annexe-Maree.tex | 8 +- Annexe-Maree/Annexe-Maree.tex.bak | 80 +- .../Annexe-MesuresDistances.tex | 4 +- .../Annexe-MesuresDistances.tex.bak | 6 +- Annexe-Rotations/Annexe-Rotations.tex | 8 +- Annexe-Satellites/Annexe-Satellites.tex | 4 +- Cinematique/Cinematique.tex | 12 +- Cinematique/Cinematique.tex.bak | 12 +- CoursMecaniqueOSDF-blx.bib | 11 + CoursMecaniqueOSDF.bbl | 760 +++-- CoursMecaniqueOSDF.bcf | 2434 +++++++++++++++++ CoursMecaniqueOSDF.blg | 90 +- CoursMecaniqueOSDF.out | 2 + CoursMecaniqueOSDF.pdf | Bin 13392577 -> 13433949 bytes CoursMecaniqueOSDF.run.xml | 86 + CoursMecaniqueOSDF.tex | 26 +- CoursMecaniqueOSDF.tex.bak | 26 +- Dynamique/Dynamique.tex | 8 +- Energie/Energie.tex | 32 +- Energie/Energie.tex.bak | 24 +- Introduction/Introduction.tex | 69 +- Introduction/Introduction.tex.bak | 61 +- PhysiqueTheorique/PhysiqueTheorique.tex | 2 +- PhysiqueTheorique/PhysiqueTheorique.tex.bak | 8 +- Preambule.tex | 25 +- Preambule.tex.bak | 27 +- Solutions.tex | 2 +- Thermodynamique/Thermodynamique.tex | 4 +- ThermodynamiqueOS/ThermodynamiqueOS.tex | 4 +- 30 files changed, 3411 insertions(+), 428 deletions(-) create mode 100644 CoursMecaniqueOSDF-blx.bib create mode 100644 CoursMecaniqueOSDF.bcf create mode 100644 CoursMecaniqueOSDF.run.xml diff --git a/Annexe-MRUA/Annexe-MRUA.tex b/Annexe-MRUA/Annexe-MRUA.tex index 082a249..7d6232c 100644 --- a/Annexe-MRUA/Annexe-MRUA.tex +++ b/Annexe-MRUA/Annexe-MRUA.tex @@ -36,7 +36,7 @@ C'est ce qu'il fallait démontrer. \begin{figure}[t] \centering -\caption[\emph{Discours concernant deux sciences nouvelles} de Galilée]{\emph{Discours concernant deux sciences nouvelles} de Galilée\label{deuxsciences} \par \scriptsize{Discours dans lesquels Galilée présente ses expériences sur la chute des corps et fonde la mécanique. Il tente aussi d'y créer une science de la résistance des matériaux\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Galileo\_Galilei\%2C\_Discorsi\_e\_Dimostrazioni\_Matematiche\_Intorno\_a\_Due\_Nuove\_Scienze\%2C\_1638\_\%281400x1400\%29.png=.}}} +\caption[\emph{Discours concernant deux sciences nouvelles} de Galilée]{\emph{Discours concernant deux sciences nouvelles} de Galilée\label{deuxsciences} \par \scriptsize{Discours dans lesquels Galilée présente ses expériences sur la chute des corps et fonde la mécanique. Il tente aussi d'y créer une science de la résistance des matériaux}} \includegraphics[width=6cm]{Discorsi_e_Dimostrazioni_Matematiche.eps} \end{figure} @@ -44,7 +44,7 @@ C'est ce qu'il fallait démontrer. \subsection{Cinématique} -Jusqu'à présent, les relations obtenues (la vitesse et la position) sont fonctions du temps. Il est néanmoins pratique dans bien des cas de disposer d'une relation où le facteur temps n'apparaît pas. Cette relation est facilement obtenue en éliminant le temps des deux équations de la vitesse et de la position. Pour le calcul on part de équations du MRUA suivantes~: +Jusqu'à présent, les relations obtenues (la vitesse et la position) sont fonctions du temps (voir figure \ref{deuxsciences}\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Galileo\_Galilei\%2C\_Discorsi\_e\_Dimostrazioni\_Matematiche\_Intorno\_a\_Due\_Nuove\_Scienze\%2C\_1638\_\%281400x1400\%29.png=.}). Il est néanmoins pratique dans bien des cas de disposer d'une relation où le facteur temps n'apparaît pas. Cette relation est facilement obtenue en éliminant le temps des deux équations de la vitesse et de la position. Pour le calcul on part de équations du MRUA suivantes~: \begin{align*} v&=a_{o}\cdot t+v_{o}\\ diff --git a/Annexe-Maree/Annexe-Maree.tex b/Annexe-Maree/Annexe-Maree.tex index 7a5ce05..a5eb641 100644 --- a/Annexe-Maree/Annexe-Maree.tex +++ b/Annexe-Maree/Annexe-Maree.tex @@ -2,13 +2,13 @@ \chapter{Marées\index{maree@marée}}\label{chapmarees} \section{Introduction} -\lettrine{L}{'origine des marées} est un phénomène à la fois simple et complexe. Simple, car il suit d'assez près le mouvement de la Lune pour qu'on puisse naturellement le lui attribuer. Complexe, car il se produit aussi sur la Terre à l'opposé du zénith\index{zenith@zénith} de la Lune et il est souvent en retard sur son passage. +\lettrine{L}{'origine des marées} (voir figure \ref{maree}\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Bay\_of\_Fundy.jpg= notamment pour le copyright de l'image. Remerciements à son auteur Samuel Wantman.}) est un phénomène à la fois simple et complexe. Simple, car il suit d'assez près le mouvement de la Lune pour qu'on puisse naturellement le lui attribuer. Complexe, car il se produit aussi sur la Terre à l'opposé du zénith\index{zenith@zénith} de la Lune et il est souvent en retard sur son passage. Nous allons ici rappeler la simplicité du phénomène et expliquer pourquoi il se produit à la fois du côté de la Terre où se trouve la Lune et à l'opposé. L'explication des différents retards des marées sur le passage de la Lune ne sera pas abordée ici, car elle est très complexe. Une description du phénomène ayant été faite précédemment (voir paragraphe \ref{paramarees}), nous nous intéresserons ici plus particulièrement à l'aspect mathématique du phénomène, tout en expliquant le plus simplement les choses. \begin{figure}[t] \centering -\caption[Marée]{Marée\label{maree}\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Bay\_of\_Fundy.jpg= notamment pour le copyright de l'image. Remerciements à son auteur Samuel Wantman.}} +\caption[Marée]{Marée\label{maree}} \includegraphics[width=6cm]{Maree.eps} \end{figure} @@ -229,7 +229,7 @@ d_{Roche} = R\cdot \sqrt[3]{16\cdot \frac{\rho_p}{\rho_s}} \begin{figure}[t] \centering -\caption[Limite de Roche]{Limite de Roche\label{limitederoche}\endnote{Voir le site de l'encyclopédie Wikipedia~: \url{http://fr.wikipedia.org/wiki/Limite_de_Roche} notamment pour le copyright de l'image.}} +\caption[Limite de Roche]{Limite de Roche\label{limitederoche}} \includegraphics[width=6cm]{LimiteRoche1.eps} \includegraphics[width=6cm]{LimiteRoche2.eps} \includegraphics[width=6cm]{LimiteRoche3.eps} @@ -238,7 +238,7 @@ d_{Roche} = R\cdot \sqrt[3]{16\cdot \frac{\rho_p}{\rho_s}} \end{figure} \subsection{Exemples} -L'une des planètes les plus intéressantes du point de vue de la limite de Roche est certainement Saturne en raison des ses satellites et de ses anneaux. Pour se faire une idée numérique du calcul de la limite de Roche, considérons par exemple Épiméthée, l'un de ses satellites dont la masse volumique vaut~: +L'une des planètes les plus intéressantes du point de vue de la limite de Roche (voir figure \ref{limitederoche}\endnote{Voir le site de l'encyclopédie Wikipedia~: \url{http://fr.wikipedia.org/wiki/Limite_de_Roche} notamment pour le copyright de l'image.}) est certainement Saturne en raison des ses satellites et de ses anneaux. Pour se faire une idée numérique du calcul de la limite de Roche, considérons par exemple Épiméthée, l'un de ses satellites dont la masse volumique vaut~: \[\rho_s=\SI{0,61e3}{\kilo\gram\per\cubic\metre}\] Comme la masse volumique de Saturne vaut~: \[\rho_p=\SI{0,6873e3}{\kilo\gram\per\cubic\metre}\] diff --git a/Annexe-Maree/Annexe-Maree.tex.bak b/Annexe-Maree/Annexe-Maree.tex.bak index 55ca4d9..a5eb641 100644 --- a/Annexe-Maree/Annexe-Maree.tex.bak +++ b/Annexe-Maree/Annexe-Maree.tex.bak @@ -2,13 +2,13 @@ \chapter{Marées\index{maree@marée}}\label{chapmarees} \section{Introduction} -\lettrine{L}{'origine des marées} est un phénomène à la fois simple et complexe. Simple, car il suit d'assez près le mouvement de la Lune pour qu'on puisse naturellement le lui attribuer. Complexe, car il se produit aussi sur la Terre à l'opposé du zénith\index{zenith@zénith} de la Lune et il est souvent en retard sur son passage. +\lettrine{L}{'origine des marées} (voir figure \ref{maree}\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Bay\_of\_Fundy.jpg= notamment pour le copyright de l'image. Remerciements à son auteur Samuel Wantman.}) est un phénomène à la fois simple et complexe. Simple, car il suit d'assez près le mouvement de la Lune pour qu'on puisse naturellement le lui attribuer. Complexe, car il se produit aussi sur la Terre à l'opposé du zénith\index{zenith@zénith} de la Lune et il est souvent en retard sur son passage. Nous allons ici rappeler la simplicité du phénomène et expliquer pourquoi il se produit à la fois du côté de la Terre où se trouve la Lune et à l'opposé. L'explication des différents retards des marées sur le passage de la Lune ne sera pas abordée ici, car elle est très complexe. Une description du phénomène ayant été faite précédemment (voir paragraphe \ref{paramarees}), nous nous intéresserons ici plus particulièrement à l'aspect mathématique du phénomène, tout en expliquant le plus simplement les choses. \begin{figure}[t] \centering -\caption[Marée]{Marée\label{maree}\endnote{Voir le site de l'encyclopédie Wikipedia : \url=http://commons.wikimedia.org/wiki/Image:Bay_of_Fundy.jpg= notamment pour le copyright de l'image. Remerciements à son auteur Samuel Wantman.}} +\caption[Marée]{Marée\label{maree}} \includegraphics[width=6cm]{Maree.eps} \end{figure} @@ -19,7 +19,7 @@ L'analyse se fait en trois étapes. Tout d'abord, la détermination du centre de \section{Centre de gravité\index{centre de gravité}} Une partie du problème des marées se trouve dans le fait que le système Terre-Lune a un centre de gravité qui ne coïncide pas avec le centre de la Terre, comme le montre la figure \ref{systterrelune}. -La notion de centre de gravité est ici relativement aisée à saisir. Imaginons deux masses \(m\) identiques situées à une distance \(d\) l'une de l'autre. On comprend bien que le centre de gravité de ce système se trouve exactement au milieu entre les masses. Maintenant, si l'une des masses double (\(M=2\cdot m\)), le centre de gravité va se rapprocher d'elle. La masse totale du système valant \(3\cdot m\), on comprend bien que la plus grande des masses compte pour deux tiers et la plus petite pour un tiers. Le centre de gravité se trouve donc à un tiers de la distance entre les corps, du côté de la plus grande masse. Depuis le centre de la plus grande masse, la distance \(r\) au centre de gravité se calcule donc ainsi : +La notion de centre de gravité est ici relativement aisée à saisir. Imaginons deux masses \(m\) identiques situées à une distance \(d\) l'une de l'autre. On comprend bien que le centre de gravité de ce système se trouve exactement au milieu entre les masses. Maintenant, si l'une des masses double (\(M=2\cdot m\)), le centre de gravité va se rapprocher d'elle. La masse totale du système valant \(3\cdot m\), on comprend bien que la plus grande des masses compte pour deux tiers et la plus petite pour un tiers. Le centre de gravité se trouve donc à un tiers de la distance entre les corps, du côté de la plus grande masse. Depuis le centre de la plus grande masse, la distance \(r\) au centre de gravité se calcule donc ainsi~: \begin{equation}\label{distgrav} r=\frac{m}{M+m}\cdot d \end{equation} @@ -33,7 +33,7 @@ r=\frac{m}{M+m}\cdot d \input{Annexe-Maree/Images/Systterrelune.pst} \end{figure} -En substance, le problème des marées est posé par la rotation d'une masse \(m\) d'eau non pas autour du centre de la Terre, mais autour du centre de gravité du système Terre-Lune. Il s'agit d'un mouvent circulaire uniforme\index{mouvement!circulaire uniforme} et l'une des composantes de la seconde loi de Newton est l'accélération centripète\index{acceleration@accélération!centripète} \(a_c\) de cette masse. On peut l'exprimer sous différentes formes présentées dans l'équation \ref{acccentr} : +En substance, le problème des marées est posé par la rotation d'une masse \(m\) d'eau non pas autour du centre de la Terre, mais autour du centre de gravité du système Terre-Lune. Il s'agit d'un mouvent circulaire uniforme\index{mouvement!circulaire uniforme} et l'une des composantes de la seconde loi de Newton est l'accélération centripète\index{acceleration@accélération!centripète} \(a_c\) de cette masse. On peut l'exprimer sous différentes formes présentées dans l'équation \ref{acccentr}~: \begin{equation}\label{acccentr} a_c=\frac{v^2}{R}=\omega^2\cdot R \end{equation} @@ -41,7 +41,7 @@ où \(v\) est la vitesse linéaire\index{vitesse!linéaire} de la masse \(m\) d' \subsection{Vitesse angulaire\index{vitesse!angulaire}} -Or, la vitesse linéaire de la masse d'eau n'est pas celle qui résulte de sa rotation diurne autour du centre de la Terre, mais celle correspondant au déplacement de \(m\) sous l'influence de la Lune, c'est-à-dire celle correspondant à sa rotation autour du centre de gravité du système Terre-Lune. Avec les grandeurs présentées à la figure \ref{systterrelune} et l'équation \ref{distgrav}, le calcul de la vitesse angulaire \(\omega\) de ce dernier est le suivant : +Or, la vitesse linéaire de la masse d'eau n'est pas celle qui résulte de sa rotation diurne autour du centre de la Terre, mais celle correspondant au déplacement de \(m\) sous l'influence de la Lune, c'est-à-dire celle correspondant à sa rotation autour du centre de gravité du système Terre-Lune. Avec les grandeurs présentées à la figure \ref{systterrelune} et l'équation \ref{distgrav}, le calcul de la vitesse angulaire \(\omega\) de ce dernier est le suivant~: \begin{align} F&=M_L\cdot \omega^2\cdot R\nonumber\\ G\cdot \frac{M_T\cdot M_L}{d_{T-L}^2}&=M_L\cdot \omega^2\cdot (d_{T-L}-r)\nonumber\\ @@ -60,9 +60,9 @@ G\cdot \frac{M_T}{d_{T-L}^3}&=\omega^2\cdot \frac{M_T}{M_L+M_T}\nonumber\\ \input{Annexe-Maree/Images/Systterreluneeau.pst} \end{figure} -On peut alors calculer la force d'inertie à ajouter à la seconde loi de Newton dans le cas de référentiels en rotation, puisque le référentiel lié au centre de la Terre est en rotation autour du centre de masse du système Terre-Lune. En considérant la distance du centre de gravité au centre de la Terre : +On peut alors calculer la force d'inertie à ajouter à la seconde loi de Newton dans le cas de référentiels en rotation, puisque le référentiel lié au centre de la Terre est en rotation autour du centre de masse du système Terre-Lune. En considérant la distance du centre de gravité au centre de la Terre~: \[r=\frac{M_L}{M_T+M_L}\cdot d_{T-L}\] -et l'équation \ref{omega}, on peut écrire cette force sous la forme : +et l'équation \ref{omega}, on peut écrire cette force sous la forme~: \begin{align} F_{in}&=m\cdot \omega^2\cdot r\nonumber\\ &=m\cdot G\frac{M_L+M_T}{d_{T-L}^3}\cdot \frac{M_L}{M_L+M_T}\cdot d_{T-L}\nonumber\\ @@ -70,11 +70,11 @@ F_{in}&=m\cdot \omega^2\cdot r\nonumber\\ \end{align} \section{Poids relatif\index{poids!relatif}} -On peut maintenant calculer le poids relatif à l'aide de la seconde loi de Newton. La masse d'eau \(m\) est en équilibre statique dans le référentiel lié au centre de la Terre et son accélération est nulle. On peut s'imaginer cette masse comme posée sur une balance. Les forces qui s'exercent sur elle sont son poids \(P\), correspondant à l'attraction de la Terre, l'attraction \(F_L\) de la Lune, la force d'inertie\index{force@force!d'inertie} \(F_{in}\) et la réaction \(R\) de la balance\index{balance} qui constitue le poids apparent de la masse d'eau. Si on choisit un axe dirigé vers le centre de la Terre, on peut ainsi écrire : +On peut maintenant calculer le poids relatif à l'aide de la seconde loi de Newton. La masse d'eau \(m\) est en équilibre statique dans le référentiel lié au centre de la Terre et son accélération est nulle. On peut s'imaginer cette masse comme posée sur une balance. Les forces qui s'exercent sur elle sont son poids \(P\), correspondant à l'attraction de la Terre, l'attraction \(F_L\) de la Lune, la force d'inertie\index{force@force!d'inertie} \(F_{in}\) et la réaction \(R\) de la balance\index{balance} qui constitue le poids apparent de la masse d'eau. Si on choisit un axe dirigé vers le centre de la Terre, on peut ainsi écrire~: \begin{equation}\label{Newacc} \sum F=P-R-F_L+F_{in}=0(=m\cdot a_m) \end{equation} -Soit, en utilisant la loi de la gravitation universelle et l'équation \ref{forceinertie} dans l'équation \ref{Newacc} : +Soit, en utilisant la loi de la gravitation universelle et l'équation \ref{forceinertie} dans l'équation \ref{Newacc}~: \begin{align} P-R-G\frac{M_L\cdot m}{(d_{T-L}-R_T)^2}+G\frac{M_L}{d_{T-L}^2}&=0\nonumber\\ P-R-\nonumber\\ @@ -83,7 +83,7 @@ P-R-G\frac{M_L\cdot m}{d_{T-L}^2}-\nonumber\\ 2\dot G\frac{M_L\cdot m}{d_{T-L}^3}\cdot R_T+G\frac{M_L\cdot m}{d_{T-L}^2}&=0\nonumber\\ P-R-2\cdot G\frac{M_L\cdot m}{d_{T-L}^3}\cdot R_T&=0\label{secondeloimaree} \end{align} -Pour établir l'équation \ref{DLmaree}, on a utilisé le développement limité : \((1+x)^p\simeq1+p\cdot x\). +Pour établir l'équation \ref{DLmaree}, on a utilisé le développement limité~: \((1+x)^p\simeq1+p\cdot x\). \begin{align*} \frac{1}{(d_{T-L}-R_T)^2}&=\frac{1}{d_{T-L}^2}\cdot \frac{1}{(1-R_T/d_{T-L})^2}\\ &=\frac{1}{d_{T-L}^2}\cdot (1-R_T/d_{T-L})^{-2}\\ @@ -91,7 +91,7 @@ Pour établir l'équation \ref{DLmaree}, on a utilisé le développement limité &=\frac{1}{d_{T-L}^2}\cdot (1+\frac{2\cdot R_T}{d_{T-L}}) \end{align*} -En réorganisant les termes de l'équation \ref{secondeloimaree}, on obtient finalement la force de réaction d'une balance qu'on placerait sous la masse \(m\) d'eau : +En réorganisant les termes de l'équation \ref{secondeloimaree}, on obtient finalement la force de réaction d'une balance qu'on placerait sous la masse \(m\) d'eau~: \begin{equation}\label{forcedemareebalance} R=P-2\cdot G\frac{M_L\cdot m}{d_{T-L}^3}\cdot R_T \end{equation} @@ -103,16 +103,16 @@ La force de marée de l'équation \ref{forcedemareebalance} correspond à la for L'analyse du rapport des forces de marées lunaire et solaire qui suit l'équation \ref{eqmaree}, page \pageref{eqmaree}, et qui est issue de la forme de l'équation \ref{forcedemareebalance}, constitue aussi une suite logique au calcul présenté ci-dessus que nous ne reprendrons pas ici. \section{Analyse différentielle} -Le cadre de l'analyse présentée ci-dessus est celui de la seconde loi de Newton. Insistons sur le fait que l'ensemble des forces considérées s'exercent sur le même système, soit la masse $m$ d'eau. Cette analyse est donc cohérente avec la formulation de la seconde loi qui s'applique sur un système de masse \(m\). +Le cadre de l'analyse présentée ci-dessus est celui de la seconde loi de Newton. Insistons sur le fait que l'ensemble des forces considérées s'exercent sur le même système, soit la masse m d'eau. Cette analyse est donc cohérente avec la formulation de la seconde loi qui s'applique sur un système de masse \(m\). \medskip -On va maintenant présenter une autre analyse du problème qui est moins consistante puisque les forces qu'elle utilise ne s'appliquent pas sur un système unique. Cependant, non seulement elle mène au même résultat, mais encore elle permet de mettre en évidence le caractère différentiel des forces de marées, caractère qui apparaitra alors plus clair dans l'étude des forces de marées exercées sur des satellites comme Io autour de Jupiter. La notion de limite de Roche pourra donc être mieux abordée au paragraphe \ref{limroche}. +On va maintenant présenter une autre analyse du problème qui est moins consistante puisque les forces qu'elle utilise ne s'appliquent pas sur un système unique. Cependant, non seulement elle mène au même résultat, mais encore elle permet de mettre en évidence le caractère différentiel des forces de marées, caractère qui apparaîtra alors plus clair dans l'étude des forces de marées exercées sur des satellites comme Io autour de Jupiter. La notion de limite de Roche pourra donc être mieux abordée au paragraphe \ref{limroche}. \section{Autres rythmes} L'explication de la présence de deux marées par jour (\emph{dites de pleines\index{pleine mer} et basses mers\index{basse mer}}) ne constitue qu'une partie de la compréhension du phénomène de marée. Même dans le cadre de la théorie de Newton, et sans entrer dans la théorie ondulatoire, d'autres périodes sont associées aux marées. Dans ce paragraphe on va entrer dans ce qu'on peut appeler la dimension astronomique du phénomène. Évidemment, c'est la gravitation qui reste le moteur des influences. Mais celles-ci varient en fonction de la position des astres. \subsection{Décalages} -Une première conséquence du mouvement relatif de la Lune sur les marées se présente sous la forme d'un déplacement perpétuel des heure de pleine et basse mer. Si la Lune ne tournait pas autour de la Terre, les pleine\index{pleine mer} et basse\index{basse mer} mer auraient lieu toujours au même moment dans la journée. Ce n'est pas le cas en raison du déplacement de la Lune autour de la Terre. En effet, comme le montre la figure \ref{decalage}, pendant que la Terre fait un tour sur elle-même en vingtquatre heures, la lune se déplace. Comme cette dernière fait un tour autour de la Terre en trente jours, en vingt quatre heures, c'est-à-dire en une journée, la Lune parcours un angle de \(360/30=12^{\circ}\). Au bout de vingt quatre heures, une personne située au point \(P\) ne verrait plus la Lune au zénith\index{zenith@zénith} (au-dessus d'elle). Il lui faudrait parcourir encore un angle de \(12^{\circ}\) pour cela. Comme la terre parcours \SI{360}{\degree} en vingt quatre heures, il lui faut encore attendre \SI{48}{minutes} pour se retrouver en situation de pleine mer. Chaque jour, les pleines et basses mers se produisent avec environ cinquante minutes de retard sur le jour précédent. +Une première conséquence du mouvement relatif de la Lune sur les marées se présente sous la forme d'un déplacement perpétuel des heure de pleine et basse mer. Si la Lune ne tournait pas autour de la Terre, les pleine\index{pleine mer} et basse\index{basse mer} mer auraient lieu toujours au même moment dans la journée. Ce n'est pas le cas en raison du déplacement de la Lune autour de la Terre. En effet, comme le montre la figure \ref{decalage}, pendant que la Terre fait un tour sur elle-même en vingt quatre heures, la lune se déplace. Comme cette dernière fait un tour autour de la Terre en trente jours, en vingt quatre heures, c'est-à-dire en une journée, la Lune parcours un angle de \(360/30=12^{\circ}\). Au bout de vingt quatre heures, une personne située au point \(P\) ne verrait plus la Lune au zénith\index{zenith@zénith} (au-dessus d'elle). Il lui faudrait parcourir encore un angle de \(12^{\circ}\) pour cela. Comme la terre parcours \SI{360}{\degree} en vingt quatre heures, il lui faut encore attendre \SI{48}{minutes} pour se retrouver en situation de pleine mer. Chaque jour, les pleines et basses mers se produisent avec environ cinquante minutes de retard sur le jour précédent. \begin{figure}[t] \centering @@ -121,7 +121,7 @@ Une première conséquence du mouvement relatif de la Lune sur les marées se pr \end{figure} \subsection{Marées de vives et mortes eaux\index{maree@marée!de vives et mortes eaux}} -Le marnage\index{marnage}, la différence de hauteur d'eau entre une pleine et une basse mer, varie dans le temps. Chaque mois, on constate un marnage maximum (marée de vive eau\index{vive eau}) et un minimum (marée de morte eau\index{morte eau}). On remarque aussi que ces marées particulières correspondent à certaines phases de la lune (voir la figure \ref{phasesdelalune}, page \pageref{phasesdelalune}) : lors des nouvelle\index{nouvelle lune} et pleine lune\index{pleine lune}, la marée est de vive eau et lors des quartiers, elle est de morte eau. +Le marnage\index{marnage}, la différence de hauteur d'eau entre une pleine et une basse mer, varie dans le temps. Chaque mois, on constate un marnage maximum (marée de vive eau\index{vive eau}) et un minimum (marée de morte eau\index{morte eau}). On remarque aussi que ces marées particulières correspondent à certaines phases de la lune (voir la figure \ref{phasesdelalune}, page \pageref{phasesdelalune})~: lors des nouvelle\index{nouvelle lune} et pleine lune\index{pleine lune}, la marée est de vive eau et lors des quartiers, elle est de morte eau. Comme les phases de la Lune correspondent à des positions particulières de notre satellite par rapport à l'axe Terre-Soleil, on peut en trouver une explication dans le rapport des actions gravifiques de la Lune et du Soleil. Comme on l'a vu (voir \ref{eqmaree}, page \pageref{eqmaree}), ce rapport est défavorable au Soleil, dont la masse est plus grande que celle de la Lune, mais qui se trouve plus loin que la Lune, en raison de la dépendance en \(1/d^3\) de la force de marée. Mais, même si elle est moins importante que celle de la Lune, l'action du Soleil existe. @@ -134,12 +134,12 @@ Comme les phases de la Lune correspondent à des positions particulières de not L'explication est simple. Comme le montre la figure \ref{vivemorteeau}, quand le Soleil, la Terre et la Lune sont alignés, les forces lunaires et solaires s'additionnent. On a des marées de vives eaux à la nouvelle et à la pleine lune. Par contre, aux premiers et derniers quartiers, les actions de la Lune et du Soleil ne se produisent pas dans le même axe et les marées sont de basses eaux. \subsection{Marées d'équinoxes\index{maree@marée!d'équinoxe}} -On entend souvent parler des ``grandes marées d'équinoxes''. On se limitera ici à évoquer le phénomène, car il ne trouve une explication convainquante que dans la théorie ondulatoire des marées. Tout se passe comme si la force de marée exercée par le Soleil était maximale quand l'axe de rotation de la Terre est perpendiculaire à la direction Terre-Soleil. Si on considère que la direction de cet axe reste fixe dans l'espace, la figure \ref{saisonsperso}, page \pageref{saisonsperso}, présente la situation : aux solstices\index{solstice}, l'angle \(\alpha\simeq \SI{66,5}{\degree}\), alors qu'aux équinoxes\index{equinoxe@équinoxe}, il vaut \SI{90}{\degree}. Pour bien s'en rendre compte, il faut considérer le plan constitué par l'axe de rotation de la Terre et le Soleil aux solstices. Ce plan est perpendiculaire au plan de l'écliptique\index{ecliptique@écliptique}. Mais si aux solstices l'axe de rotation de la Terre fait un angle non droit avec la direction Terre-Soleil, aux équinoxes cet angle est droit car ce plan est perpendiculaire à l'écliptique. +On entend souvent parler des ``grandes marées d'équinoxes''. On se limitera ici à évoquer le phénomène, car il ne trouve une explication convaincante que dans la théorie ondulatoire des marées. Tout se passe comme si la force de marée exercée par le Soleil était maximale quand l'axe de rotation de la Terre est perpendiculaire à la direction Terre-Soleil. Si on considère que la direction de cet axe reste fixe dans l'espace, la figure \ref{saisonsperso}, page \pageref{saisonsperso}, présente la situation~: aux solstices\index{solstice}, l'angle \(\alpha\simeq \SI{66,5}{\degree}\), alors qu'aux équinoxes\index{equinoxe@équinoxe}, il vaut \SI{90}{\degree}. Pour bien s'en rendre compte, il faut considérer le plan constitué par l'axe de rotation de la Terre et le Soleil aux solstices. Ce plan est perpendiculaire au plan de l'écliptique\index{ecliptique@écliptique}. Mais si aux solstices l'axe de rotation de la Terre fait un angle non droit avec la direction Terre-Soleil, aux équinoxes cet angle est droit car ce plan est perpendiculaire à l'écliptique. \subsection{Marées de périgée et périhélie\index{maree@marée!de périgée}\index{maree@marée!de périhélie}} On sait grâce à Kepler (voir le paragraphe \ref{loiskepler}, page \pageref{loiskepler}) que l'orbite de la Lune est une ellipse\index{ellipse}. Cela signifie que la distance Terre-Lune varie. On nomme \emph{périgée}\index{perigee@périgée} le point de l'orbite de la Lune où cette distance est minimale et \emph{apogée}\index{apogee@apogée} celui où elle est maximale. -Au périgée, la distance Terre-Lune vaut : \SI{3,654e8}{\metre} et à l'apogée \SI{4,067e8}{\metre}. Comme la force de marée est inversément proportionnelle au cube de la distance (ce qui donne une puissance \(^{-3}\)), la différence de force de marée lunaire entre le maximum et le minimum par rapport au minimum vaut : +Au périgée, la distance Terre-Lune vaut~: \SI{3,654e8}{\metre} et à l'apogée \SI{4,067e8}{\metre}. Comme la force de marée est inversement proportionnelle au cube de la distance (ce qui donne une puissance \(^{-3}\)), la différence de force de marée lunaire entre le maximum et le minimum par rapport au minimum vaut~: \begin{align*} \Delta F_{mar\acute ee}^{lunaire}&=\frac{d_{p\acute erig\acute ee}^{-3}-d_{apog\acute ee}^{-3}}{d_{apo\acute ee}^{-3}}\\ &=\frac{(3,654\cdot 10^8)^{-3}-(4,067\cdot 10^8)^{-3}}{(4,067\cdot 10^8)^{-3}}\\ @@ -150,7 +150,7 @@ Ce rapport n'est de loin pas négligeable et il faut en tenir compte. \medskip L'orbite de la Terre autour du Soleil est aussi une ellipse\index{ellipse} et la distance Terre-Soleil varie aussi. On nome \emph{périhélie}\index{perihelie@périhélie} le point de l'orbite de la terre où cette distance est minimale et \emph{aphélie}\index{aphelie@aphélie} le point le plus éloigné. -Au périhélie (le 3 janvier) la distance Terre-Soleil vaut : \SI{1,471\cdot 10^{11}}{\metre} et à l'aphélie (le 3 juillet) \SI{1,521e11}{\metre}. Comme la force de marée est inversement proportionnelle au cube de la distance (ce qui donne une puissance \(^{-3}\)), la différence de force de marée solaire entre le maximum et le minimum par rapport au minimum vaut : +Au périhélie (le 3 janvier) la distance Terre-Soleil vaut~: \SI{1,471e11}{\metre} et à l'aphélie (le 3 juillet) \SI{1,521e11}{\metre}. Comme la force de marée est inversement proportionnelle au cube de la distance (ce qui donne une puissance \(^{-3}\)), la différence de force de marée solaire entre le maximum et le minimum par rapport au minimum vaut~: \begin{align*} \Delta F_{mar\acute ee}^{solaire}&=\frac{d_{p\acute erih\acute elie}^{-3}-d_{aph\acute elie}^{-3}}{d_{aph\acute elie}^{-3}}\\ &=\frac{(1,471\cdot 10^{11})^{-3}-(1,521\cdot 10^{11})^{-3}}{(1,521\cdot 10^{11})^{-3}}\\ @@ -172,9 +172,9 @@ De plus, si les prédictions de la théorie newtonienne sont bons en haute mer, La théorie ondulatoire de la marée repose sur de complexes équations dites de Laplace et inaccessible dans le cadre de ce cours. Mais on peut trouver une bonne description mathématique de cette théorie dans \cite{BS07}. \section{Limite de Roche\index{limite de Roche}}\label{limroche} -Les effets de marée présentés ci-dessus sont bien connus de tous puisqu'ils se manifestent clairement à nous sur les plages. Il faut aussi dire qu'il existe des marées terrestres : simultanément à la surface océanique, la Lune déforme la croute terrestre\index{croute terrestre}. Et il faut savoir que ces effets sont réciproques. Si la Lune exerce son influence sur la Terre, la Terre exerce aussi des forces de marée sur la Lune et celle-ci se déforme sous leurs effets. De la même manière, le satellite Io\index{Io} a un volcanisme\index{volcanisme} très actif dû aux effets de marées produits sur lui par la planète Jupiter. +Les effets de marée présentés ci-dessus sont bien connus de tous puisqu'ils se manifestent clairement à nous sur les plages. Il faut aussi dire qu'il existe des marées terrestres~: simultanément à la surface océanique, la Lune déforme la croûte terrestre\index{croûte terrestre}. Et il faut savoir que ces effets sont réciproques. Si la Lune exerce son influence sur la Terre, la Terre exerce aussi des forces de marée sur la Lune et celle-ci se déforme sous leurs effets. De la même manière, le satellite Io\index{Io} a un volcanisme\index{volcanisme} très actif dû aux effets de marées produits sur lui par la planète Jupiter. -Tant qu'un satellite est assez éloigné de la planète qui l'attire, les effets de marée se limitent à des frictions et à des déformations. Par contre, si le satellite s'en approche trop, il peut être détruit par les tensions internes qu'il va subir. C'est ce qui explique en partie pourquoi les anneaux d'astèroïdes\index{anneau d'astéroïdes}, comme ceux de Saturne\index{Saturne}, ne donnent pas naissance à des satellites sous l'effet de leur attraction mutuelle. La distance à partir de laquelle cela se produit est complexe à déterminer. Cependant, à l'aide de quelques approximations judicieuses, il est possible d'évaluer cette distance, qui porte le nom de \emph{limite de Roche} en hommage au physicien qui la découvrit. +Tant qu'un satellite est assez éloigné de la planète qui l'attire, les effets de marée se limitent à des frictions et à des déformations. Par contre, si le satellite s'en approche trop, il peut être détruit par les tensions internes qu'il va subir. C'est ce qui explique en partie pourquoi les anneaux d’astéroïdes\index{anneau d'astéroïdes}, comme ceux de Saturne\index{Saturne}, ne donnent pas naissance à des satellites sous l'effet de leur attraction mutuelle. La distance à partir de laquelle cela se produit est complexe à déterminer. Cependant, à l'aide de quelques approximations judicieuses, il est possible d'évaluer cette distance, qui porte le nom de \emph{limite de Roche} en hommage au physicien qui la découvrit. \subsection{Modèle simplifié} L'idée est de considérer un satellite situé à une distance \(d\) d'une planète comme composé de deux corps distincts maintenus ensemble par leur action gravifique mutuelle. La figure \ref{roche} présente la situation. @@ -185,16 +185,16 @@ L'idée est de considérer un satellite situé à une distance \(d\) d'une plan \includegraphics[width=6cm]{Roche.eps} \end{figure} -En raison de sa plus grande proximité, la force de gravitation exercée par la planète sur la partie du satellite la plus proche d'elle est plus importante que celle exercée sur la partie la plus éloignée. En supposant que les centres de masse des deux parties du satellite sont séparés par une distance \(2\cdot r\), on peut calculer la différence de force qui s'exerce : +En raison de sa plus grande proximité, la force de gravitation exercée par la planète sur la partie du satellite la plus proche d'elle est plus importante que celle exercée sur la partie la plus éloignée. En supposant que les centres de masse des deux parties du satellite sont séparés par une distance \(2\cdot r\), on peut calculer la différence de force qui s'exerce~: \[\Delta F=G\cdot \frac{M\cdot m}{(d-r)^2}-G\cdot \frac{M\cdot m}{(d+r)^2}\] -Pour simplifier cette expression, on peut écrire : +Pour simplifier cette expression, on peut écrire~: \begin{align*} \Delta F&=G\cdot \frac{m\cdot m}{d^2\cdot (1-r/d)^2}-G\cdot \frac{M\cdot m}{d^2\cdot (1+r/d)^2} \\ &=G\cdot \frac{M\cdot m}{d^2}\cdot ((1-r/d)^{-2})-(1+r/d)^{-2}) \end{align*} -En raison de la relation (de développement limité) suivante : +En raison de la relation (de développement limité) suivante~: \[(1+x)^p\simeq 1+p\cdot x\] -et du fait que \(r\ll d\), on peut réécrire la différence de force : +et du fait que \(r\ll d\), on peut réécrire la différence de force~: \begin{align*} \Delta F&=G\cdot \frac{M\cdot m}{d^2}\cdot ((1+2\cdot r/d)-(1-2\cdot r/d)) \\ &=G\cdot \frac{M\cdot m}{d^2}\cdot 4\cdot r/d \\ @@ -202,34 +202,34 @@ et du fait que \(r\ll d\), on peut réécrire la différence de force : \end{align*} \medskip -D'autre part, la force de cohésion gravitationnelle entre les deux parties du satellite est donnée par : +D'autre part, la force de cohésion gravitationnelle entre les deux parties du satellite est donnée par~: \[F_c=G\cdot \frac{m\cdot m}{(2\cdot r)^2}\] \medskip -Mais, le satellite est détruit quand la différence de force gravitationnelle (force de marée) produite par la planète sur le satellite est plus grande que la force de cohésion, c'est-à-dire : +Mais, le satellite est détruit quand la différence de force gravitationnelle (force de marée) produite par la planète sur le satellite est plus grande que la force de cohésion, c'est-à-dire~: \[4\cdot G\cdot \frac{M\cdot m}{d^3}\cdot r > G\cdot \frac{m\cdot m}{(2\cdot r)^2}\] \medskip -En utilisant les masses volumiques des deux corps, \(\rho_p\) pour la planète et \(\rho_s\) pour le satellite, on a : +En utilisant les masses volumiques des deux corps, \(\rho_p\) pour la planète et \(\rho_s\) pour le satellite, on a~: \begin{align*} M&=\frac{4}{3}\cdot \pi\cdot R^3\cdot \rho_p \\ m&=\frac{4}{3}\cdot \pi\cdot r^3\cdot \rho_s \end{align*} -où \(R\) est le rayon de la planète. Cela permet d'écrire : +où \(R\) est le rayon de la planète. Cela permet d'écrire~: \begin{align*} 4\cdot \frac{R^3\cdot \rho_p\cdot r^3\cdot \rho_s}{d^3}\cdot r &> \frac{(r^3\cdot \rho_s)^2}{4\cdot r^2} \\ 4\cdot \frac{R^3\cdot \rho_p}{d^3} &> \frac{\rho_s}{4} \\ 16\cdot R^3\cdot \frac{\rho_p}{\rho_s} &> d^3 \\ d &< R\cdot \sqrt[3]{16\cdot \frac{\rho_p}{\rho_s}} \end{align*} -avec finalement l'expression de la limite de Roche, c'est-à-dire la distance minimale, par rapport à la planète, à laquelle le satellite est détruit : +avec finalement l'expression de la limite de Roche, c'est-à-dire la distance minimale, par rapport à la planète, à laquelle le satellite est détruit~: \begin{equation} d_{Roche} = R\cdot \sqrt[3]{16\cdot \frac{\rho_p}{\rho_s}} \end{equation} \begin{figure}[t] \centering -\caption[Limite de Roche]{Limite de Roche\label{limitederoche}\endnote{Voir le site de l'encyclopédie Wikipedia : \url{http://fr.wikipedia.org/wiki/Limite_de_Roche} notamment pour le copyright de l'image.}} +\caption[Limite de Roche]{Limite de Roche\label{limitederoche}} \includegraphics[width=6cm]{LimiteRoche1.eps} \includegraphics[width=6cm]{LimiteRoche2.eps} \includegraphics[width=6cm]{LimiteRoche3.eps} @@ -238,23 +238,23 @@ d_{Roche} = R\cdot \sqrt[3]{16\cdot \frac{\rho_p}{\rho_s}} \end{figure} \subsection{Exemples} -L'une des planètes les plus intéressantes du point de vue de la limite de Roche est certainement Saturne en raison des ses satellites et de ses anneaux. Pour se faire une idée numérique du calcul de la limite de Roche, considérons par exemple Épiméthée, l'un de ses satellites dont la masse volumique vaut : -\[\rho_s=\SI{0,61\cdot 10^3}{\kilogrampercubicmetre}\] -Comme la masse volumique de Saturne vaut : -\[\rho_p=\SI{0,6873\cdot 10^3}{\kilogrampercubicmetre}\] -et que son rayon équatorial est \(R=\SI{60'268}{\kilo\metre}\), on peut calculer la limite de Roche : +L'une des planètes les plus intéressantes du point de vue de la limite de Roche (voir figure \ref{limitederoche}\endnote{Voir le site de l'encyclopédie Wikipedia~: \url{http://fr.wikipedia.org/wiki/Limite_de_Roche} notamment pour le copyright de l'image.}) est certainement Saturne en raison des ses satellites et de ses anneaux. Pour se faire une idée numérique du calcul de la limite de Roche, considérons par exemple Épiméthée, l'un de ses satellites dont la masse volumique vaut~: +\[\rho_s=\SI{0,61e3}{\kilo\gram\per\cubic\metre}\] +Comme la masse volumique de Saturne vaut~: +\[\rho_p=\SI{0,6873e3}{\kilo\gram\per\cubic\metre}\] +et que son rayon équatorial est \(R=\SI{60268}{\kilo\metre}\), on peut calculer la limite de Roche~: \begin{align*} d_{Roche} &= R\cdot \sqrt[3]{16\cdot \frac{\rho_p}{\rho_s}}\\ -&= 60'268\cdot \sqrt[3]{16\cdot \frac{0,6873\cdot 10^3}{0,61\cdot 10^3}}=\SI{158'027}{\kilo\metre} +&= 60'268\cdot \sqrt[3]{16\cdot \frac{0,6873\cdot 10^3}{0,61\cdot 10^3}}=\SI{158027}{\kilo\metre} \end{align*} -Sachant que le rayon de l'orbite d'Épiméthée est de 2,51 fois le rayon de Saturne, soit environ \SI{151'400}{\kilo\metre}, on peut calculer le rapport \(r\) de la distance d'Épiméthée-Saturne à la distance de Roche : +Sachant que le rayon de l'orbite d'Épiméthée est de 2,51 fois le rayon de Saturne, soit environ \SI{151400}{\kilo\metre}, on peut calculer le rapport \(r\) de la distance d'Épiméthée-Saturne à la distance de Roche~: \[r=\frac{151'400}{158'027}=0,96\] Épiméthée est donc à une distance de Saturne correspondant à 96\% de la limite de Roche. Cela peut s'expliquer par le fait que d'autres forces de cohésion que la gravité s'exercent dans le satellite. -Il est aussi intéressant de constater que les anneaux G et E de Saturne, situés respectivement de \SI{170'000}{} à \SI{175'000}{\kilo\metre} et de \SI{181'000}{} à \SI{483'000}{\kilo\metre} de Saturne, sont bien au-delà de la limite de Roche. Pour l'anneau E, il pourrait s'agir de matière volcanique éjectée par Encelade, l'un des satellites de Saturne. +Il est aussi intéressant de constater que les anneaux G et E de Saturne, situés respectivement de \SI{170000}{} à \SI{175000}{\kilo\metre} et de \SI{181000}{} à \SI{483000}{\kilo\metre} de Saturne, sont bien au-delà de la limite de Roche. Pour l'anneau E, il pourrait s'agir de matière volcanique éjectée par Encelade, l'un des satellites de Saturne. -En réalité le calcul de la limite de Roche réelle est plus compliqué que celui présenté ci-dessus et il mène à la distance suivante : +En réalité le calcul de la limite de Roche réelle est plus compliqué que celui présenté ci-dessus et il mène à la distance suivante~: \begin{equation} d_{roche} = 2,422649865\cdot R\cdot \sqrt[3]{\frac{\rho_p}{\rho_s}} \end{equation} -soit pour Épiméthée la valeur de \SI{151'932}{\kilo\metre}. +soit pour Épiméthée la valeur de \SI{151932}{\kilo\metre}. diff --git a/Annexe-MesuresDistances/Annexe-MesuresDistances.tex b/Annexe-MesuresDistances/Annexe-MesuresDistances.tex index 2f9d7af..cbf647c 100644 --- a/Annexe-MesuresDistances/Annexe-MesuresDistances.tex +++ b/Annexe-MesuresDistances/Annexe-MesuresDistances.tex @@ -54,11 +54,11 @@ Une première méthode simple consiste à observer une éclipse de Lune\index{ec \item La distance du Soleil à la Terre est finie et le Soleil a une taille importante par rapport à la Terre. Ainsi, l'ombre portée par la Terre sur la Lune n'a pas exactement la taille de la Terre. \item Sans photographie d'éclipses de Lune, il est très difficile de trouver le rapport de la taille de l'ombre de la Terre à celle de la Lune. \end{itemize} -Même de nos jours, si on utilise des images trop petites, l'incertitude sur le rayon du cercle qui sous-tend l'ombre de la Terre sur la Lune est important. La figure \ref{tailledelalune} montre en effet, suivant l'image choisie, un rapport de \(95/28,9=3,3\) à \(60/28,9=2,1\). +Même de nos jours, si on utilise des images trop petites, l'incertitude sur le rayon du cercle qui sous-tend l'ombre de la Terre sur la Lune est important. La figure \ref{tailledelalune}\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Eclipse\_lune.jpg=. notamment pour le copyright de l'image. Remerciements à son auteur Luc Viatour.} montre en effet, suivant l'image choisie, un rapport de \(95/28,9=3,3\) à \(60/28,9=2,1\). \begin{figure}[ht] \centering -\caption[Taille de la lune]{Taille de la lune\label{tailledelalune} \par \scriptsize{Une taille incertaine\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Eclipse\_lune.jpg=. notamment pour le copyright de l'image. Remerciements à son auteur Luc Viatour.}}} +\caption[Taille de la lune]{Taille de la lune\label{tailledelalune} \par \scriptsize{Une taille incertaine}} \includegraphics[width=6cm]{RayonLune.eps} \end{figure} diff --git a/Annexe-MesuresDistances/Annexe-MesuresDistances.tex.bak b/Annexe-MesuresDistances/Annexe-MesuresDistances.tex.bak index f06417c..2f9d7af 100644 --- a/Annexe-MesuresDistances/Annexe-MesuresDistances.tex.bak +++ b/Annexe-MesuresDistances/Annexe-MesuresDistances.tex.bak @@ -58,7 +58,7 @@ Même de nos jours, si on utilise des images trop petites, l'incertitude sur le \begin{figure}[ht] \centering -\caption[Taille de la lune]{Taille de la lune\label{tailledelalune} \par \scriptsize{Une taille incertaine\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Eclipse_lune.jpg=. notamment pour le copyright de l'image. Remerciements à son auteur Luc Viatour.}}} +\caption[Taille de la lune]{Taille de la lune\label{tailledelalune} \par \scriptsize{Une taille incertaine\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Eclipse\_lune.jpg=. notamment pour le copyright de l'image. Remerciements à son auteur Luc Viatour.}}} \includegraphics[width=6cm]{RayonLune.eps} \end{figure} @@ -93,7 +93,7 @@ en raison du fait que deux droites parallèles sont toujours coupées par une tr L'astronome Cassini, qui détermina pour la première fois la distance Terre-Soleil à partir de la parallaxe de Mars, décrit la mesure ainsi~: \begin{quotation} -``\textit{La meilleure méthode pour chercher la parallaxe de Mars par la correspondance des observations faites à Paris \& en Caïenne auroit été d'observer, par la lunette, la conjonction précise de cette planète avec une étoile fixe. Car si cette conjonction avoit été vue de l'un \& de l'autre lieu au même instant \& précisément de la même manière sans aucune distance, c'eût été une marque qu'il n'y avoit point de parallaxe sensible. S'il y en avoit eu quelque peu, à l'instant que Mars auroit paru toucher par son bord supérieur une Etoile fixe en Caïenne, il auroit paru à Paris un peu éloigné de la même Etoile vers l'Horizon, \& quand il auroit paru à Paris toucher l'Etoile par son bord inférieur, il auroit paru en Caïenne éloigné de la même Etoile vers le Zénit \& cette distance vue d'un lieu \& non pas de l'autre, aurait été attribuée à la parallaxe}'' J. D. Cassini, dans ``Mémoires de l'Académie Royale des Sciences'', volume 8, année 1730.\endnote{\url=http://www.iap.fr/InformationCommunication/ArticlesGrandPublic/Etoiles/Transit/transit_parallaxe_mars_1672.html=} +``\textit{La meilleure méthode pour chercher la parallaxe de Mars par la correspondance des observations faites à Paris \& en Caïenne auroit été d'observer, par la lunette, la conjonction précise de cette planète avec une étoile fixe. Car si cette conjonction avoit été vue de l'un \& de l'autre lieu au même instant \& précisément de la même manière sans aucune distance, c'eût été une marque qu'il n'y avoit point de parallaxe sensible. S'il y en avoit eu quelque peu, à l'instant que Mars auroit paru toucher par son bord supérieur une Etoile fixe en Caïenne, il auroit paru à Paris un peu éloigné de la même Etoile vers l'Horizon, \& quand il auroit paru à Paris toucher l'Etoile par son bord inférieur, il auroit paru en Caïenne éloigné de la même Etoile vers le Zénit \& cette distance vue d'un lieu \& non pas de l'autre, aurait été attribuée à la parallaxe}'' J. D. Cassini, dans ``Mémoires de l'Académie Royale des Sciences'', volume 8, année 1730.\endnote{\url=http://www.iap.fr/InformationCommunication/ArticlesGrandPublic/Etoiles/Transit/transit\_parallaxe\_mars\_1672.html=} \end{quotation} \begin{figure}[ht] @@ -113,7 +113,7 @@ où \(R_T\) est le rayon de la Terre. \smallskip Le résultat est donné par Cassini\index{Cassini} lui-même~: \begin{quotation} -``\textit{Le 5 septembre 1672, trois jours avant l'opposition du Soleil à Mars, nous observâmes à Paris trois Etoiles dans l'Eau Aquarius marquées par Bayerus \(\Psi\), vers lesquelles Mars alloit par son mouvement particulier rétrograde, de sorte que l'on jugeoit qu'il en auroit pu cacher une. Il étoit alors un peu plus septentrional que la plus septentrionale des trois. On prit la hauteur Méridienne de celle-ci qui passoit la première; \& celle de la moyenne vers laquelle le mouvement particulier de Mars s'adressoit. Par le choix des Observations les plus exactes \& les plus conformes entre elles, on fixa à 15" la parallaxe que fait Mars de Paris à Caïenne}'' J. D. Cassini, dans ``Mémoires de l'Académie Royale des Sciences'', volume 8, année 1730.\endnote{\url=http://www.iap.fr/InformationCommunication/ArticlesGrandPublic/Etoiles/Transit/transit_parallaxe_mars_1672.html=} +``\textit{Le 5 septembre 1672, trois jours avant l'opposition du Soleil à Mars, nous observâmes à Paris trois Etoiles dans l'Eau Aquarius marquées par Bayerus \(\Psi\), vers lesquelles Mars alloit par son mouvement particulier rétrograde, de sorte que l'on jugeoit qu'il en auroit pu cacher une. Il étoit alors un peu plus septentrional que la plus septentrionale des trois. On prit la hauteur Méridienne de celle-ci qui passoit la première; \& celle de la moyenne vers laquelle le mouvement particulier de Mars s'adressoit. Par le choix des Observations les plus exactes \& les plus conformes entre elles, on fixa à 15" la parallaxe que fait Mars de Paris à Caïenne}'' J. D. Cassini, dans ``Mémoires de l'Académie Royale des Sciences'', volume 8, année 1730.\endnote{\url=http://www.iap.fr/InformationCommunication/ArticlesGrandPublic/Etoiles/Transit/transit\_parallaxe\_mars\_1672.html=} \end{quotation} Le résultat de la mesure est donc de quinze secondes d'arc. Mais attention, il s'agit de la parallaxe qui est la moitié de l'angle \(\delta\). Celui-ci vaut donc~: \(\delta=0,008332^{\circ}\) ou \SI{1,454e-4}{\radian}. Avec une distance de Paris à Cayenne de \SI{7082,1}{\kilo\metre} cela donne~: \[MO=\frac{7,0821\cdot 10^6}{1,454\cdot 10^{-4}}=\SI{4,87e10}{\metre}\] diff --git a/Annexe-Rotations/Annexe-Rotations.tex b/Annexe-Rotations/Annexe-Rotations.tex index 33d7984..ee21d85 100644 --- a/Annexe-Rotations/Annexe-Rotations.tex +++ b/Annexe-Rotations/Annexe-Rotations.tex @@ -62,21 +62,21 @@ Le second problème tient dans la cinématique des planètes du système solaire \begin{figure}[t] \centering -\caption[Le système géocentrique de Tycho Brahé]{Le système géocentrique de Tycho Brahé\label{tychosystem} \par \scriptsize{Un modèle encore actuel\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://en.wikipedia.org/wiki/Image:Tychonian.gif= notamment pour le copyright de l'image.}.}} +\caption[Le système géocentrique de Tycho Brahé]{Le système géocentrique de Tycho Brahé\label{tychosystem} \par \scriptsize{Un modèle encore actuel.}} \includegraphics[width=6cm]{TychoSystem.eps} \end{figure} -Cette erreur, qui est celle du modèle de Ptolémée, si elle est bien une erreur, n'empêche pas qu'on puisse considérer que le Soleil tourne autour de la Terre, \emph{vu depuis la Terre}. Elle fut d'ailleurs reconnue et corrigée par Tycho Brahé\index{Tycho Brahe@Tycho Brahé} qui proposa un modèle (voir figure \ref{tychosystem}) où la Terre restait fixe dans l'univers, où le Soleil tournait autour d'elle et les autres planètes tournaient autour\dots\ du Soleil. Ce modèle, excepté la fixité de la Terre dans l'univers qui relève du premier problème énoncé ci-dessus, est parfaitement valide. Il s'agit tout simplement de la vision du système solaire \emph{relativement à la Terre}. Et la description actuelle des mouvements célestes vu depuis la Terre adopte un point de vue très proche de celui de Tycho Brahé, exception faite des orbites circulaires\index{orbite!circulaire} qui sont devenues des ellipses. +Cette erreur, qui est celle du modèle de Ptolémée, si elle est bien une erreur, n'empêche pas qu'on puisse considérer que le Soleil tourne autour de la Terre, \emph{vu depuis la Terre}. Elle fut d'ailleurs reconnue et corrigée par Tycho Brahé\index{Tycho Brahe@Tycho Brahé} qui proposa un modèle (voir figure \ref{tychosystem}\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://en.wikipedia.org/wiki/Image:Tychonian.gif= notamment pour le copyright de l'image.}) où la Terre restait fixe dans l'univers, où le Soleil tournait autour d'elle et les autres planètes tournaient autour\dots\ du Soleil. Ce modèle, excepté la fixité de la Terre dans l'univers qui relève du premier problème énoncé ci-dessus, est parfaitement valide. Il s'agit tout simplement de la vision du système solaire \emph{relativement à la Terre}. Et la description actuelle des mouvements célestes vu depuis la Terre adopte un point de vue très proche de celui de Tycho Brahé, exception faite des orbites circulaires\index{orbite!circulaire} qui sont devenues des ellipses. \section{Rotation du Soleil\index{rotation!du Soleil} dans la Voie Lactée\index{Voie Lactée}} On se propose de calculer la vitesse de rotation du Soleil dans notre galaxie, la Voie Lactée. -La figure \ref{milky_way_2005} présente une vue d'artiste de la Voie Lactée telle qu'on se la représente. La position du Soleil y figure sous la forme d'un point jaune. +La figure \ref{milky_way_2005}\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Milky\_Way\_2005.jpg=. Image dans le domaine public. Remerciements à la NASA.} présente une vue d'artiste de la Voie Lactée telle qu'on se la représente. La position du Soleil y figure sous la forme d'un point jaune. \begin{figure}[th] \centering -\caption[Le Soleil dans la Voie Lactée]{Le soleil dans la Voie Lactée\label{milky_way_2005} \par \scriptsize{Représentation artistique\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Milky\_Way\_2005.jpg=. Image dans le domaine public. Remerciements à la NASA.}}} +\caption[Le Soleil dans la Voie Lactée]{Le soleil dans la Voie Lactée\label{milky_way_2005} \par \scriptsize{Représentation artistique}} \includegraphics[width=6cm]{Milky_Way_2005_soleil.eps} \end{figure} diff --git a/Annexe-Satellites/Annexe-Satellites.tex b/Annexe-Satellites/Annexe-Satellites.tex index 17edf23..f670c05 100644 --- a/Annexe-Satellites/Annexe-Satellites.tex +++ b/Annexe-Satellites/Annexe-Satellites.tex @@ -49,7 +49,7 @@ De là on tire (faites les calculs vous-même)~: \begin{figure}[t] \centering -\caption[Satellite]{Satellite\label{satellite} \par \scriptsize{En orbite géostationnaire\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://fr.wikipedia.org/wiki/Image:Navstar-2.jpg= notamment pour le copyright de l'image. Remerciements à la NASA.}}} +\caption[Satellite]{Satellite\label{satellite} \par \scriptsize{En orbite géostationnaire}} \includegraphics[width=6cm]{Satellite.eps} \end{figure} @@ -61,7 +61,7 @@ h=\;&(\frac{6,67\cdot10^{-11}\cdot5,97\cdot10^{24}\cdot(24\cdot60\cdot60)^{2}}{4 & -6,37\cdot10^{6}=\SI{35857}{\kilo\metre} \end{align*} -Il s'agit de l'altitude des satellites en orbite géostationnaire au-dessus de l'équateur. Pour des latitudes plus élevées, on comprend bien que plus on monte vers le pôle, plus le satellite sera bas sur l'horizon. Il se peut même qu'ils soient sous l'horizon. C'est pourquoi d'autres types d'orbites sont nécessaires, comme l'orbite de Molniya, qui permet de couvrir à l'aide de plusieurs satellites les régions polaires vingt-quatre heures sur vingt-quatre. +Il s'agit de l'altitude des satellites en orbite géostationnaire (voir figure \ref{satellite}\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://fr.wikipedia.org/wiki/Image:Navstar-2.jpg= notamment pour le copyright de l'image. Remerciements à la NASA.}) au-dessus de l'équateur. Pour des latitudes plus élevées, on comprend bien que plus on monte vers le pôle, plus le satellite sera bas sur l'horizon. Il se peut même qu'ils soient sous l'horizon. C'est pourquoi d'autres types d'orbites sont nécessaires, comme l'orbite de Molniya, qui permet de couvrir à l'aide de plusieurs satellites les régions polaires vingt-quatre heures sur vingt-quatre. \smallskip L'équation \ref{vitessesatgeostat} permet alors de déterminer la vitesse du satellite sur son orbite. Pour un rayon de la terre \(R_T=\SI{6,37e6}{\metre}\) et une altitude \(h=\SI{35,857e6}{\metre}\), on a~: diff --git a/Cinematique/Cinematique.tex b/Cinematique/Cinematique.tex index 0939bc1..fcbf156 100644 --- a/Cinematique/Cinematique.tex +++ b/Cinematique/Cinematique.tex @@ -195,7 +195,7 @@ Ainsi, on peut écrire~: Cette équation donne la position\index{position@position} \(x(t)\) d'un objet au cours du temps en fonction de sa vitesse \(v_{o}\) (constante), de l'instant \(t\) qu'on considère et de sa position initiale \(x_{o}\). C'est une droite affine de pente \(v_{o}\) et d'ordonnée\index{ordonnee@ordonnée} initiale \(x_{o}\). \subsubsection{Un exemple~: Apollo\index{Apollo@Apollo} en route vers la Lune\index{Lune@Lune}} -Il s'agit ici d'un exemple - contre-exemple, comme nous allons le voir par la suite. D'une manière très grossière, on peut décrire le mouvement d'une capsule Apollo en route vers la Lune en trois phases~: +Il s'agit ici d'un exemple - contre-exemple, comme nous allons le voir par la suite. D'une manière très grossière, on peut décrire le mouvement d'une capsule Apollo (voir figure \ref{apollo16}\endnote{Voir le site de la NASA (notamment pour le copyright~: sans copyright)~: \url=http://grin.hq.nasa.gov/ABSTRACTS/GPN-2002-000069.html=}) en route vers la Lune en trois phases~: \begin{enumerate} \item La fusée décolle et amène la capsule à une altitude de \SI{370}{\kilo\metre} environ. Celle-ci est alors en orbite\index{orbite@orbite} autour de la Terre. \item On allume la propulsion pour la faire dégager de son orbite autour de la Terre. Elle se dirige alors vers la Lune. @@ -204,7 +204,7 @@ Il s'agit ici d'un exemple - contre-exemple, comme nous allons le voir par la su \begin{figure} \centering -\caption[Apollo 16]{Apollo 16\label{apollo16} \par \scriptsize{Rencontre du module de commande et du module lunaire d'Apollo 16 le 23 avril 1972\endnote{Voir le site de la NASA (notamment pour le copyright~: sans copyright)~: \url=http://grin.hq.nasa.gov/ABSTRACTS/GPN-2002-000069.html=}.}} +\caption[Apollo 16]{Apollo 16\label{apollo16} \par \scriptsize{Rencontre du module de commande et du module lunaire d'Apollo 16 le 23 avril 1972.}} \includegraphics[width=7cm]{Apollo16.eps} \end{figure} @@ -278,11 +278,11 @@ Contrairement à la plupart des galaxies\index{galaxie@galaxie} qui s'éloignent \begin{figure} \centering -\caption[Collision Andromède-Voie Lactée]{Collision Andromède-Voie Lactée\label{andromede_collision} \par \scriptsize{Rencontre, vue depuis la Terre, d'Andromède et de la Voie Lactée. Vue d'artiste\endnote{Voir le site de Wikicommon (notamment pour le copyright~: sans copyright)~: \url=http://commons.wikimedia.org/wiki/Image:Andromeda\_collision.jpg=}.}} +\caption[Collision Andromède-Voie Lactée]{Collision Andromède-Voie Lactée\label{andromede_collision} \par \scriptsize{Rencontre, vue depuis la Terre, d'Andromède et de la Voie Lactée. Vue d'artiste.}} \includegraphics[width=7cm]{Andromede_collision.eps} \end{figure} -A l'aide des données ci-dessous, calculez dans combien d'années elle rencontrera notre galaxie, la Voie Lactée\index{Voie@Voie!Lactée} (voir la figure \ref{andromede_collision}). +A l'aide des données ci-dessous, calculez dans combien d'années elle rencontrera notre galaxie, la Voie Lactée\index{Voie@Voie!Lactée} (voir la figure \ref{andromede_collision}\endnote{Voir le site de Wikicommon (notamment pour le copyright~: sans copyright)~: \url=http://commons.wikimedia.org/wiki/Image:Andromeda\_collision.jpg=}). \begin{center} \begin{tabular}{ll} @@ -700,7 +700,7 @@ Avec les observations de Galilée\index{Galilee@Galilée} (cratères sur la Lune \begin{figure}[t] \centering -\caption[Astronomica pars Optica]{Astronomica pars Optica\label{oeil}\endnote{Voir le site de wikipedia~: \url=http://fr.wikipedia.org/wiki/Image:Kepler\_Optica.jpg= notamment pour le copyright de l'image.}} +\caption[Astronomica pars Optica]{Astronomica pars Optica\label{oeil}} \includegraphics[width=6cm]{Kepler_Optica.eps} \end{figure} @@ -736,7 +736,7 @@ Ainsi, pour deux corps \(A\) et \(B\) tournant autour du même corps central, on Un exemple intéressant d'utilisation de la troisième loi de Kepler est celui de la rotation de la Lune autour de la Terre qui permet le calcul de l'altitude des satellites\index{satellite@satellite} en orbite géostationnaire\index{orbite@orbite!géostationnaire}. Il est traité au paragraphe \ref{keplergeostat} de l'annexe \ref{geostat}. \medskip -Notons encore que Kepler s'est aussi intéressé au fonctionnement de l'\oe il et aux théories de la lumière. En 1604, il rédige \emph{Astronomia pars Optica} un ouvrage d'optique où le rôle de la rétine\index{retine@rétine} et celui du cristallin\index{cristallin@cristallin} sont justement exposés. La figure \ref{oeil} présente un planche illustrant le fonctionnement de l'\oe il tirée de cet ouvrage. +Notons encore que Kepler s'est aussi intéressé au fonctionnement de l'\oe il et aux théories de la lumière. En 1604, il rédige \emph{Astronomia pars Optica} un ouvrage d'optique où le rôle de la rétine\index{retine@rétine} et celui du cristallin\index{cristallin@cristallin} sont justement exposés. La figure \ref{oeil}\endnote{Voir le site de wikipedia~: \url=http://fr.wikipedia.org/wiki/Image:Kepler\_Optica.jpg= notamment pour le copyright de l'image.} présente un planche illustrant le fonctionnement de l'\oe il tirée de cet ouvrage. \begin{sidewaysfigure*} %\begin{figure*}[!b] diff --git a/Cinematique/Cinematique.tex.bak b/Cinematique/Cinematique.tex.bak index 516985f..c18d81e 100644 --- a/Cinematique/Cinematique.tex.bak +++ b/Cinematique/Cinematique.tex.bak @@ -195,7 +195,7 @@ Ainsi, on peut écrire~: Cette équation donne la position\index{position@position} \(x(t)\) d'un objet au cours du temps en fonction de sa vitesse \(v_{o}\) (constante), de l'instant \(t\) qu'on considère et de sa position initiale \(x_{o}\). C'est une droite affine de pente \(v_{o}\) et d'ordonnée\index{ordonnee@ordonnée} initiale \(x_{o}\). \subsubsection{Un exemple~: Apollo\index{Apollo@Apollo} en route vers la Lune\index{Lune@Lune}} -Il s'agit ici d'un exemple - contre-exemple, comme nous allons le voir par la suite. D'une manière très grossière, on peut décrire le mouvement d'une capsule Apollo en route vers la Lune en trois phases~: +Il s'agit ici d'un exemple - contre-exemple, comme nous allons le voir par la suite. D'une manière très grossière, on peut décrire le mouvement d'une capsule Apollo (voir figure \ref{apollo16}\endnote{Voir le site de la NASA (notamment pour le copyright~: sans copyright)~: \url=http://grin.hq.nasa.gov/ABSTRACTS/GPN-2002-000069.html=}) en route vers la Lune en trois phases~: \begin{enumerate} \item La fusée décolle et amène la capsule à une altitude de \SI{370}{\kilo\metre} environ. Celle-ci est alors en orbite\index{orbite@orbite} autour de la Terre. \item On allume la propulsion pour la faire dégager de son orbite autour de la Terre. Elle se dirige alors vers la Lune. @@ -204,7 +204,7 @@ Il s'agit ici d'un exemple - contre-exemple, comme nous allons le voir par la su \begin{figure} \centering -\caption[Apollo 16]{Apollo 16\label{apollo16} \par \scriptsize{Rencontre du module de commande et du module lunaire d'Apollo 16 le 23 avril 1972\endnote{Voir le site de la NASA (notamment pour le copyright~: sans copyright)~: \url=http://grin.hq.nasa.gov/ABSTRACTS/GPN-2002-000069.html=}.}} +\caption[Apollo 16]{Apollo 16\label{apollo16} \par \scriptsize{Rencontre du module de commande et du module lunaire d'Apollo 16 le 23 avril 1972.}} \includegraphics[width=7cm]{Apollo16.eps} \end{figure} @@ -278,11 +278,11 @@ Contrairement à la plupart des galaxies\index{galaxie@galaxie} qui s'éloignent \begin{figure} \centering -\caption[Collision Andromède-Voie Lactée]{Collision Andromède-Voie Lactée\label{andromede_collision} \par \scriptsize{Rencontre, vue depuis la Terre, d'Andromède et de la Voie Lactée. Vue d'artiste\endnote{Voir le site de Wikicommon (notamment pour le copyright~: sans copyright)~: \url=http://commons.wikimedia.org/wiki/Image:Andromeda\_collision.jpg=}.}} +\caption[Collision Andromède-Voie Lactée]{Collision Andromède-Voie Lactée\label{andromede_collision} \par \scriptsize{Rencontre, vue depuis la Terre, d'Andromède et de la Voie Lactée. Vue d'artiste.}} \includegraphics[width=7cm]{Andromede_collision.eps} \end{figure} -A l'aide des données ci-dessous, calculez dans combien d'années elle rencontrera notre galaxie, la Voie Lactée\index{Voie@Voie!Lactée} (voir la figure \ref{andromede_collision}). +A l'aide des données ci-dessous, calculez dans combien d'années elle rencontrera notre galaxie, la Voie Lactée\index{Voie@Voie!Lactée} (voir la figure \ref{andromede_collision}\endnote{Voir le site de Wikicommon (notamment pour le copyright~: sans copyright)~: \url=http://commons.wikimedia.org/wiki/Image:Andromeda\_collision.jpg=}). \begin{center} \begin{tabular}{ll} @@ -687,7 +687,7 @@ Associé au très grand astronome Tycho Brahé\index{Brahe@Brahé!Tycho}, Johane Avec les observations de Galilée\index{Galilee@Galilée} (cratères sur la Lune\index{cratere@cratère!lunaire}, taches solaires\index{tache@tache!solaire}, phases de Vénus\index{phase@phase!de vénus} et satellites de Jupiter\index{satellite@satellite!de jupiter}), celles de Tycho Brahé sur le mouvement des comètes\index{comete@comète} à travers les sphères cristallines\index{sphere@sphère!cristalline} censées \og porter\fg{} les planètes, les calculs de Kepler vont non seulement permettre l'abandon de l'idée de fixité de la Terre, mais plus tard trouver une place importante dans la nouvelle physique élaborée par Newton. \smallskip -\raggedleft{\footnotesize{Portrait de Kepler tiré de Wikipedia\endnote{Voir \url=http://fr.wikipedia.org/wiki/Image:Johannes_Kepler_1610.jpg=}}} +\raggedleft{\footnotesize{Portrait de Kepler tiré de Wikipedia\endnote{Voir \url=http://fr.wikipedia.org/wiki/Image:Johannes\_Kepler\_1610.jpg=}}} \end{minipage} \hfill \begin{minipage}[b]{6.5cm} @@ -700,7 +700,7 @@ Avec les observations de Galilée\index{Galilee@Galilée} (cratères sur la Lune \begin{figure}[t] \centering -\caption[Astronomica pars Optica]{Astronomica pars Optica\label{oeil}\endnote{Voir le site de wikipedia~: \url=http://fr.wikipedia.org/wiki/Image:Kepler_Optica.jpg= notamment pour le copyright de l'image.}} +\caption[Astronomica pars Optica]{Astronomica pars Optica\label{oeil}\endnote{Voir le site de wikipedia~: \url=http://fr.wikipedia.org/wiki/Image:Kepler\_Optica.jpg= notamment pour le copyright de l'image.}} \includegraphics[width=6cm]{Kepler_Optica.eps} \end{figure} diff --git a/CoursMecaniqueOSDF-blx.bib b/CoursMecaniqueOSDF-blx.bib new file mode 100644 index 0000000..8b7e3e0 --- /dev/null +++ b/CoursMecaniqueOSDF-blx.bib @@ -0,0 +1,11 @@ +@Comment{$ biblatex control file $} +@Comment{$ biblatex bcf format version 3.9 $} +% Do not modify this file! +% +% This is an auxiliary file used by the 'biblatex' package. +% This file may safely be deleted. It will be recreated as +% required. + +@Control{biblatex-control, + options = {3.9:0:0:1:0:1:1:0:0:0:0:1:3:1:3:1:0:0:3:1:79:+:+:nty}, +} diff --git a/CoursMecaniqueOSDF.bbl b/CoursMecaniqueOSDF.bbl index 1190c23..f9d7d95 100644 --- a/CoursMecaniqueOSDF.bbl +++ b/CoursMecaniqueOSDF.bbl @@ -1,164 +1,602 @@ -\begin{thebibliography}{} -\expandafter\ifx\csname fonteauteurs\endcsname\relax -\def\fonteauteurs{\scshape}\fi -\expandafter\ifx\csname url\endcsname\relax - \def\url#1{{\tt #1}}% - \message{You should include the url package}\fi +% $ biblatex auxiliary file $ +% $ biblatex bbl format version 3.2 $ +% Do not modify the above lines! +% +% This is an auxiliary file used by the 'biblatex' package. +% This file may safely be deleted. It will be recreated by +% biber as required. +% +\begingroup +\makeatletter +\@ifundefined{ver@biblatex.sty} + {\@latex@error + {Missing 'biblatex' package} + {The bibliography requires the 'biblatex' package.} + \aftergroup\endinput} + {} +\endgroup -\bibitem[Alder, 2005]{AK05} -\bgroup\fonteauteurs\bgroup Alder\egroup\egroup{}, K. (2005). -\newblock {\em Mesurer le monde. L'incroyable histoire de l'invention du - m{\`e}tre.} -\newblock Flammarion, original 2002, 2005 pour la traduction, flammarion - \'edition. -\newblock Ouvrage remarquable qui interroge sur l'unification des syst{\`e}mes - d'unit{\'e}s. -\bibitem[Balibar \emph{et~al.}, 2005]{FB05} -\bgroup\fonteauteurs\bgroup Balibar\egroup\egroup{}, F., - \bgroup\fonteauteurs\bgroup L{\'e}vi-Leblond\egroup\egroup{}, J.-M. et - \bgroup\fonteauteurs\bgroup Lehoucq\egroup\egroup{}, R. (2005). -\newblock {\em Qu'est-ce que la mati{\`e}re}. -\newblock Le pommier/Cit{\'e} des sciences et de l'industrie, Paris. -\newblock Petit ouvrage d'une clart{\'e} extraordinaire. +\refsection{0} + \datalist[entry]{nty/global//global/global} + \entry{AK05}{book}{} + \name{author}{1}{}{% + {{hash=8c0c5de1f8c9a8409b5e6cd96ae760f4}{% + family={{Alder Ken}}, + familyi={A\bibinitperiod}}}% + } + \list{publisher}{1}{% + {Flammarion}% + } + \strng{namehash}{8c0c5de1f8c9a8409b5e6cd96ae760f4} + \strng{fullhash}{8c0c5de1f8c9a8409b5e6cd96ae760f4} + \strng{bibnamehash}{8c0c5de1f8c9a8409b5e6cd96ae760f4} + \strng{authorbibnamehash}{8c0c5de1f8c9a8409b5e6cd96ae760f4} + \strng{authornamehash}{8c0c5de1f8c9a8409b5e6cd96ae760f4} + \strng{authorfullhash}{8c0c5de1f8c9a8409b5e6cd96ae760f4} + \field{sortinit}{A} + \field{sortinithash}{2f401846e2029bad6b3ecc16d50031e2} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{edition}{Original 2002, 2005 pour la traduction, Flammarion} + \field{note}{Ouvrage remarquable qui interroge sur l'unification des systèmes d'unités.} + \field{title}{Mesurer le monde. {L}'incroyable histoire de l'invention du mètre.} + \field{year}{2005} + \endentry + \entry{AS06}{book}{} + \name{author}{1}{}{% + {{hash=71a02b3610717b0a25e22368a3f1629d}{% + family={{Arkan Simaan}}, + familyi={A\bibinitperiod}}}% + } + \list{publisher}{1}{% + {Vuibert / Adapt}% + } + \strng{namehash}{71a02b3610717b0a25e22368a3f1629d} + \strng{fullhash}{71a02b3610717b0a25e22368a3f1629d} + \strng{bibnamehash}{71a02b3610717b0a25e22368a3f1629d} + \strng{authorbibnamehash}{71a02b3610717b0a25e22368a3f1629d} + \strng{authornamehash}{71a02b3610717b0a25e22368a3f1629d} + \strng{authorfullhash}{71a02b3610717b0a25e22368a3f1629d} + \field{extraname}{1} + \field{sortinit}{A} + \field{sortinithash}{2f401846e2029bad6b3ecc16d50031e2} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{month}{3} + \field{title}{La science au péril de sa vie ; les aventuriers de la mesure du monde} + \field{year}{2006} + \endentry + \entry{AS02}{article}{} + \name{author}{1}{}{% + {{hash=71a02b3610717b0a25e22368a3f1629d}{% + family={{Arkan Simaan}}, + familyi={A\bibinitperiod}}}% + } + \strng{namehash}{71a02b3610717b0a25e22368a3f1629d} + \strng{fullhash}{71a02b3610717b0a25e22368a3f1629d} + \strng{bibnamehash}{71a02b3610717b0a25e22368a3f1629d} + \strng{authorbibnamehash}{71a02b3610717b0a25e22368a3f1629d} + \strng{authornamehash}{71a02b3610717b0a25e22368a3f1629d} + \strng{authorfullhash}{71a02b3610717b0a25e22368a3f1629d} + \field{extraname}{2} + \field{sortinit}{A} + \field{sortinithash}{2f401846e2029bad6b3ecc16d50031e2} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{journaltitle}{Bulletin de l'Union des physiciens} + \field{month}{7} + \field{note}{Suite à l'article ``Histoire des sciences : une expérience pédagogique en seconde'', BUP No 843, avril 2002.} + \field{title}{Sur l'expérience d'Érathostène} + \field{volume}{96} + \field{year}{2002} + \field{pages}{1193\bibrangedash 1196} + \range{pages}{4} + \endentry + \entry{BS07}{book}{} + \name{author}{1}{}{% + {{hash=739f0c4a0f4d7a131912111ebfc75e53}{% + family={{Bernard Simon}}, + familyi={B\bibinitperiod}}}% + } + \list{publisher}{1}{% + {Institut océanographique, Paris-Monaco}% + } + \strng{namehash}{739f0c4a0f4d7a131912111ebfc75e53} + \strng{fullhash}{739f0c4a0f4d7a131912111ebfc75e53} + \strng{bibnamehash}{739f0c4a0f4d7a131912111ebfc75e53} + \strng{authorbibnamehash}{739f0c4a0f4d7a131912111ebfc75e53} + \strng{authornamehash}{739f0c4a0f4d7a131912111ebfc75e53} + \strng{authorfullhash}{739f0c4a0f4d7a131912111ebfc75e53} + \field{sortinit}{B} + \field{sortinithash}{d7095fff47cda75ca2589920aae98399} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{month}{1} + \field{note}{Ouvrage très complet et très mathématique d'analyse du phénomène de marée. 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C'est un ouvrage qui nous place au cœur même des modèles mathématiques nécessaires pour prévoir les marées.} + \field{title}{La marée {L}a marée océanique côtière} + \field{year}{2007} + \endentry + \entry{BM85}{book}{} + \name{author}{1}{}{% + {{hash=0ab1598c0bee2b580b616b87deaf869f}{% + family={{Biarnais Marie-Françoise}}, + familyi={B\bibinitperiod}}}% + } + \list{publisher}{1}{% + {Christian Bourgois}% + } + \strng{namehash}{0ab1598c0bee2b580b616b87deaf869f} + \strng{fullhash}{0ab1598c0bee2b580b616b87deaf869f} + \strng{bibnamehash}{0ab1598c0bee2b580b616b87deaf869f} + \strng{authorbibnamehash}{0ab1598c0bee2b580b616b87deaf869f} + \strng{authornamehash}{0ab1598c0bee2b580b616b87deaf869f} + \strng{authorfullhash}{0ab1598c0bee2b580b616b87deaf869f} + \field{sortinit}{B} + \field{sortinithash}{d7095fff47cda75ca2589920aae98399} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{title}{{i}saac newton, principia mathematica} + \field{year}{1985} + \endentry + 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Il existe aussi son pendant ``Histoire de l'astronomie ancienne''.} + \field{title}{Histoire de l'astronomie moderne} + \field{year}{1821} + \endentry + \entry{JR07}{article}{} + \name{author}{1}{}{% + {{hash=16c3c73532fb66aa22bcdf1e86bfafad}{% + family={{Jean-François Robredo}}, + familyi={J\bibinitperiod}}}% + } + \strng{namehash}{16c3c73532fb66aa22bcdf1e86bfafad} + \strng{fullhash}{16c3c73532fb66aa22bcdf1e86bfafad} + \strng{bibnamehash}{16c3c73532fb66aa22bcdf1e86bfafad} + \strng{authorbibnamehash}{16c3c73532fb66aa22bcdf1e86bfafad} + \strng{authornamehash}{16c3c73532fb66aa22bcdf1e86bfafad} + \strng{authorfullhash}{16c3c73532fb66aa22bcdf1e86bfafad} + \field{sortinit}{J} + \field{sortinithash}{b2f54a9081ace9966a7cb9413811edb4} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{journaltitle}{Ciel et Espace} + \field{month}{6} + \field{title}{Comment l'univers à perdu tout point fixe} + \field{volume}{Juin 2007} + \field{year}{2007} + \endentry + \entry{JL96}{book}{} + \name{author}{1}{}{% + {{hash=aed2651c169057c92759fc831d627253}{% + family={{Jean-Marc Lévy-Leblond}}, + familyi={J\bibinitperiod}}}% + } + \list{publisher}{1}{% + {Gallimard nrf essais}% + } + \strng{namehash}{aed2651c169057c92759fc831d627253} + \strng{fullhash}{aed2651c169057c92759fc831d627253} + \strng{bibnamehash}{aed2651c169057c92759fc831d627253} + \strng{authorbibnamehash}{aed2651c169057c92759fc831d627253} + \strng{authornamehash}{aed2651c169057c92759fc831d627253} + \strng{authorfullhash}{aed2651c169057c92759fc831d627253} + \field{extraname}{1} + \field{sortinit}{J} + \field{sortinithash}{b2f54a9081ace9966a7cb9413811edb4} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{title}{Au contraires {L}'exercice de la pensée et la pratique de la science} + \field{year}{1996} + \endentry + \entry{JL06}{book}{} + \name{author}{1}{}{% + {{hash=aed2651c169057c92759fc831d627253}{% + family={{Jean-Marc Lévy-Leblond}}, + familyi={J\bibinitperiod}}}% + } + \list{publisher}{1}{% + {Traces écrites, Édition du Seuil}% + } + \strng{namehash}{aed2651c169057c92759fc831d627253} + \strng{fullhash}{aed2651c169057c92759fc831d627253} + \strng{bibnamehash}{aed2651c169057c92759fc831d627253} + \strng{authorbibnamehash}{aed2651c169057c92759fc831d627253} + \strng{authornamehash}{aed2651c169057c92759fc831d627253} + \strng{authorfullhash}{aed2651c169057c92759fc831d627253} + \field{extraname}{2} + \field{sortinit}{J} + \field{sortinithash}{b2f54a9081ace9966a7cb9413811edb4} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{month}{9} + \field{title}{De la matière relativiste quantique interactive} + \field{year}{2006} + \endentry + \entry{SU03}{book}{} + \name{author}{1}{}{% + {{hash=ee65ff54fd8fa04830a0f956f1968dc3}{% + family={{Leonard Susskind, George Hrabovsky}}, + familyi={L\bibinitperiod}}}% + } + \list{publisher}{1}{% + {Presse polytechniques et universitaires romandes, Lausanne}% + } + 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\field{sortinithash}{2cd7140a07aea5341f9e2771efe90aae} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{month}{6} + \field{note}{Excellent ouvrage qui décompose l'analyse du phénomène des marées en différents rythmes. Cela permet une très grande clarté dans l'explication astronomique et essentiellement newtonnienne (même si les marées côtières sont abordées).} + \field{title}{Tout savoir sur les marées} + \field{year}{2004} + \endentry + \entry{OP06}{book}{} + \name{author}{1}{}{% + {{hash=fb3450b713e2db55c173dbd604414d19}{% + family={{Ollivier Philippe}}, + familyi={O\bibinitperiod}}}% + } + \name{editor}{1}{}{% + {{hash=c8ab51a8e3099e70488607f1552d8fed}{% + family={{Philippe Terrancle}}, + familyi={P\bibinitperiod}}}% + } + \strng{namehash}{fb3450b713e2db55c173dbd604414d19} + \strng{fullhash}{fb3450b713e2db55c173dbd604414d19} + \strng{bibnamehash}{fb3450b713e2db55c173dbd604414d19} + \strng{authorbibnamehash}{fb3450b713e2db55c173dbd604414d19} + \strng{authornamehash}{fb3450b713e2db55c173dbd604414d19} + \strng{authorfullhash}{fb3450b713e2db55c173dbd604414d19} + \strng{editorbibnamehash}{c8ab51a8e3099e70488607f1552d8fed} + \strng{editornamehash}{c8ab51a8e3099e70488607f1552d8fed} + \strng{editorfullhash}{c8ab51a8e3099e70488607f1552d8fed} + \field{sortinit}{O} + \field{sortinithash}{2cd7140a07aea5341f9e2771efe90aae} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{month}{3} + \field{title}{Éoliennes, quand le vent nous éclaire} + \field{year}{2006} + \endentry + \entry{SH03}{book}{} + \name{author}{1}{}{% + {{hash=4f0301d41295d80fddb85377f4c6767e}{% + family={{Stephen Hawking}}, + familyi={S\bibinitperiod}}}% + } + \list{publisher}{1}{% + {Dunod, Paris}% + } + \strng{namehash}{4f0301d41295d80fddb85377f4c6767e} + \strng{fullhash}{4f0301d41295d80fddb85377f4c6767e} + \strng{bibnamehash}{4f0301d41295d80fddb85377f4c6767e} + \strng{authorbibnamehash}{4f0301d41295d80fddb85377f4c6767e} + \strng{authornamehash}{4f0301d41295d80fddb85377f4c6767e} + \strng{authorfullhash}{4f0301d41295d80fddb85377f4c6767e} + \field{sortinit}{S} + \field{sortinithash}{b164b07b29984b41daf1e85279fbc5ab} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{title}{Sur les épaules des géants} + \field{year}{2003} + \endentry + \entry{SV06}{book}{} + \name{author}{1}{}{% + {{hash=0776fd10842ddbecbd5a6f397177bfdd}{% + family={{Sylvie Vauclair}}, + familyi={S\bibinitperiod}}}% + } + \list{publisher}{1}{% + {Odile Jacob, Paris}% + } + \strng{namehash}{0776fd10842ddbecbd5a6f397177bfdd} + \strng{fullhash}{0776fd10842ddbecbd5a6f397177bfdd} + \strng{bibnamehash}{0776fd10842ddbecbd5a6f397177bfdd} + \strng{authorbibnamehash}{0776fd10842ddbecbd5a6f397177bfdd} + \strng{authornamehash}{0776fd10842ddbecbd5a6f397177bfdd} + \strng{authorfullhash}{0776fd10842ddbecbd5a6f397177bfdd} + \field{sortinit}{S} + \field{sortinithash}{b164b07b29984b41daf1e85279fbc5ab} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{month}{10} + \field{title}{La naissance des éléments. {D}u big bang à la terre.} + \field{year}{2006} + \endentry + \enddatalist +\endrefsection +\endinput -\bibitem[Biarnais, 1985]{BM85} -\bgroup\fonteauteurs\bgroup Biarnais\egroup\egroup{}, M.-F. (1985). -\newblock {\em isaac newton, principia mathematica}. -\newblock Christian Bourgois. - -\bibitem[Casoli et Encrenaz, 2005]{FC05} -\bgroup\fonteauteurs\bgroup Casoli\egroup\egroup{}, F. et - \bgroup\fonteauteurs\bgroup Encrenaz\egroup\egroup{}, T. (2005). -\newblock {\em Plan{\`e}tes extrasolaires}. -\newblock Belin Pour la science. - -\bibitem[Delambre, 1821]{JJD21} -\bgroup\fonteauteurs\bgroup Delambre\egroup\egroup{}, J.-B.~J. (1821). -\newblock {\em Histoire de l'astronomie moderne}. -\newblock Courcier, Paris. -\newblock Ce livre est publi{\'e} par google book {\`a} l'adresse - http://books.google.ch sous ``Histoire de l'astronomie moderne''. Il existe - aussi son pendant ``Histoire de l'astronomie ancienne''. - -\bibitem[Galilei, 1992]{GG92} -\bgroup\fonteauteurs\bgroup Galilei\egroup\egroup{}, G. (1992). -\newblock {\em Dialogue sur les deux grands syst{\`e}mes du monde}. -\newblock Seuil Points Sciences. - -\bibitem[Gould, 2005]{GSJ05} -\bgroup\fonteauteurs\bgroup Gould\egroup\egroup{}, S.~J. (2005). -\newblock {\em Le renard et le h{\'e}risson}. -\newblock Seuil, science ouverte, harmony books, new york, 2003 \'edition. - -\bibitem[Gruber, 1988]{GC88} -\bgroup\fonteauteurs\bgroup Gruber\egroup\egroup{}, C. (1988). -\newblock {\em M{\'e}canique g{\'e}n{\'e}rale}. -\newblock Presses polytechniques romandes, CH-1015 Lausanne, premi{\`e}re - \'edition. -\newblock Ouvrage tr{\`e}s complet mais tr{\`e}s math{\'e}matique. - -\bibitem[Gu{\'e}rin, 2004]{OG04} -\bgroup\fonteauteurs\bgroup Gu{\'e}rin\egroup\egroup{}, O. (2004). -\newblock {\em Tout savoir sur les mar{\'e}es}. -\newblock {\'E}ditions Ouest-France. -\newblock Excellent ouvrage qui d{\'e}compose l'analyse du ph{\'e}nom{\`e}ne - des mar{\'e}es en diff{\'e}rents rythmes. Cela permet une tr{\`e}s grande - clart{\'e} dans l'explication astronomique et essentiellement newtonienne - (m{\^e}me si les mar{\'e}es c{\^o}ti{\`e}res sont abord{\'e}es). - -\bibitem[Hawking, 2003]{SH03} -\bgroup\fonteauteurs\bgroup Hawking\egroup\egroup{}, S. (2003). -\newblock {\em Sur les {\'e}paules des g{\'e}ants}. -\newblock Dunod, Paris. - -\bibitem[L{\'e}vy-Leblond, 1996]{JL96} -\bgroup\fonteauteurs\bgroup L{\'e}vy-Leblond\egroup\egroup{}, J.-M. (1996). -\newblock {\em Aux contraires L'exercice de la pens{\'e}e et la pratique de la - science}. -\newblock Gallimard nrf essais. - -\bibitem[L{\'e}vy-Leblond, 2006]{JL06} -\bgroup\fonteauteurs\bgroup L{\'e}vy-Leblond\egroup\egroup{}, J.-M. (2006). -\newblock {\em De la mati{\`e}re relativiste quantique interactive}. -\newblock Traces {\'e}crites, {\'E}dition du Seuil. - -\bibitem[Lhomme, 2004]{LJ04} -\bgroup\fonteauteurs\bgroup Lhomme\egroup\egroup{}, J.-C. (2004). -\newblock {\em Les {\'e}nergies renouvelables}. -\newblock Delachaux et Niestl{\'e}, r{\'e}impression 2005, second tirage - \'edition. - -\bibitem[Lindemann, 1999]{EL99} -\bgroup\fonteauteurs\bgroup Lindemann\egroup\egroup{}, E. (1999). -\newblock {\em M{\'e}canique}. -\newblock DeBoeck Universit{\'e}. - -\bibitem[Nollert et Ruder, 2008]{HNHR08} -\bgroup\fonteauteurs\bgroup Nollert\egroup\egroup{}, H.-P. et - \bgroup\fonteauteurs\bgroup Ruder\egroup\egroup{}, H. (2008). -\newblock {\em Carnets de voyages relativistes. De la terre vers un trou noir.} -\newblock Belin, Pour la science. - -\bibitem[Ollivier, 2006]{OP06} -\bgroup\fonteauteurs\bgroup Ollivier\egroup\egroup{}, P. (2006). -\newblock {\em {\'E}oliennes, quand le vent nous {\'e}claire}. -\newblock Privat. - -\bibitem[Reeves et Lenoir, 2003]{HRaFL03} -\bgroup\fonteauteurs\bgroup Reeves\egroup\egroup{}, H. et - \bgroup\fonteauteurs\bgroup Lenoir\egroup\egroup{}, F. (2003). -\newblock {\em Mal de Terre}. -\newblock {\'E}dition du Seuil, Paris. - -\bibitem[Robredo, 2007]{JR07} -\bgroup\fonteauteurs\bgroup Robredo\egroup\egroup{}, J.-F. (2007). -\newblock Comment l'univers {\`a} perdu tout point fixe. -\newblock {\em Ciel et Espace}, Juin 2007. - -\bibitem[Rocchi, 2000]{JR00} -\bgroup\fonteauteurs\bgroup Rocchi\egroup\egroup{}, J. (2000). -\newblock {\em Giordano Bruno apr{\`e}s le b{\^u}cher}. -\newblock Complexe. -\newblock Un ouvrage fantastique qui remet Galil{\'e}e {\`a} sa juste place. - -\bibitem[Simaan, 2002]{AS02} -\bgroup\fonteauteurs\bgroup Simaan\egroup\egroup{}, A. (2002). -\newblock Sur l'exp{\'e}rience d'{\'e}rathost{\`e}ne. -\newblock {\em Bulletin de l'Union des physiciens}, 96\string:\penalty500\relax - 1193--1196. -\newblock Suite {\`a} l'article ``Histoire des sciences : une exp{\'e}rience - p{\'e}dagogique en seconde'', BUP No 843, avril 2002. - -\bibitem[Simaan, 2006]{AS06} -\bgroup\fonteauteurs\bgroup Simaan\egroup\egroup{}, A. (2006). -\newblock {\em La science au p{\'e}ril de sa vie ; les aventuriers de la mesure - du monde}. -\newblock Vuibert / Adapt. - -\bibitem[Simon, 2007]{BS07} -\bgroup\fonteauteurs\bgroup Simon\egroup\egroup{}, B. (2007). -\newblock {\em La mar{\'e}e La mar{\'e}e oc{\'e}anique c{\^o}ti{\`e}re}. -\newblock Institut oc{\'e}anographique, Paris-Monaco. -\newblock Ouvrage tr{\`e}s complet et tr{\`e}s math{\'e}matique d'analyse du - ph{\'e}nom{\`e}ne de mar{\'e}e. La description statique de Newton est - donn{\'e}e en terme de changement de r{\'e}f{\'e}rentiel non intertiel et en - language vectoriel. Mais la construction de Procor y est tr{\`e}s - pr{\'e}cis{\'e}ment justifi{\'e}e, ce qui est un grand m{\'e}rite. La - description dynamique constitue le principal de l'ouvrage et se fonde sur - l'analyse de Laplace. C'est un ouvrage qui nous place au coeur m{\^e}me des - mod{\`e}les math{\'e}matiques n{\'e}cessaires pour pr{\'e}voir les - mar{\'e}es. - -\bibitem[Susskind et Hrabovsky, 2017]{SU03} -\bgroup\fonteauteurs\bgroup Susskind\egroup\egroup{}, L. et - \bgroup\fonteauteurs\bgroup Hrabovsky\egroup\egroup{}, G. (2017). -\newblock {\em Le minimum th\'eorique}. -\newblock Presse polytechniques et universitaires romandes, Lausanne. - -\bibitem[Vauclair, 2006]{SV06} -\bgroup\fonteauteurs\bgroup Vauclair\egroup\egroup{}, S. (2006). -\newblock {\em La naissance des {\'e}l{\'e}ments. Du big bang {\`a} la Terre.} -\newblock Odile Jacob, Paris. - -\end{thebibliography} diff --git a/CoursMecaniqueOSDF.bcf b/CoursMecaniqueOSDF.bcf new file mode 100644 index 0000000..3486e96 --- /dev/null +++ b/CoursMecaniqueOSDF.bcf @@ -0,0 +1,2434 @@ + + + + + + output_encoding + utf8 + + + input_encoding + utf8 + + + debug + 0 + + + mincrossrefs + 2 + + + minxrefs + 2 + + + sortcase + 1 + + + sortupper + 1 + + + + + + + alphaothers + + + + + labelalpha + 0 + + + labelnamespec + shortauthor + author + shorteditor + editor + translator + + + labeltitle + 0 + + + labeltitlespec + shorttitle + title + maintitle + + + labeltitleyear + 0 + + + labeldateparts + 0 + + + labeldatespec + date + year + eventdate + origdate + urldate + nodate + + + julian + 0 + + + gregorianstart + 1582-10-15 + + + maxalphanames + 3 + + + maxbibnames + 3 + + + maxcitenames + 3 + + + maxsortnames + 3 + + + maxitems + 3 + + + minalphanames + 1 + + + minbibnames + 1 + + + mincitenames + 1 + + + minsortnames + 1 + + 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MecaniqueDim/MecaniqueDim.aux -A level-1 auxiliary file: MecaniqueDifferentielle/MecaniqueDifferentielle.aux -A level-1 auxiliary file: QtiteMvt/QtiteMvt.aux -A level-1 auxiliary file: Energie/Energie.aux -A level-1 auxiliary file: EnergieOS/EnergieOS.aux -A level-1 auxiliary file: PhysiqueTheorique/PhysiqueTheorique.aux -A level-1 auxiliary file: Thermodynamique/Thermodynamique.aux -A level-1 auxiliary file: ThermodynamiqueOS/ThermodynamiqueOS.aux -A level-1 auxiliary file: Annexe-UnitesInternationales/Annexe-UnitesInternationales.aux -A level-1 auxiliary file: Annexe-SystemeCoordonnees/Annexe-SystemeCoordonnees.aux -A level-1 auxiliary file: Annexe-MesuresDistances/Annexe-MesuresDistances.aux -A level-1 auxiliary file: Annexe-TravauxPratiques/Annexe-TravauxPratiques.aux -A level-1 auxiliary file: Annexe-Rotations/Annexe-Rotations.aux -A level-1 auxiliary file: Annexe-MRUA/Annexe-MRUA.aux -A level-1 auxiliary file: Annexe-ChuteLune/Annexe-ChuteLune.aux -A level-1 auxiliary file: 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'variable = shifted' with 'variable = non-ignorable' +[434] UCollate.pm:68> INFO - Overriding locale 'fr-FR' defaults 'normalization = NFD' with 'normalization = prenormalized' +[435] Biber.pm:4221> INFO - Sorting list 'nty/global//global/global' of type 'entry' with template 'nty' and locale 'fr-FR' +[435] Biber.pm:4227> INFO - No sort tailoring available for locale 'fr-FR' +[456] bbl.pm:654> INFO - Writing 'CoursMecaniqueOSDF.bbl' with encoding 'UTF-8' +[465] bbl.pm:757> INFO - Output to CoursMecaniqueOSDF.bbl diff --git a/CoursMecaniqueOSDF.out b/CoursMecaniqueOSDF.out index 885fc52..01aa3f0 100644 --- a/CoursMecaniqueOSDF.out +++ b/CoursMecaniqueOSDF.out @@ -421,3 +421,5 @@ \BOOKMARK [2][-]{subsection.M.3.5}{\376\377\000R\000\351\000s\000u\000m\000\351}{section.M.3}% 421 \BOOKMARK [2][-]{subsection.M.3.6}{\376\377\000E\000x\000e\000m\000p\000l\000e\000s}{section.M.3}% 422 \BOOKMARK 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+ + + + + + + + + + + + + + +]> + + + latex + + CoursMecaniqueOSDF.bcf + + + CoursMecaniqueOSDF.bbl + + + blx-dm.def + blx-compat.def + biblatex.def + standard.bbx + numeric.bbx + numeric.cbx + biblatex.cfg + french.lbx + english.lbx + + + + biber + + biber + CoursMecaniqueOSDF + + + CoursMecaniqueOSDF.bcf + + + CoursMecaniqueOSDF.bbl + + + CoursMecaniqueOSDF.bbl + + + CoursMecaniqueOSDF.bcf + + + Bibliographies/BiblioCoursOS.bib + + + diff --git a/CoursMecaniqueOSDF.tex b/CoursMecaniqueOSDF.tex index fd97c52..53709ca 100644 --- a/CoursMecaniqueOSDF.tex +++ b/CoursMecaniqueOSDF.tex @@ -8,6 +8,8 @@ \usepackage[arrow,matrix,tips,frame]{xy} %\renewcommand{\bibname}{Bibliographie} +% Attention, à la fin du fichier Préambule.tex il faut choisir +% la bibliographie pour DF ou OS %\usepackage[DF]{optional} % Pour réaliser le cours de base de Discipline Fondamentale (DF) \usepackage[OS]{optional} % Pour réaliser le cours complet d'Option Spécifique (OS) % La commande pour ajouter les parties d'OS est \opt{OS}{parties} @@ -156,16 +158,32 @@ \opt{OS}{\include{Annexe-Incertitudes/Annexe-Incertitudes}} %-------------------------------------------------------------- -\theendnotes +\printendnotes +%\theendnotes \myclearpage + \renewcommand{\bibname}{Bibliographie} +% !!! c'est maintenant biber qui est utilisé !!! +%\printbibheading[heading=bibintoc] +\sloppy % pour une meilleures césure des url dans les références biblio. Retirez si nécessaire. + +% Les livres ou autres, à l'exception des sites internet +\printbibliography[heading=bibintoc]%[heading=subbibliography,heading=subbibintoc,category=cited,title={La biblio}] + %\nocite{*} % pour mettre toutes les entrées dans la biblio, y compris celles non citées ds le texte -\bibliographystyle{apalike-fr} % le style de bibliographie apalike francisé. Attention, il ne faut pas le module apalike, mais il faut le module natbib. + +%\bibliographystyle{apalike-fr} % le style de bibliographie apalike francisé. Attention, il ne faut pas le module apalike, mais il faut le module natbib. %\bibliographystyle{apalike} % le style de bibliographie -\bibliography{Bibliographies/BiblioCours} % définit le fichier des réf. biblio. nom.bib + +% !!! Cette commande est dans le préambule ou deux bibliographies +% différentes pour DF et OS sont présentes +%%%%%\bibliography{Bibliographies/BiblioCours} % définit le fichier des réf. biblio. nom.bib + % le logiciel utilisé pour faire la biblio est pybliographic (pybliographer en ligne de commande) !!! suite à la suppression de - % pybliographic (pybliographer a maintenant une ui) de Lenny, j'utilise JABREF <-- très très bien. + % pybliographic (pybliographer a maintenant une ui) de Lenny, j'utilise JABREF <-- très très bien. + +% L'index \printindex{} % attention, pour que l'index soit mis à jour il faut lancer la commande de konsole~: makeindex -s ../Perso.ist nom_du_cours.idx % le Perso.ist est un fichier disant qu'il faut mettre des lettres entre les parties de l'index % les clés d'index doivent être sous la forme \index{energie@énergie!potentielle} voire avec plus de ! ; le premier mot doit être sans accents et la forme @ systèmatiquement présente. diff --git a/CoursMecaniqueOSDF.tex.bak b/CoursMecaniqueOSDF.tex.bak index fd97c52..53709ca 100644 --- a/CoursMecaniqueOSDF.tex.bak +++ b/CoursMecaniqueOSDF.tex.bak @@ -8,6 +8,8 @@ \usepackage[arrow,matrix,tips,frame]{xy} %\renewcommand{\bibname}{Bibliographie} +% Attention, à la fin du fichier Préambule.tex il faut choisir +% la bibliographie pour DF ou OS %\usepackage[DF]{optional} % Pour réaliser le cours de base de Discipline Fondamentale (DF) \usepackage[OS]{optional} % Pour réaliser le cours complet d'Option Spécifique (OS) % La commande pour ajouter les parties d'OS est \opt{OS}{parties} @@ -156,16 +158,32 @@ \opt{OS}{\include{Annexe-Incertitudes/Annexe-Incertitudes}} %-------------------------------------------------------------- -\theendnotes +\printendnotes +%\theendnotes \myclearpage + \renewcommand{\bibname}{Bibliographie} +% !!! c'est maintenant biber qui est utilisé !!! +%\printbibheading[heading=bibintoc] +\sloppy % pour une meilleures césure des url dans les références biblio. Retirez si nécessaire. + +% Les livres ou autres, à l'exception des sites internet +\printbibliography[heading=bibintoc]%[heading=subbibliography,heading=subbibintoc,category=cited,title={La biblio}] + %\nocite{*} % pour mettre toutes les entrées dans la biblio, y compris celles non citées ds le texte -\bibliographystyle{apalike-fr} % le style de bibliographie apalike francisé. Attention, il ne faut pas le module apalike, mais il faut le module natbib. + +%\bibliographystyle{apalike-fr} % le style de bibliographie apalike francisé. Attention, il ne faut pas le module apalike, mais il faut le module natbib. %\bibliographystyle{apalike} % le style de bibliographie -\bibliography{Bibliographies/BiblioCours} % définit le fichier des réf. biblio. nom.bib + +% !!! Cette commande est dans le préambule ou deux bibliographies +% différentes pour DF et OS sont présentes +%%%%%\bibliography{Bibliographies/BiblioCours} % définit le fichier des réf. biblio. nom.bib + % le logiciel utilisé pour faire la biblio est pybliographic (pybliographer en ligne de commande) !!! suite à la suppression de - % pybliographic (pybliographer a maintenant une ui) de Lenny, j'utilise JABREF <-- très très bien. + % pybliographic (pybliographer a maintenant une ui) de Lenny, j'utilise JABREF <-- très très bien. + +% L'index \printindex{} % attention, pour que l'index soit mis à jour il faut lancer la commande de konsole~: makeindex -s ../Perso.ist nom_du_cours.idx % le Perso.ist est un fichier disant qu'il faut mettre des lettres entre les parties de l'index % les clés d'index doivent être sous la forme \index{energie@énergie!potentielle} voire avec plus de ! ; le premier mot doit être sans accents et la forme @ systèmatiquement présente. diff --git a/Dynamique/Dynamique.tex b/Dynamique/Dynamique.tex index 98d2d31..74b1034 100644 --- a/Dynamique/Dynamique.tex +++ b/Dynamique/Dynamique.tex @@ -265,7 +265,7 @@ Dans le cadre de ce cours de mécanique nous en étudierons quatre, dont une seu \begin{figure}[!t] \centering -\caption[La balance de Cavendish]{La balance de Cavendish\label{balancedecavendish} \par \scriptsize{Mesurer la force de gravitation\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Cavendish-lab.jpg= notamment pour le copyright de l'image.}}} +\caption[La balance de Cavendish]{La balance de Cavendish\label{balancedecavendish} \par \scriptsize{Mesurer la force de gravitation}} \includegraphics[width=6cm]{Balance_de_Cavendish.eps} \end{figure} @@ -328,7 +328,7 @@ Remarquons que~: \item la loi de la gravitation universelle\index{loi@loi!de la gravitation universelle} n'est valable que pour des corps ponctuels\index{corps@corps!ponctuel} ou sphériques\index{corps@corps!sphérique}, \item qu'elle traduit une action à distance\index{action@action!à distance}, ce qui posera par la suite de graves problèmes, \item que Newton était conscient des problèmes qu'une action à distance pouvait poser, mais qu'il n'y a pas trouvé de réponse satisfaisante, -\item que la constante G est une constante fondamentale appelée \og constante de la gravitation universelle\index{constante@constante!de la gravitation universelle}\fg{}, et vaut \(G=\SI{6,67e-11}{\newton\metre\squared\per\kilo\gram\squared}\). Cette constante est très petite. Cela traduit une force relativement faible (même si pour des masses conséquentes comme la Terre et le Soleil par exemple, elle peut avoir une valeur importante). Nous verrons, avec la force électrique\index{force@force!électrique}, un exemple de force beaucoup plus forte. +\item que la constante G est une constante fondamentale appelée \og constante de la gravitation universelle\index{constante@constante!de la gravitation universelle}\fg{}, et vaut \(G=\SI{6,67e-11}{\newton\metre\squared\per\kilo\gram\squared}\). Cette constante est très petite. Elle a été déterminée grâce à la balance de Cavendish (voir figure \ref{balancedecavendish}\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Cavendish-lab.jpg= notamment pour le copyright de l'image.}). Cela traduit une force relativement faible (même si pour des masses conséquentes comme la Terre et le Soleil par exemple, elle peut avoir une valeur importante). Nous verrons, avec la force électrique\index{force@force!électrique}, un exemple de force beaucoup plus forte. \end{itemize} \subsubsection{Le poids\index{poids@poids}} @@ -470,11 +470,11 @@ Une des nombreuses applications intéressantes de la loi de la gravitation unive \begin{figure}[t] \centering -\caption[La sensation des mouvements]{La sensation des mouvements\label{mcun} \par \scriptsize{Gravitation, poids et mouvement circulaire\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Rollercoaster\_Tornado\_Avonturenpark\_Hellendoorn\_Netherlands.jpg=}}} +\caption[La sensation des mouvements]{La sensation des mouvements\label{mcun} \par \scriptsize{Gravitation, poids et mouvement circulaire}} \includegraphics[width=6cm]{MCU2.eps} \end{figure} -Comme on l'a vu (voir paragraphe \ref{MvtCU}), le MCU\index{MCU@MCU} est un mouvement à vitesse constante, mais à accélération non nulle. La présence d'une accélération implique celle d'une force\index{force@force}. Celle-ci est naturellement dans la même direction et le même sens que l'accélération. En effet, cela découle de la deuxième loi de Newton et du fait que la masse est toujours positive. Cette accélération, nommée centripète\index{centripete@centripète} (et non centrifuge\index{centrifuge@centrifuge}), est donc créée par une force dirigée vers le centre de rotation qui dévie l'objet de sa trajectoire. Cela est parfaitement compatible avec la première loi de Newton puisque selon elle, seule la présence d'une force peut expliquer une trajectoire non rectiligne. +Comme on l'a vu (voir paragraphe \ref{MvtCU}), le MCU\index{MCU@MCU} (voir figure \ref{mcun}\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Rollercoaster\_Tornado\_Avonturenpark\_Hellendoorn\_Netherlands.jpg=}) est un mouvement à vitesse constante, mais à accélération non nulle. La présence d'une accélération implique celle d'une force\index{force@force}. Celle-ci est naturellement dans la même direction et le même sens que l'accélération. En effet, cela découle de la deuxième loi de Newton et du fait que la masse est toujours positive. Cette accélération, nommée centripète\index{centripete@centripète} (et non centrifuge\index{centrifuge@centrifuge}), est donc créée par une force dirigée vers le centre de rotation qui dévie l'objet de sa trajectoire. Cela est parfaitement compatible avec la première loi de Newton puisque selon elle, seule la présence d'une force peut expliquer une trajectoire non rectiligne. Il est important de bien différencier la force centripète, qui est dirigée vers le centre du cercle de la trajectoire, de la pseudo-force centrifuge qui traduit l'impression d'être éjectée que peut avoir une personne qui est en rotation dans un manège, par exemple. Nous sommes là, comme au paragraphe \ref{poidsapparent}, dans le cadre d'un mouvement accéléré~: le mouvement circulaire uniforme. L'étude de ce mouvement peut se faire en observant sa dynamique de l'extérieur. On écrit alors l'équation du mouvement naturellement ainsi~: \[F_{centrip\grave ete}=m\cdot a_{centrip\grave ete}=m\cdot \frac{v^2}{R}\] diff --git a/Energie/Energie.tex b/Energie/Energie.tex index f89ab6e..ba9aad2 100644 --- a/Energie/Energie.tex +++ b/Energie/Energie.tex @@ -35,11 +35,11 @@ Remarquons finalement que la définition du travail donnée ci-dessus n'est vala \begin{figure}[t] \centering -\caption[Puissance]{Puissance\label{chevalvapeur} \par \scriptsize{Le cheval vapeur\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Finowkanal-treidel.jpg=}}} +\caption[Puissance]{Puissance\label{chevalvapeur} \par \scriptsize{Le cheval vapeur}} \includegraphics[width=6cm]{ChevalVapeur.eps} \end{figure} -On voit que le travail ne dépend pas du temps. Or, on peut produire un même travail lentement (voir figure \ref{chevalvapeur}) ou rapidement. La manière dont ce travail est produit dans le temps donne lieu à la définition de la notion de puissance\index{puissance}. Plus le temps mis pour produire un travail donné est court, plus il faudra de la puissance. On doit donc écrire~: +On voit que le travail ne dépend pas du temps. Or, on peut produire un même travail lentement (voir figure \ref{chevalvapeur}\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Finowkanal-treidel.jpg=}) ou rapidement. La manière dont ce travail est produit dans le temps donne lieu à la définition de la notion de puissance\index{puissance}. Plus le temps mis pour produire un travail donné est court, plus il faudra de la puissance. On doit donc écrire~: \begin{equation}\label{puiss} \fbox{\(\displaystyle P=\frac{A}{t}\)} @@ -101,11 +101,11 @@ Nous verrons au paragraphe \ref{enmecdef} que le théorème de conservation de l Il existe cependant une autre façon de prendre en compte les forces de frottement au sein d'un théorème analogue à celui de conservation de l'énergie mécanique. Au paragraphe \ref{varenmec} nous montrerons qu'il suffit pour cela de considérer la variation de l'énergie mécanique comme équivalente au travail des seules forces non conservatives (forces de frottement). \section{Conservation de l'énergie mécanique}\label{enmecdef} -Qu'elle soit potentielle ou cinétique, il s'agit toujours d'énergie. On comprend donc facilement qu'il puisse exister des transferts entre ces deux formes d'énergie (comme avec d'autre formes d'énergie que nous verrons par la suite d'ailleurs !). +Qu'elle soit potentielle ou cinétique, il s'agit toujours d'énergie. On comprend donc facilement qu'il puisse exister des transferts entre ces deux formes d'énergie (comme avec d'autre formes d'énergie que nous verrons par la suite d'ailleurs ! Voir figure \ref{encinpotcirc}\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Mozaic-garden009.jpg=}). \begin{figure}[t] \centering -\caption[Énergie cinétique et potentielle]{Énergie cinétique et potentielle\label{encinpotcirc} \par \scriptsize{L'énergie se transforme\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Mozaic-garden009.jpg=}}} +\caption[Énergie cinétique et potentielle]{Énergie cinétique et potentielle\label{encinpotcirc} \par \scriptsize{L'énergie se transforme}} \includegraphics[width=6cm]{En_cin_pot_circ.eps} \end{figure} @@ -193,11 +193,11 @@ La relation liant ces deux grandeurs est, rappelons-le, \(E=P\cdot t\). Les énergies renouvelables les plus importantes (hydraulique, biomasse, solaire et éolien) représentent environ 20\% de la production mondiale \cite[p. 67.]{HRaFL03}. \subsection{Énergie hydraulique\index{energie@énergie!hydraulique}} -Elle représente 18\% de la production mondiale, soit plus de \SI{700}{\giga\watt}. Il s'agit de la puissance installée\index{puissance!installée}, c'est-à-dire la puissance maximale permise par la totalité des installations. En réalité, toutes ne produisent pas toujours au maximum. En effet, comme on peut la stoker, l'énergie hydraulique est souvent sous utilisée pour compléter la demande. Elle représente donc en fait environ 10\% de la production totale mondiale. En France, par exemple, environ \SI{25}{\giga\watt} sont installés, pour 22\% de la consommation électrique, alors que seulement 15\% sont produits. Relevons qu'en Suisse, la production d'électricité est assurée à 56\% par l'hydraulique. +Elle représente 18\% de la production mondiale, soit plus de \SI{700}{\giga\watt}. Il s'agit de la puissance installée\index{puissance!installée}, c'est-à-dire la puissance maximale permise par la totalité des installations. En réalité, toutes ne produisent pas toujours au maximum. En effet, comme on peut la stoker, l'énergie hydraulique est souvent sous utilisée pour compléter la demande. Elle représente donc en fait environ 10\% de la production totale mondiale. En France, par exemple, environ \SI{25}{\giga\watt} sont installés, pour 22\% de la consommation électrique, alors que seulement 15\% sont produits. Relevons qu'en Suisse, la production d'électricité est assurée à 56\% par l'hydraulique (voir figure \ref{Emosson}\endnote{Voir le site~: \url=http://www.emosson-lac.ch/barrage.htm=}). \begin{figure}[t] \centering -\caption[Barrage d'Emosson]{Barrage d'Emosson\label{Emosson} (Suisse) \par \scriptsize{D'une hauteur de \SI{180}{\metre} et largeur de \SI{560}{\metre}\endnote{Voir le site~: \url=http://www.emosson-lac.ch/barrage.htm=}}} +\caption[Barrage d'Emosson]{Barrage d'Emosson\label{Emosson} (Suisse) \par \scriptsize{D'une hauteur de \SI{180}{\metre} et largeur de \SI{560}{\metre}}} \includegraphics[width=6cm]{Emosson.eps} \end{figure} @@ -250,14 +250,14 @@ Différents types de turbines correspondent à différentes plages d'utilisation \begin{figure}[H] \centering -\caption[Turbine Pelton]{Turbine Pelton\label{pelton} \par \scriptsize{Des godets propulseurs\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://fr.wikipedia.org/wiki/Image:S\_vs\_pelton\_schnitt\_1\_zoom.png=}}} +\caption[Turbine Pelton]{Turbine Pelton\label{pelton} \par \scriptsize{Des godets propulseurs}} \includegraphics[width=6cm]{Pelton.eps} \end{figure} \begin{itemize} \item \textit{Les turbines Kaplan\index{turbine!Kaplan}} sont à réaction\index{reaction@réaction}~: totalement immergée dans l'eau, elles fonctionnent comme une aile d'avion. Elles ressemblent à une hélice (comme pour un bateau) généralement verticale. Elles sont utilisées pour de faibles chutes, jusqu'à \SI{30}{\metre}, et un débit de 4 à \SI{350}{\metre\cubed\per\second}. \item \textit{Les turbines Francis\index{turbine!Francis}} sont aussi à réaction et ont des pales qui les font ressembler à un réacteur d'avion. Elles sont utilisées pour de moyennes chutes, entre 10 et \SI{700}{\metre}, et un débit de 4 à \SI{55}{\metre\cubed\per\second}. -\item \textit{Les turbines Pelton\index{turbine!Pelton}} (voir figure \ref{pelton} et \ref{turbinepelton}), elles, sont à action\index{action}~: c'est la poussée du fluide qui les fait tourner. Elles ressemblent aux anciennes roues à aube\index{roue a aube@roue à aube}, mais tournent horizontalement et sont munies de godets. Elles sont utilisées pour de hautes chutes, entre 200 et \SI{2000}{\metre}, et un débit de 4 à \SI{15}{\metre\cubed\per\second}. +\item \textit{Les turbines Pelton\index{turbine!Pelton}} (voir figure \ref{pelton}\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://fr.wikipedia.org/wiki/Image:S\_vs\_pelton\_schnitt\_1\_zoom.png=} et \ref{turbinepelton}), elles, sont à action\index{action}~: c'est la poussée du fluide qui les fait tourner. Elles ressemblent aux anciennes roues à aube\index{roue a aube@roue à aube}, mais tournent horizontalement et sont munies de godets. Elles sont utilisées pour de hautes chutes, entre 200 et \SI{2000}{\metre}, et un débit de 4 à \SI{15}{\metre\cubed\per\second}. \end{itemize} Le rendement de ces turbines varie entre 80 et 90\%. @@ -442,20 +442,20 @@ Ainsi, une installation de \SI{5}{\metre\squared} de surface permet d'obtenir un Relevons enfin de nouvelles dispositions en faveur du solaire thermique\index{energie@énergie!solaire!thermique}. Comme dans le cas de la ville de Barcelone qui impose à toute nouvelle construction ou pour les bâtiments réhabilités que la consommation d'eau chaude sanitaire\index{eau!chaude sanitaire} soit couverte au minimum à 60\% par du solaire thermique. Cette législation a déjà créé beaucoup d'emplois localement pour subvenir aux besoins. \subsubsection{Énergie solaire électrique\index{energie@énergie!solaire!électrique}} -Le principe de base est celui découvert par Heinrich Rudolf Hertz en 1887 et expliqué par Albert Einstein en 1905~: l'effet photoélectrique\index{effet!photoélectrique}. Sans vouloir tenter ici l'explication d'un phénomène complexe touchant à la lumière et à l'électricité, on peut dire simplement que certaines matières émettent spontanément des électrons, et donc un courant électrique, quand elles sont soumises à de la lumière (voir figure \ref{effetphotoelectrique}). +Le principe de base est celui découvert par Heinrich Rudolf Hertz en 1887 et expliqué par Albert Einstein en 1905~: l'effet photoélectrique\index{effet!photoélectrique}. Sans vouloir tenter ici l'explication d'un phénomène complexe touchant à la lumière et à l'électricité, on peut dire simplement que certaines matières émettent spontanément des électrons, et donc un courant électrique, quand elles sont soumises à de la lumière (voir figure \ref{effetphotoelectrique}\endnote{Voir le site de l'encyclopédie~: \url=http://fr.wikipedia.org/wiki/Image:Photoelectric\_effect.png=}). \begin{figure}[t] \centering -\caption[Effet photoélectrique]{Effet photoélectrique\label{effetphotoelectrique} \par \scriptsize{Ou effet photovoltaïque\endnote{Voir le site de l'encyclopédie~: \url=http://fr.wikipedia.org/wiki/Image:Photoelectric\_effect.png=}}} +\caption[Effet photoélectrique]{Effet photoélectrique\label{effetphotoelectrique} \par \scriptsize{Ou effet photovoltaïque}} \includegraphics[width=6cm]{Photoelectric_effect.eps} \end{figure} -Le rendement courant des cellules photoélectriques\index{rendement!photoélectrique} (voir figure \ref{cellulephotoelectrique}) actuelles se situe entre 10 et 20\% de la puissance solaire incidente (silicium polycristallin\index{silicium!polycristallin}~: \(\sim\)13\% et monocristallin\index{silicium!monocristallin}~: \(\sim\)17\%). Ainsi, la puissance développée par de telles cellules se situe-t-elle, pour une puissance incidente de \SI{160}{\watt\per\metre\squared} (voir l'équation \ref{puissincidphoto}), aux alentours des \SI{20}{\watt\per\metre\squared}. Sachant que la consommation électrique annuelle d'une famille de cinq personnes en Europe est d'environ \SI{2000}{\kWh}, la puissance nécessaire est de~: +Le rendement courant des cellules photoélectriques\index{rendement!photoélectrique} (voir figure \ref{cellulephotoelectrique}\endnote{Voir le site de l'encyclopédie~: \url=http://fr.wikipedia.org/wiki/Image:4inch\_poly\_solar\_cell.jpg=}) actuelles se situe entre 10 et 20\% de la puissance solaire incidente (silicium polycristallin\index{silicium!polycristallin}~: \(\sim\)13\% et monocristallin\index{silicium!monocristallin}~: \(\sim\)17\%). Ainsi, la puissance développée par de telles cellules se situe-t-elle, pour une puissance incidente de \SI{160}{\watt\per\metre\squared} (voir l'équation \ref{puissincidphoto}), aux alentours des \SI{20}{\watt\per\metre\squared}. Sachant que la consommation électrique annuelle d'une famille de cinq personnes en Europe est d'environ \SI{2000}{\kWh}, la puissance nécessaire est de~: \[P=\frac{E}{t}=\frac{2'000\cdot 10^3}{365\cdot 24}=\SI{228}{\watt}\] \begin{figure}[t] \centering -\caption[Cellule photoélectrique]{Cellule photoélectrique\label{cellulephotoelectrique} \par \scriptsize{Ou cellule photovoltaïque\endnote{Voir le site de l'encyclopédie~: \url=http://fr.wikipedia.org/wiki/Image:4inch\_poly\_solar\_cell.jpg=}}} +\caption[Cellule photoélectrique]{Cellule photoélectrique\label{cellulephotoelectrique} \par \scriptsize{Ou cellule photovoltaïque}} \includegraphics[width=6cm]{CellulePhotoElectrique.eps} \end{figure} @@ -479,11 +479,11 @@ On distingue essentiellement deux types de géothermie, exception faite de la g \item[la géothermie à haute énergie,] qui exploite des sources très chaudes, supérieures à \SIrange{100}{150}{\celsius}, grâce à des forages\index{forage} très profonds dans lesquels de l'eau sous pression est injectée. Elle permet d'utiliser de la vapeur d'eau sous pression pour faire tourner une turbine\index{turbine} productrice d'électricité. \item[la géothermie à basse énergie,] qui exploite des sources d'une température variant de \SIrange{30}{100}{\celsius}, à des profondeurs allant de quelques centaines de mètres à plusieurs kilomètres. Elle sert essentiellement aux réseaux de chauffages urbains\index{chauffage!urbain}. \end{description} -Différentes applications peuvent être envisagées industriellement. Elle sont présentées dans le tableau \ref{geothermieapplications}. +Différentes applications peuvent être envisagées industriellement. Elle sont présentées dans le tableau \ref{geothermieapplications}\endnote{Voir le site de l'encyclopédie~: \url=http://fr.wikipedia.org/wiki/Image:Tableau-lindal.jpg=}. \begin{figure*}[t] \centering -\caption[Applications de la géothermie]{Applications de la géothermie\label{geothermieapplications} \par \scriptsize{Selon Lindal\endnote{Voir le site de l'encyclopédie~: \url=http://fr.wikipedia.org/wiki/Image:Tableau-lindal.jpg=}}} +\caption[Applications de la géothermie]{Applications de la géothermie\label{geothermieapplications} \par \scriptsize{Selon Lindal}} \includegraphics[width=15.5cm]{GeothermieApplications.eps} \end{figure*} @@ -592,11 +592,11 @@ Et il faut bien reconnaître qu'à part dans les bombes à hydrogène\index{bomb \subsection{Énergie de combustion\index{energie@énergie!de combustion}~: pétrole et gaz} Elle représente 74\% de la production mondiale \cite[p. 67.]{HRaFL03}. -Ce n'est pas ici le lieu d'expliquer la combustion chimique du fioul\index{fioul} (mazout\index{mazout}) qui est la principale source de chauffage des bâtiments dans le monde. Il faut cependant évoquer les deux problèmes principaux de ces deux types d'énergie~: le pétrole\index{petrole@pétrole} et le gaz naturel\index{gaz!naturel}. Ce sont des énergies hautement polluantes et non-renouvelables. La figure \ref{combustiongaz} présente la combustion du méthane\index{combustion!du méthane}. +Ce n'est pas ici le lieu d'expliquer la combustion chimique du fioul\index{fioul} (mazout\index{mazout}) qui est la principale source de chauffage des bâtiments dans le monde. Il faut cependant évoquer les deux problèmes principaux de ces deux types d'énergie~: le pétrole\index{petrole@pétrole} et le gaz naturel\index{gaz!naturel}. Ce sont des énergies hautement polluantes et non-renouvelables. La figure \ref{combustiongaz}\endnote{Voir le site de l'encyclopédie~: \url=http://commons.wikimedia.org/wiki/Image:Combustion\_methane.png=} présente la combustion du méthane\index{combustion!du méthane}. \begin{figure}[H] \centering -\caption[Combustion du méthane]{Combustion du méthane\label{combustiongaz} \par \scriptsize{Gaz naturel\endnote{Voir le site de l'encyclopédie~: \url=http://commons.wikimedia.org/wiki/Image:Combustion\_methane.png=}}} +\caption[Combustion du méthane]{Combustion du méthane\label{combustiongaz} \par \scriptsize{Gaz naturel}} \includegraphics[width=7cm]{Combustion_methane.eps} \end{figure} diff --git a/Energie/Energie.tex.bak b/Energie/Energie.tex.bak index 08ef262..ba67f0c 100644 --- a/Energie/Energie.tex.bak +++ b/Energie/Energie.tex.bak @@ -35,11 +35,11 @@ Remarquons finalement que la définition du travail donnée ci-dessus n'est vala \begin{figure}[t] \centering -\caption[Puissance]{Puissance\label{chevalvapeur} \par \scriptsize{Le cheval vapeur\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Finowkanal-treidel.jpg=}}} +\caption[Puissance]{Puissance\label{chevalvapeur} \par \scriptsize{Le cheval vapeur}} \includegraphics[width=6cm]{ChevalVapeur.eps} \end{figure} -On voit que le travail ne dépend pas du temps. Or, on peut produire un même travail lentement (voir figure \ref{chevalvapeur}) ou rapidement. La manière dont ce travail est produit dans le temps donne lieu à la définition de la notion de puissance\index{puissance}. Plus le temps mis pour produire un travail donné est court, plus il faudra de la puissance. On doit donc écrire~: +On voit que le travail ne dépend pas du temps. Or, on peut produire un même travail lentement (voir figure \ref{chevalvapeur}\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Finowkanal-treidel.jpg=}) ou rapidement. La manière dont ce travail est produit dans le temps donne lieu à la définition de la notion de puissance\index{puissance}. Plus le temps mis pour produire un travail donné est court, plus il faudra de la puissance. On doit donc écrire~: \begin{equation}\label{puiss} \fbox{\(\displaystyle P=\frac{A}{t}\)} @@ -101,11 +101,11 @@ Nous verrons au paragraphe \ref{enmecdef} que le théorème de conservation de l Il existe cependant une autre façon de prendre en compte les forces de frottement au sein d'un théorème analogue à celui de conservation de l'énergie mécanique. Au paragraphe \ref{varenmec} nous montrerons qu'il suffit pour cela de considérer la variation de l'énergie mécanique comme équivalente au travail des seules forces non conservatives (forces de frottement). \section{Conservation de l'énergie mécanique}\label{enmecdef} -Qu'elle soit potentielle ou cinétique, il s'agit toujours d'énergie. On comprend donc facilement qu'il puisse exister des transferts entre ces deux formes d'énergie (comme avec d'autre formes d'énergie que nous verrons par la suite d'ailleurs !). +Qu'elle soit potentielle ou cinétique, il s'agit toujours d'énergie. On comprend donc facilement qu'il puisse exister des transferts entre ces deux formes d'énergie (comme avec d'autre formes d'énergie que nous verrons par la suite d'ailleurs ! Voir figure \ref{encinpotcirc}\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Mozaic-garden009.jpg=}). \begin{figure}[t] \centering -\caption[Énergie cinétique et potentielle]{Énergie cinétique et potentielle\label{encinpotcirc} \par \scriptsize{L'énergie se transforme\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Mozaic-garden009.jpg=}}} +\caption[Énergie cinétique et potentielle]{Énergie cinétique et potentielle\label{encinpotcirc} \par \scriptsize{L'énergie se transforme}} \includegraphics[width=6cm]{En_cin_pot_circ.eps} \end{figure} @@ -193,11 +193,11 @@ La relation liant ces deux grandeurs est, rappelons-le, \(E=P\cdot t\). Les énergies renouvelables les plus importantes (hydraulique, biomasse, solaire et éolien) représentent environ 20\% de la production mondiale \cite[p. 67.]{HRaFL03}. \subsection{Énergie hydraulique\index{energie@énergie!hydraulique}} -Elle représente 18\% de la production mondiale, soit plus de \SI{700}{\giga\watt}. Il s'agit de la puissance installée\index{puissance!installée}, c'est-à-dire la puissance maximale permise par la totalité des installations. En réalité, toutes ne produisent pas toujours au maximum. En effet, comme on peut la stoker, l'énergie hydraulique est souvent sous utilisée pour compléter la demande. Elle représente donc en fait environ 10\% de la production totale mondiale. En France, par exemple, environ \SI{25}{\giga\watt} sont installés, pour 22\% de la consommation électrique, alors que seulement 15\% sont produits. Relevons qu'en Suisse, la production d'électricité est assurée à 56\% par l'hydraulique. +Elle représente 18\% de la production mondiale, soit plus de \SI{700}{\giga\watt}. Il s'agit de la puissance installée\index{puissance!installée}, c'est-à-dire la puissance maximale permise par la totalité des installations. En réalité, toutes ne produisent pas toujours au maximum. En effet, comme on peut la stoker, l'énergie hydraulique est souvent sous utilisée pour compléter la demande. Elle représente donc en fait environ 10\% de la production totale mondiale. En France, par exemple, environ \SI{25}{\giga\watt} sont installés, pour 22\% de la consommation électrique, alors que seulement 15\% sont produits. Relevons qu'en Suisse, la production d'électricité est assurée à 56\% par l'hydraulique (voir figure \ref{Emosson}\endnote{Voir le site~: \url=http://www.emosson-lac.ch/barrage.htm=}). \begin{figure}[t] \centering -\caption[Barrage d'Emosson]{Barrage d'Emosson\label{Emosson} (Suisse) \par \scriptsize{D'une hauteur de \SI{180}{\metre} et largeur de \SI{560}{\metre}\endnote{Voir le site~: \url=http://www.emosson-lac.ch/barrage.htm=}}} +\caption[Barrage d'Emosson]{Barrage d'Emosson\label{Emosson} (Suisse) \par \scriptsize{D'une hauteur de \SI{180}{\metre} et largeur de \SI{560}{\metre}}} \includegraphics[width=6cm]{Emosson.eps} \end{figure} @@ -250,7 +250,7 @@ Différents types de turbines correspondent à différentes plages d'utilisation \begin{figure}[H] \centering -\caption[Turbine Pelton]{Turbine Pelton\label{pelton} \par \scriptsize{Des godets propulseurs\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://fr.wikipedia.org/wiki/Image:S_vs_pelton_schnitt_1_zoom.png=}}} +\caption[Turbine Pelton]{Turbine Pelton\label{pelton} \par \scriptsize{Des godets propulseurs\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://fr.wikipedia.org/wiki/Image:S\_vs\_pelton\_schnitt\_1\_zoom.png=}}} \includegraphics[width=6cm]{Pelton.eps} \end{figure} @@ -446,7 +446,7 @@ Le principe de base est celui découvert par Heinrich Rudolf Hertz en 1887 et ex \begin{figure}[t] \centering -\caption[Effet photoélectrique]{Effet photoélectrique\label{effetphotoelectrique} \par \scriptsize{Ou effet photovoltaïque\endnote{Voir le site de l'encyclopédie~: \url=http://fr.wikipedia.org/wiki/Image:Photoelectric_effect.png=}}} +\caption[Effet photoélectrique]{Effet photoélectrique\label{effetphotoelectrique} \par \scriptsize{Ou effet photovoltaïque\endnote{Voir le site de l'encyclopédie~: \url=http://fr.wikipedia.org/wiki/Image:Photoelectric\_effect.png=}}} \includegraphics[width=6cm]{Photoelectric_effect.eps} \end{figure} @@ -455,7 +455,7 @@ Le rendement courant des cellules photoélectriques\index{rendement!photoélectr \begin{figure}[t] \centering -\caption[Cellule photoélectrique]{Cellule photoélectrique\label{cellulephotoelectrique} \par \scriptsize{Ou cellule photovoltaïque\endnote{Voir le site de l'encyclopédie~: \url=http://fr.wikipedia.org/wiki/Image:4inch_poly_solar_cell.jpg=}}} +\caption[Cellule photoélectrique]{Cellule photoélectrique\label{cellulephotoelectrique} \par \scriptsize{Ou cellule photovoltaïque\endnote{Voir le site de l'encyclopédie~: \url=http://fr.wikipedia.org/wiki/Image:4inch\_poly\_solar\_cell.jpg=}}} \includegraphics[width=6cm]{CellulePhotoElectrique.eps} \end{figure} @@ -465,7 +465,7 @@ Ce qui représente plus de \SI{10}{\metre\squared} de surface et est important. Deux autres points doivent aussi être abordés. Celui de l'énergie ``grise''\index{energie@énergie!grise} nécessaire pour la construction des cellules et celui de leur recyclage. En effet, une idée fausse court à propos de l'énergie solaire électrique. Il s'agit du fait que les cellules nécessiteraient plus d'énergie pour être produites qu'elles ne sont capables d'en fournir. Or, l'énergie nécessaire\endnote{voir le site OutilsSolaires~: \url=http://www.outilssolaires.com/pv/prin-bilan.htm=} pour fabriquer et installer les cellules est de l'ordre de \(E_{fab}=\SI{420}{\KWH\per\metre\squared}\). Avec une puissance de l'ordre de \SI{20}{\watt\per\metre\squared}, qui représente une énergie \(E=20\cdot 24\cdot 365=\SI{175,2}{\KWH\per\year}\), il faut~: \[n=\frac{420}{175,2}=\SI{2,4}{ans}\] -pour que la cellule ait produit l'équivalent de ce que sa production a nécessité. Sur une durée de fonctionnement entre vingt et trente ans, le bilan énergétique est très favorable\endnote{voir aussi l'étude~: \og Compared assessment of selected environmental indicators of photovoltaic electricity in OECD cities\fg{} à l'adresse~: \url=http://www.eupvplatform.org/fileadmin/Documents/Brochure-indicateurs_26_pays.pdf=}. En effet, pour vingt ans d'utilisation, l'énergie produite est~: +pour que la cellule ait produit l'équivalent de ce que sa production a nécessité. Sur une durée de fonctionnement entre vingt et trente ans, le bilan énergétique est très favorable\endnote{voir aussi l'étude~: \og Compared assessment of selected environmental indicators of photovoltaic electricity in OECD cities\fg{} à l'adresse~: \url=http://www.eupvplatform.org/fileadmin/Documents/Brochure-indicateurs\_26\_pays.pdf=}. En effet, pour vingt ans d'utilisation, l'énergie produite est~: \[E=20\cdot 20\cdot 24\cdot 365=\SI{3504}{\kWh}\] L'énergie nécessaire à la fabrication est donc de l'ordre de 12\% de l'énergie totale produite sur vingt ans, ce qui constitue une durée minimum d'exploitation. @@ -540,7 +540,7 @@ On voit qu'il est nécessaire de disposer d'un neutron pour casser le noyau d'ur \caption{Réacteur nucléaire\label{reacteurnucleaire}} \smallskip -\centering \scriptsize{Réacteur à eau bouillante\endnote{Voir le site de l'encyclopédie~: \url=http://fr.wikipedia.org/wiki/Image:Boiling_nuclear_reactor.png=} +\centering \scriptsize{Réacteur à eau bouillante\endnote{Voir le site de l'encyclopédie~: \url=http://fr.wikipedia.org/wiki/Image:Boiling\_nuclear\_reactor.png=} \smallskip \begin{minipage}{4cm} @@ -596,7 +596,7 @@ Ce n'est pas ici le lieu d'expliquer la combustion chimique du fioul\index{fioul \begin{figure}[H] \centering -\caption[Combustion du méthane]{Combustion du méthane\label{combustiongaz} \par \scriptsize{Gaz naturel\endnote{Voir le site de l'encyclopédie~: \url=http://commons.wikimedia.org/wiki/Image:Combustion_methane.png=}}} +\caption[Combustion du méthane]{Combustion du méthane\label{combustiongaz} \par \scriptsize{Gaz naturel\endnote{Voir le site de l'encyclopédie~: \url=http://commons.wikimedia.org/wiki/Image:Combustion\_methane.png=}}} \includegraphics[width=7cm]{Combustion_methane.eps} \end{figure} diff --git a/Introduction/Introduction.tex b/Introduction/Introduction.tex index a05c957..4fca71b 100644 --- a/Introduction/Introduction.tex +++ b/Introduction/Introduction.tex @@ -17,19 +17,20 @@ Qui dit périodes dit donc mouvement et, plus précisément, mouvement répétit \subsection{L'Univers\index{univers@univers}} \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.}}} +\caption[L'univers profond]{\label{fig:universprofond}L'univers profond\par \scriptsize{Image du télescope spatial Hubble}} \includegraphics[width=7cm]{universprofond.eps} \end{figure} +%\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.} 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. -Les super-amas de galaxies sont des amas d'amas de galaxies. C'est au niveau de ces super-amas de galaxies que l'univers apparaît assez homogène bien que constitué aussi d'une structure filamenteuse. L'ordre de grandeur de telles structures est de \SI{100}{\mega\parsec} soit \SI{3e24}{\metre} pour les super-amas de galaxies, voire \SI{150}{\mega\parsec} soit \SI{5e24}{\metre} pour les filaments. +Les super-amas de galaxies sont des amas d'amas de galaxies (voir la figure \ref{modeledecourbure}\endnote{Voir le site de l'encyclopédie Wikipedia~: \protect\url{http://fr.wikipedia.org/wiki/Image:End\_of\_universe.jpg} notamment pour le copyright de l'image. Remerciements à la NASA.}). C'est au niveau de ces super-amas de galaxies que l'univers apparaît assez homogène bien que constitué aussi d'une structure filamenteuse. L'ordre de grandeur de telles structures est de \SI{100}{\mega\parsec} soit \SI{3e24}{\metre} pour les super-amas de galaxies, voire \SI{150}{\mega\parsec} soit \SI{5e24}{\metre} pour les filaments. L'univers est en expansion\index{expansion@expansion}, ce qui signifie qu'il s'agrandit. Selon les dernières mesures effectuées par les astrophysiciens, sa forme serait plate\footnote{Voir l'article \og Quelle est la forme de l'univers\fg{}, Science et Vie junior, avril 2001}. Qu'est-ce que cela signifie pour un univers qui est manifestement un volume ? En fait, cela veut dire qu'on peut se l'imaginer comme une feuille de papier dont les dimensions augmenteraient indéfiniment. Nous serions alors des êtres à deux dimensions incapables de se déplacer ailleurs que sur cette feuille. En particulier incapables d'en sortir. Cette feuille s'étendrait donc dans une (troisième) dimensions inaccessible pour nous. Ainsi, notre univers à trois dimensions s'étend dans une dimension supplémentaire qui nous est inaccessible (c'est-à-dire qu'on ne peut s'y déplacer librement), une quatrième dimension\index{dimension@dimension}, le temps\index{temps@temps}. \begin{figure}[t] \centering -\caption[Modèles de courbure]{Modèles de courbure\label{modeledecourbure} \par \scriptsize{Trois modèles issus de la relativité générale\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://fr.wikipedia.org/wiki/Image:End\_of\_universe.jpg= notamment pour le copyright de l'image. Remerciements à la NASA.}}} +\caption[Modèles de courbure]{Modèles de courbure\label{modeledecourbure} \par \scriptsize{Trois modèles issus de la relativité générale}} \includegraphics[width=6cm]{End_of_universe.eps} \end{figure} @@ -59,7 +60,7 @@ Giordano Bruno fut brûlé vif en 1600, pour avoir, sur la base d'une analyse du \begin{figure*}[t] \centering -\caption[L'évolution du Soleil]{L'évolution du soleil\label{evosol} \par \scriptsize{Vers une nébuleuse planétaire\endnote{Voir le site de l'encyclopédie wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Vie\_du\_soleil.jpg=}}} +\caption[L'évolution du Soleil]{L'évolution du soleil\label{evosol} \par \scriptsize{Vers une nébuleuse planétaire}} \includegraphics[width=14cm]{Vie_du_soleil.eps} \end{figure*} @@ -70,44 +71,44 @@ En réalité, les choses sont plus complexes encore, puisqu'aujourd'hui les phys \subsection{Les amas de galaxies} \begin{figure}[t] \centering -\caption[Groupe local]{Groupe local\label{localesgalaxies} \par \scriptsize{Les galaxies proches\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://fr.wikipedia.org/wiki/Accueil= notamment pour le copyright de l'image. Remerciements à son auteur Greg Goebel.}}} +\caption[Groupe local]{Groupe local\label{localesgalaxies} \par \scriptsize{Les galaxies proches}} \includegraphics[width=6cm]{Groupelocal.eps} \end{figure} Viennent ensuite les amas de galaxies\index{amas@amas!de galaxies}. Leur nombre dans l'univers est estimé à \num{25} milliards. La répartition de ces amas de galaxies n'est pas homogène, contrairement à celle des super-amas de galaxies. Cette répartition est celle de filaments qui laissent apparaître des zones plus ou moins denses d'amas de galaxies. -Cette répartition est complexe et encore sujette à de nombreuses discussions. En particulier elle est l'objet d'études approfondies en relation avec la naissance de l'univers\index{univers@univers}. En effet, il est difficile d'expliquer comment, à partir des conditions homogènes propres au big-bang\index{big@big!bang}, sont nées des structures aussi particulières. La figure \ref{universprofond} montre ce que l'on peut voir au-delà des étoiles de notre galaxie. Sur la photo de cette \og petite\fg{} partie de l'espace ne figurent que des galaxies. Leur nombre et leur diversité sont saisissants. La figure \ref{localesgalaxies} montre quant à elle le groupe local dans lequel se trouve notre galaxie la Voie Lactée. Il s'agit d'un amas de galaxies. +Cette répartition est complexe et encore sujette à de nombreuses discussions. En particulier elle est l'objet d'études approfondies en relation avec la naissance de l'univers\index{univers@univers}. En effet, il est difficile d'expliquer comment, à partir des conditions homogènes propres au big-bang\index{big@big!bang}, sont nées des structures aussi particulières. La figure \ref{universprofond} montre ce que l'on peut voir au-delà des étoiles de notre galaxie. Sur la photo de cette \og petite\fg{} partie de l'espace ne figurent que des galaxies. Leur nombre et leur diversité sont saisissants. La figure \ref{localesgalaxies}\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://fr.wikipedia.org/wiki/Accueil= notamment pour le copyright de l'image. Remerciements à son auteur Greg Goebel.} montre quant à elle le groupe local dans lequel se trouve notre galaxie la Voie Lactée. Il s'agit d'un amas de galaxies. \subsection{Les galaxies\index{galaxie@galaxie}} \begin{figure}[t] \centering -\caption[Galaxie du Sombrero]{Galaxie du Sombrero\label{galaxies} \par \scriptsize{Image du télescope spatial Hubble\endnote{Voir le site du télescope spatial Hubble~: op cit. Remerciements à la NASA.}}} +\caption[Galaxie du Sombrero]{Galaxie du Sombrero\label{galaxies} \par \scriptsize{Image du télescope spatial Hubble}} \includegraphics[width=6cm]{Sombrero.eps} \end{figure} -Au nombre d'environ trois cent cinquante milliards dans l'univers, les galaxies\index{galaxie@galaxie} sont des structures composées de centaines de milliards d'étoiles\index{etoile@étoile} qui se regroupent sous l'effet de la force de gravitation\index{gravitation@gravitation}. Dans l'espace interstellaire\index{espace@espace!interstellaire} constituant le \og vide\fg{} autour des étoiles se trouvent aussi des nuages de poussières et de gaz (des nébuleuses\index{nebuleuse@nébuleuse}). +Au nombre d'environ trois cent cinquante milliards dans l'univers, les galaxies\index{galaxie@galaxie} sont des structures composées de centaines de milliards d'étoiles\index{etoile@étoile} qui se regroupent sous l'effet de la force de gravitation\index{gravitation@gravitation}(voir figure \ref{galaxies}\endnote{Voir le site du télescope spatial Hubble~: op cit. Remerciements à la NASA.}). Dans l'espace interstellaire\index{espace@espace!interstellaire} constituant le \og vide\fg{} autour des étoiles se trouvent aussi des nuages de poussières et de gaz (des nébuleuses\index{nebuleuse@nébuleuse}). A cette échelle, les mouvements des galaxies sont perceptibles. Presque toutes s'éloignent de nous. Ce phénomène est appelé \og expansion\index{expansion@expansion}\fg. Il est interprété comme un mouvement dû au \og gonflement\fg{} de l'univers\index{univers@univers} lui-même. Le mouvement local des galaxies\index{galaxie@galaxie} étant faible par rapport à celui général de l'expansion\index{expansion@expansion} de l'univers, il est rare de voir des galaxies se rapprocher de nous. Pourtant, cela est le cas de la très fameuse (parce qu'observable à l'\oe il nu et la plus proche galaxie massive (autre que naine) de nous) galaxie d'Andromède\index{Andromede@Andromède}. \begin{figure*}[t] \centering -\caption[Interaction de deux galaxies]{Interaction de deux galaxies\label{choc} \par \scriptsize{Image du télescope spatial Hubble\endnote{Voir le site du télescope spatial Hubble~: ibid. Remerciements à la NASA.}}} +\caption[Interaction de deux galaxies]{Interaction de deux galaxies\label{choc} \par \scriptsize{Image du télescope spatial Hubble}} \includegraphics[width=14cm]{HubbleChienChasse.eps} \end{figure*} -Les mouvements locaux des galaxies entre elles donnent lieu à des \og chocs\fg{}\index{choc@choc!galactique} spectaculaires entre galaxies. Le résultat est par exemple le système des deux galaxies dites des \og Chiens de chasse\fg{} ou sur la figure \ref{choc} \og la grande spirale NGC 2207\fg{} (à gauche), située à 114 millions d'années-lumière de la terre, étendant et disloquant sur plusieurs centaines de milliers d'années-lumière la \og petite IC2163\fg{} en longs filaments de \og gaz et de poussières\fg{}. +Les mouvements locaux des galaxies entre elles donnent lieu à des \og chocs\fg{}\index{choc@choc!galactique} spectaculaires entre galaxies. Le résultat est par exemple le système des deux galaxies dites des \og Chiens de chasse\fg{} ou sur la figure \ref{choc}\endnote{Voir le site du télescope spatial Hubble~: ibid. Remerciements à la NASA.} \og la grande spirale NGC 2207\fg{} (à gauche), située à 114 millions d'années-lumière de la terre, étendant et disloquant sur plusieurs centaines de milliers d'années-lumière la \og petite IC2163\fg{} en longs filaments de \og gaz et de poussières\fg{}. \subsection{Les étoiles\index{etoile@étoile}} 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{}. +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}\endnote{Voir le site de l'encyclopédie wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Vie\_du\_soleil.jpg=}) 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}\endnote{Voir le site du télescope spatial Hubble~: ibid. Remerciements à la NASA.}) 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 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}. \begin{figure} \centering -\caption[Nébuleuse planétaire]{Nébuleuse planétaire\label{planetaire} \par \scriptsize{Image du télescope spatial Hubble\endnote{Voir le site du télescope spatial Hubble~: ibid. Remerciements à la NASA.}}} +\caption[Nébuleuse planétaire]{Nébuleuse planétaire\label{planetaire} \par \scriptsize{Image du télescope spatial Hubble}} \includegraphics[width=6cm]{NebuleusePlanetaire.eps} \end{figure} @@ -121,34 +122,34 @@ La première exoplanète découverte l'a été en 1995 par l'observatoire de Gen \begin{figure}[t] \centering -\caption[Première exoplanète]{Première image d'une exoplanète\label{2M1207} \par \scriptsize{Il s'agit d'une image dans le proche infrarouge. La planète est en bas à droite. Image de Hubble\endnote{Voir le site de Hubble~: \url=http://hubblesite.org/newscenter/archive/releases/2005/03/image/a/=}}} +\caption[Première exoplanète]{Première image d'une exoplanète\label{2M1207} \par \scriptsize{Il s'agit d'une image dans le proche infrarouge. La planète est en bas à droite. Image de Hubble}} \includegraphics[width=6cm]{2M1207.eps} \end{figure} -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. +En 2005, soit dix ans après, la première image d'une exoplanète (voir figure \ref{2M1207}\endnote{Voir le site de Hubble~: \url=http://hubblesite.org/newscenter/archive/releases/2005/03/image/a/=}) 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. \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. +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}\endnote{Voir le site de l'encyclopédie wikipedia~: \url=http://fr.wikipedia.org/wiki/Image:Solar\_sys.jpg= Remerciements à la NASA.} présente le système solaire sans respecter les ordres de grandeurs. \begin{figure*}[t] \centering -\caption[Système solaire]{Système solaire\label{systemesolaire} \par \scriptsize{Image de la Nasa\endnote{Voir le site de l'encyclopédie wikipedia~: \url=http://fr.wikipedia.org/wiki/Image:Solar\_sys.jpg= Remerciements à la NASA.}}} +\caption[Système solaire]{Système solaire\label{systemesolaire} \par \scriptsize{Image de la Nasa}} \includegraphics[width=14cm]{Systemesolaire.eps} \end{figure*} -La rotation des planètes se fait dans un seul plan que l'on nomme le plan de l'écliptique\index{ecliptique@écliptique}. Relativement à la Terre, ce plan est décrit par l'orbite du soleil. La nuit, c'est donc le long de la trajectoire du Soleil qu'on peut voir certaines planètes\index{planete@planète}. Car, si certaines sont visibles en pleine nuit, d'autres ne le seront jamais. C'est le cas, par exemple, de Vénus\index{Venus@Vénus}. C'est une planète qui tourne près du Soleil. Elle tourne aussi à l'intérieur du cercle (en réalité c'est une ellipse\index{ellipse@ellipse} quasiment circulaire) que décrit la Terre sur sa trajectoire\index{trajectoire@trajectoire} (on parle de l'orbite\index{orbite@orbite} de la Terre et on parle de planète interne). C'est pourquoi, depuis la Terre, nous ne la verrons que dans le voisinage du Soleil. Ainsi, on peut la voir le matin avant que le soleil se lève (on l'appelle alors l'Étoile du matin\index{etoile@étoile!du matin}) ou le soir, peu de temps après que le Soleil se soit couché (elle porte alors le nom d'Étoile du soir\index{etoile@étoile!du soir}), mais pas au cours de la nuit. Les planètes se divisent en trois groupes~: les quatre planètes dites telluriques\index{planete@planète!tellurique} sont celles qui sont le plus proche du soleil. Elles sont petites, solides et relativement semblables à la Terre. Les quatre planètes dites joviennes\index{planete@planète!jovienne} sont, à l'image de Jupiter\index{Jupiter@Jupiter}, très grosses et gazeuses. Enfin, à partir de Pluton\index{Pluton@Pluton}, les corps sont très petits, très éloignés et ne sont plus considérés comme des planètes (même si on parle de planètes naines). La figure \ref{lesplanetes} présente les planètes en respectant les ordres de grandeurs de leurs tailles respectives. +La rotation des planètes se fait dans un seul plan que l'on nomme le plan de l'écliptique\index{ecliptique@écliptique}. Relativement à la Terre, ce plan est décrit par l'orbite du soleil. La nuit, c'est donc le long de la trajectoire du Soleil qu'on peut voir certaines planètes\index{planete@planète}. Car, si certaines sont visibles en pleine nuit, d'autres ne le seront jamais. C'est le cas, par exemple, de Vénus\index{Venus@Vénus}. C'est une planète qui tourne près du Soleil. Elle tourne aussi à l'intérieur du cercle (en réalité c'est une ellipse\index{ellipse@ellipse} quasiment circulaire) que décrit la Terre sur sa trajectoire\index{trajectoire@trajectoire} (on parle de l'orbite\index{orbite@orbite} de la Terre et on parle de planète interne). C'est pourquoi, depuis la Terre, nous ne la verrons que dans le voisinage du Soleil. Ainsi, on peut la voir le matin avant que le soleil se lève (on l'appelle alors l'Étoile du matin\index{etoile@étoile!du matin}) ou le soir, peu de temps après que le Soleil se soit couché (elle porte alors le nom d'Étoile du soir\index{etoile@étoile!du soir}), mais pas au cours de la nuit. Les planètes se divisent en trois groupes~: les quatre planètes dites telluriques\index{planete@planète!tellurique} sont celles qui sont le plus proche du soleil. Elles sont petites, solides et relativement semblables à la Terre. Les quatre planètes dites joviennes\index{planete@planète!jovienne} sont, à l'image de Jupiter\index{Jupiter@Jupiter}, très grosses et gazeuses. Enfin, à partir de Pluton\index{Pluton@Pluton}, les corps sont très petits, très éloignés et ne sont plus considérés comme des planètes (même si on parle de planètes naines). La figure \ref{lesplanetes}\endnote{Voir le site de l'encyclopédie~: \planete{} Remerciements à la NASA.} présente les planètes en respectant les ordres de grandeurs de leurs tailles respectives. % la commande ci-dessous est nécessaire car on a des % dans l'url \urldef\planete\url{http://fr.wikipedia.org/wiki/Image:Portrait_de_famille_%281_px_%3D_1000_km%29.jpg} \begin{figure*}[t] \centering -\caption[La taille des planètes]{La taille des planètes\label{lesplanetes} \par \scriptsize{Image de la Nasa\endnote{Voir le site de l'encyclopédie~: \planete{} Remerciements à la NASA.}}} +\caption[La taille des planètes]{La taille des planètes\label{lesplanetes} \par \scriptsize{Image de la Nasa}} \includegraphics[width=14cm]{Lesplanetes.eps} \end{figure*} -Il existe encore d'autres corps importants dans le système solaire~: les \emph{comètes}\index{comete@comète} (voir figure \ref{comete}). Ce sont de très petits corps (quelques dizaines de kilomètres de diamètre) qui viennent de régions très éloignées du système solaire (le nuage de Oort\index{nuage@nuage!de Oort}~: \og il s'agirait d'une vaste enveloppe de corps orbitant entre \SI{40000}{\astronomicalunit} et \SI{150000}{\astronomicalunit} (\SI{0,73}{pc}) de distance du Soleil, et donc située bien au-delà de l'orbite des planètes et de la ceinture de Kuiper\fg{}\endnote{voir~: \url=http://fr.wikipedia.org/wiki/Nuage\_de\_Oort=}) et qui, pour ainsi dire, tombent sur le Soleil selon une trajectoire très elliptique\index{elliptique@elliptique}. +Il existe encore d'autres corps importants dans le système solaire~: les \emph{comètes}\index{comete@comète} (voir figure \ref{comete}\endnote{Voir le site du télescope spatial Hubble~: ibid. Remerciements à la NASA.}). Ce sont de très petits corps (quelques dizaines de kilomètres de diamètre) qui viennent de régions très éloignées du système solaire (le nuage de Oort\index{nuage@nuage!de Oort}~: \og il s'agirait d'une vaste enveloppe de corps orbitant entre \SI{40000}{\astronomicalunit} et \SI{150000}{\astronomicalunit} (\SI{0,73}{pc}) de distance du Soleil, et donc située bien au-delà de l'orbite des planètes et de la ceinture de Kuiper\fg{}\endnote{voir~: \url=http://fr.wikipedia.org/wiki/Nuage\_de\_Oort=}) et qui, pour ainsi dire, tombent sur le Soleil selon une trajectoire très elliptique\index{elliptique@elliptique}. En passant elles laissent sur leur orbite\index{orbite@orbite} une traînée de poussières qui se manifeste sous la forme d'une magnifique queue. Celle-ci est produite par le vent solaire qui emporte les éléments à la surface de la comète. La direction de la queue est donc toujours à l'opposé du soleil et peu être perpendiculaire à la trajectoire de la comète. La figure \ref{billetcomete} présente pourtant un billet de banque suisse sur lequel est représenté une comète dont la queue ne pointe pas à tort vers le soleil. @@ -158,17 +159,17 @@ 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}\endnote{Voir le site de l'encyclopédie wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Leonid\_Meteor\_Storm\_1833.jpg=} 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 -\caption[Une comète]{Une comète\label{comete} \par \scriptsize{Image du télescope spatial Hubble\endnote{Voir le site du télescope spatial Hubble~: ibid. Remerciements à la NASA.}}} +\caption[Une comète]{Une comète\label{comete} \par \scriptsize{Image du télescope spatial Hubble}} \includegraphics[width=6cm]{comete.eps} \end{figure} \begin{figure} \centering -\caption[Étoiles filantes]{Pluie d'étoiles filantes des Léonides\label{Leonides} \par \scriptsize{Leonid Meteor Strom, as seen over North America in the night of November 12./13., 1833.\endnote{Voir le site de l'encyclopédie wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Leonid\_Meteor\_Storm\_1833.jpg=}}} +\caption[Étoiles filantes]{Pluie d'étoiles filantes des Léonides\label{Leonides} \par \scriptsize{Leonid Meteor Strom, as seen over North America in the night of November 12./13., 1833.}} \includegraphics[width=6cm]{Leonid_Meteor_Storm_1833.eps} \end{figure} @@ -201,12 +202,12 @@ De plus, on ne peut comprendre que les saison\index{saison@saison} soient diffé \begin{figure}[t] \centering -\caption[La terre et la lune]{La terre et la lune\label{terrelune} \par \scriptsize{Image de la Nasa\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Moon\_Earth\_Comparison.png=. Remerciements à la NASA.}}} +\caption[La terre et la lune]{La terre et la lune\label{terrelune} \par \scriptsize{Image de la Nasa}} \includegraphics[width=6cm]{Terrelune.eps} \end{figure} \subsubsection{La Lune} -Finissons ce petit voyage dans le monde céleste en parlant de la Lune. La figure \ref{terrelune} montre le rapport de taille entre la Lune et la Terre, ainsi que les différences d'aspect de leur surface. +Finissons ce petit voyage dans le monde céleste en parlant de la Lune. La figure \ref{terrelune}\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Moon\_Earth\_Comparison.png=. Remerciements à la NASA.} montre le rapport de taille entre la Lune et la Terre, ainsi que les différences d'aspect de leur surface. Il peut sembler au premier abord que le mouvement de la Lune est simple. En effet, elle gravite sur une ellipse (on la voit donc parfois un peu plus grosse et parfois un peu plus petite~: au périgée\index{perigee@périgée} où la distance terre-lune est de \SI{3,654e8}{\metre}, son diamètre apparent\index{diametre@diamètre!apparent} est de \ang{;33,5;} et à l'apogée\index{apogee@apogée} où la distance vaut \SI{4,067e8}{,metre}, son diamètre apparent vaut \ang{;29,3;}, soit \(\sim\) 10\% de la distance moyenne) en un mois environ. La variation apparente de sa taille, ainsi que de celle du soleil due à la trajectoire elliptique que suit la terre et qui oscille entre \ang{;31,5;} et \ang{;32,5;}, expliquent l'allure des différentes éclipses de Soleil. Quand la Lune est éloignée de la Terre, elle ne cache pas tout le disque solaire et l'éclipse présente un anneau de lumière autour de la Lune, on parle alors d'éclipse annulaire\index{eclipse@éclipse!annulaire}. Par contre, quand la Lune est proche de la Terre, son diamètre apparent est plus grand et la Lune couvre tout le disque solaire. On parle alors d'éclipse totale\index{eclipse@éclipse!totale}. @@ -220,11 +221,11 @@ Quand la Lune ne nous présente plus que sa partie éclairée, elle est alors \o Enfin, la Lune se présente une nouvelle fois en demi-Lune, c'est-à-dire qu'on en voit que l'autre quart. C'est le Dernier Quartier. -La figure \ref{phasesdelalune} résume la situation décrite ci-dessus. +La figure \ref{phasesdelalune}\endnote{Voir le site de l'encyclopédie~: \url=http://commons.wikimedia.org/wiki/Image:TerreOrbiteLuneEtPhases.png=} résume la situation décrite ci-dessus. \begin{figure*}[t] \centering -\caption[Les phases de la lune]{Les phases de la lune\label{phasesdelalune} \par \scriptsize{Ce n'est pas l'ombre de la terre\endnote{Voir le site de l'encyclopédie~: \url=http://commons.wikimedia.org/wiki/Image:TerreOrbiteLuneEtPhases.png=}}} +\caption[Les phases de la lune]{Les phases de la lune\label{phasesdelalune} \par \scriptsize{Ce n'est pas l'ombre de la terre}} \includegraphics[width=14cm]{TerreOrbiteLuneEtPhases.eps} \end{figure*} @@ -232,11 +233,11 @@ La question se pose alors de la différence entre éclipse de Soleil\index{eclip \begin{figure} \centering -\caption[Orbites de la lune et du soleil]{Orbites de la lune et du soleil\label{Orbite-lune-soleil} \par \scriptsize{Des plans différents\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://fr.wikipedia.org/wiki/Image:Orbite-lune-soleil.png=}}} +\caption[Orbites de la lune et du soleil]{Orbites de la lune et du soleil\label{Orbite-lune-soleil} \par \scriptsize{Des plans différents}} \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 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}. +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}\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://fr.wikipedia.org/wiki/Image:Orbite-lune-soleil.png=}, 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. @@ -274,7 +275,7 @@ Comme cette force agit seulement à faible distance, c'est-à-dire qu'elle a une \begin{figure} \centering -\caption[La nébuleuse du Crabe]{La nébuleuse du Crabe\label{crabnebula} \par \scriptsize{Les restes d'une supernovae\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://fr.wikipedia.org/wiki/Image:Crab\_Nebula.jpg= notamment pour le copyright de l'image.}}} +\caption[La nébuleuse du Crabe]{La nébuleuse du Crabe\label{crabnebula} \par \scriptsize{Les restes d'une supernovae}} \includegraphics[width=6cm]{Crab_Nebula.eps} \end{figure} @@ -284,7 +285,7 @@ La genèse de ces atomes est complexe. On peut distinguer plusieurs étapes. \begin{figure} \centering -\caption[L'atome de Bohr]{L'atome de Bohr\label{Bohr} \par \scriptsize{Un système planétaire\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://fr.wikipedia.org/wiki/Accueil= notamment pour le copyright de l'image. Remerciements à son auteur Christophe Dang Ngoc Chan.}}} +\caption[L'atome de Bohr]{L'atome de Bohr\label{Bohr} \par \scriptsize{Un système planétaire}} \includegraphics[width=6cm]{Atome_bohr.eps} \end{figure} @@ -298,7 +299,7 @@ Lorsque l'hydrogène a été consommé, l'étoile se contracte et il se forme de Dans certaines étoiles (les géantes rouges\index{geante@géante!rouge} par exemple) la création des éléments encore plus lourds ne se fait plus par fusion\index{fusion@fusion}. En effet, la répulsion électrique entre les noyaux qui devraient fusionner devient si importante en raison du nombre élevé de protons qu'ils ne fusionnent plus. Par contre, ils s'entourent progressivement de neutrons (produits de la fusion des éléments précédents) qui ne sont pas repoussés par la force électrique\index{force@force!électrique} et grossissent tellement qu'ils deviennent instables. Alors certains neutrons se transforment par désintégration\index{desintegration@désintégration} en protons créant ainsi de nouveaux éléments plus lourds que le fer. -\item[Lors de l'explosion d'une étoile,] phénomène appelé supernov\ae\index{supernovae@supernovae} (voir la figure \ref{crabnebula}), se forment les éléments plus lourds que le carbone, l'azote et l'oxygène et cela jusqu'au fer, atome si stable que les conditions d'une telle explosion ne suffisent même pas à former des éléments plus lourds. +\item[Lors de l'explosion d'une étoile,] phénomène appelé supernov\ae\index{supernovae@supernovae} (voir la figure \ref{crabnebula}\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://fr.wikipedia.org/wiki/Image:Crab\_Nebula.jpg= notamment pour le copyright de l'image.}), se forment les éléments plus lourds que le carbone, l'azote et l'oxygène et cela jusqu'au fer, atome si stable que les conditions d'une telle explosion ne suffisent même pas à former des éléments plus lourds. Puis, comme précédemment, les éléments plus lourds sont aussi formés par désintégration des neutrons insensibles à la force électrique qui se sont liés au fer. \item[Dans le gaz interstellaire\index{gaz@gaz!interstellaire}] enfin, se forment les trois éléments légers particuliers que sont le lithium\index{lithium@lithium}, le béryllium\index{beryllium@béryllium} et le bore\index{bore@bore} par fission du carbone, de l'azote et de l'oxygène. @@ -306,13 +307,13 @@ Puis, comme précédemment, les éléments plus lourds sont aussi formés par d \begin{figure} \centering -\caption[L'atome~: onde de probabilité]{L'atome~: onde de probabilité\label{ondeproba} \par \scriptsize{Une image bien plus complexe\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://fr.wikipedia.org/wiki/Accueil= notamment pour le copyright de l'image. Remerciements à son auteur Pickwick.}}} +\caption[L'atome~: onde de probabilité]{L'atome~: onde de probabilité\label{ondeproba} \par \scriptsize{Une image bien plus complexe}} \includegraphics[width=6cm]{Atome_proba.eps} \end{figure} \begin{figure}[t] \centering -\caption[L'orbitale~: onde de probabilité]{L'orbitale~: onde de probabilité\label{orbitale} \par \scriptsize{Une autre image complexe\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:8orbitals.jpg= notamment pour le copyright de l'image.}}} +\caption[L'orbitale~: onde de probabilité]{L'orbitale~: onde de probabilité\label{orbitale} \par \scriptsize{Une autre image complexe}} \includegraphics[width=7cm]{Orbitales.eps} \end{figure} @@ -344,7 +345,7 @@ Puis, comme précédemment, les éléments plus lourds sont aussi formés par d \end{center} \end{table*} -Mais la physique ne s'arrête pas là dans sa description de l'infiniment petit. Elle s'intéresse encore à d'autres objets extraordinaires. En effet, si les mouvements des atomes\index{atome@atome} peuvent encore facilement être représentés en termes de trajectoire\index{trajectoire@trajectoire}, ceux de leurs composants sont bien plus étranges. Car on peut autant les voir comme de petites particules\index{particule@particule} (et, à l'origine, cela à donné lieu à un modèle de l'atome dit de Bohr (voir fig. \ref{Bohr}) où les électrons orbitaient autour du noyau, comme les planètes autour du soleil) que comme des \og choses\fg{} infiniment étendues que l'on appelle ondes\index{onde@onde}. Cette dualité du mode d'existence des particules élémentaires\index{particule@particule!élémentaire} comme les électrons\index{electron@électron}, les protons\index{proton@proton}, les neutrons\index{neutron@neutron} et bien d'autres encore traduit l'existence d'un objet physique bien particulier, \emph{le quanton}, et présente des difficultés d'analyse de son mouvement. Au niveau des \og trajectoires\fg{} électroniques, par exemple, on constate que certaines orbitales semblent passer par le noyau (voir fig. \ref{orbitale}). En outre, celles-ci ne peuvent être précisément représentées comme l'orbite d'une planète pourrait l'être. En fait, elles ne sont même pas des surfaces, mais plutôt des zones étendues de l'espace dans lesquelles la probabilité de trouver un électron est importante (voir fig. \ref{ondeproba}). Car, à cette échelle, on ne peut plus décrire la position de l'électron que par une probabilité de présence. En effet, un principe d'indétermination\footnote{Le terme d'indétermination est préférable à celui d'incertitude, communément attribué au principe de Heisenberg, qui laisse penser que l'indétermination est uniquement due à la mauvaise qualité de nos instruments de mesure et non à la caractéristique fondamentale des quantons de ne pas être localisés.}\index{principe@principe!d'indétermination}\index{principe@principe!d'incertitude}, dit de Heisenberg\index{Heisenberg@Heisenberg}, règle la relation entre leur position et leur vitesse\index{vitesse@vitesse}. Celui-ci exprime la constatation que si l'on connaît parfaitement la position d'un tel objet, alors sa vitesse ne peut nous être que totalement inconnue. Et inversement, si sa vitesse est parfaitement déterminée, alors on ne peut savoir où est l'objet. Ainsi, au niveau microscopique, la notion même de mouvement n'est pas claire, ou plutôt est bien plus complexe que celle que nous rencontrons dans la vie quotidienne. +Mais la physique ne s'arrête pas là dans sa description de l'infiniment petit. Elle s'intéresse encore à d'autres objets extraordinaires. En effet, si les mouvements des atomes\index{atome@atome} peuvent encore facilement être représentés en termes de trajectoire\index{trajectoire@trajectoire}, ceux de leurs composants sont bien plus étranges. Car on peut autant les voir comme de petites particules\index{particule@particule} (et, à l'origine, cela à donné lieu à un modèle de l'atome dit de Bohr (voir fig. \ref{Bohr}\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://fr.wikipedia.org/wiki/Accueil= notamment pour le copyright de l'image. Remerciements à son auteur Christophe Dang Ngoc Chan.}) où les électrons orbitaient autour du noyau, comme les planètes autour du soleil) que comme des \og choses\fg{} infiniment étendues que l'on appelle ondes\index{onde@onde}. Cette dualité du mode d'existence des particules élémentaires\index{particule@particule!élémentaire} comme les électrons\index{electron@électron}, les protons\index{proton@proton}, les neutrons\index{neutron@neutron} et bien d'autres encore traduit l'existence d'un objet physique bien particulier, \emph{le quanton}, et présente des difficultés d'analyse de son mouvement. Au niveau des \og trajectoires\fg{} électroniques, par exemple, on constate que certaines orbitales semblent passer par le noyau (voir fig. \ref{orbitale}\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:8orbitals.jpg= notamment pour le copyright de l'image.}). En outre, celles-ci ne peuvent être précisément représentées comme l'orbite d'une planète pourrait l'être. En fait, elles ne sont même pas des surfaces, mais plutôt des zones étendues de l'espace dans lesquelles la probabilité de trouver un électron est importante (voir fig. \ref{ondeproba}\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://fr.wikipedia.org/wiki/Accueil= notamment pour le copyright de l'image. Remerciements à son auteur Pickwick.}). Car, à cette échelle, on ne peut plus décrire la position de l'électron que par une probabilité de présence. En effet, un principe d'indétermination\footnote{Le terme d'indétermination est préférable à celui d'incertitude, communément attribué au principe de Heisenberg, qui laisse penser que l'indétermination est uniquement due à la mauvaise qualité de nos instruments de mesure et non à la caractéristique fondamentale des quantons de ne pas être localisés.}\index{principe@principe!d'indétermination}\index{principe@principe!d'incertitude}, dit de Heisenberg\index{Heisenberg@Heisenberg}, règle la relation entre leur position et leur vitesse\index{vitesse@vitesse}. Celui-ci exprime la constatation que si l'on connaît parfaitement la position d'un tel objet, alors sa vitesse ne peut nous être que totalement inconnue. Et inversement, si sa vitesse est parfaitement déterminée, alors on ne peut savoir où est l'objet. Ainsi, au niveau microscopique, la notion même de mouvement n'est pas claire, ou plutôt est bien plus complexe que celle que nous rencontrons dans la vie quotidienne. \begin{quotation} \og \textit{Il n'y a pour les quantons\index{quanton@quanton} plus de mouvement au sens d'une trajectoire\index{trajectoire@trajectoire}, comme celle que suit une particule classique. Puisqu'un quanton possède une spatialité continue, a une extension spatiale indéfinie, son mode d'évolution temporelle est plus proche de la propagation des ondes\index{onde@onde} que du mouvement des corpuscules\index{corpuscule@corpuscule}. Il faut donc ici rompre avec le projet cartésien qui était de décrire le monde \og par figures et mouvements\fg. Plus de figures, plus de mouvement, mais d'autres caractérisations, bien sûr, qui ne correspondent pas à nos intuitions immédiates et à nos pratique communes -- ce sont de nouvelles notions que les théories physiques font émerger de l'expérience du monde quantique\index{quantique@quantique}.}\fg{} \footnotesize{\cite[p. 33]{JL06}} diff --git a/Introduction/Introduction.tex.bak b/Introduction/Introduction.tex.bak index fee7c99..b691992 100644 --- a/Introduction/Introduction.tex.bak +++ b/Introduction/Introduction.tex.bak @@ -17,19 +17,20 @@ Qui dit périodes dit donc mouvement et, plus précisément, mouvement répétit \subsection{L'Univers\index{univers@univers}} \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.}}} +\caption[L'univers profond]{\label{fig:universprofond}L'univers profond\par \scriptsize{Image du télescope spatial Hubble}} \includegraphics[width=7cm]{universprofond.eps} \end{figure} +%\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.} 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. -Les super-amas de galaxies sont des amas d'amas de galaxies. C'est au niveau de ces super-amas de galaxies que l'univers apparaît assez homogène bien que constitué aussi d'une structure filamenteuse. L'ordre de grandeur de telles structures est de \SI{100}{\mega\parsec} soit \SI{3e24}{\metre} pour les super-amas de galaxies, voire \SI{150}{\mega\parsec} soit \SI{5e24}{\metre} pour les filaments. +Les super-amas de galaxies sont des amas d'amas de galaxies (voir la figure \ref{modeledecourbure}\endnote{Voir le site de l'encyclopédie Wikipedia~: \protect\url{http://fr.wikipedia.org/wiki/Image:End\_of\_universe.jpg} notamment pour le copyright de l'image. Remerciements à la NASA.}). C'est au niveau de ces super-amas de galaxies que l'univers apparaît assez homogène bien que constitué aussi d'une structure filamenteuse. L'ordre de grandeur de telles structures est de \SI{100}{\mega\parsec} soit \SI{3e24}{\metre} pour les super-amas de galaxies, voire \SI{150}{\mega\parsec} soit \SI{5e24}{\metre} pour les filaments. L'univers est en expansion\index{expansion@expansion}, ce qui signifie qu'il s'agrandit. Selon les dernières mesures effectuées par les astrophysiciens, sa forme serait plate\footnote{Voir l'article \og Quelle est la forme de l'univers\fg{}, Science et Vie junior, avril 2001}. Qu'est-ce que cela signifie pour un univers qui est manifestement un volume ? En fait, cela veut dire qu'on peut se l'imaginer comme une feuille de papier dont les dimensions augmenteraient indéfiniment. Nous serions alors des êtres à deux dimensions incapables de se déplacer ailleurs que sur cette feuille. En particulier incapables d'en sortir. Cette feuille s'étendrait donc dans une (troisième) dimensions inaccessible pour nous. Ainsi, notre univers à trois dimensions s'étend dans une dimension supplémentaire qui nous est inaccessible (c'est-à-dire qu'on ne peut s'y déplacer librement), une quatrième dimension\index{dimension@dimension}, le temps\index{temps@temps}. \begin{figure}[t] \centering -\caption[Modèles de courbure]{Modèles de courbure\label{modeledecourbure} \par \scriptsize{Trois modèles issus de la relativité générale\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://fr.wikipedia.org/wiki/Image:End\_of\_universe.jpg= notamment pour le copyright de l'image. Remerciements à la NASA.}}} +\caption[Modèles de courbure]{Modèles de courbure\label{modeledecourbure} \par \scriptsize{Trois modèles issus de la relativité générale}} \includegraphics[width=6cm]{End_of_universe.eps} \end{figure} @@ -49,7 +50,7 @@ Un grand homme rebelle qui eut le malheur d'avoir raison avant les autres. Pour \smallskip Giordano Bruno fut brûlé vif en 1600, pour avoir, sur la base d'une analyse du mouvement de la terre qui annonce la relativité restreinte\index{relativite@relativité!restreinte} de Galilée, remis en cause sa fixité et la finitude de l'univers. -\raggedleft{\footnotesize{Portrait de Giordano Bruno tiré de Wikipedia\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://en.wikipedia.org/wiki/Image:Giordano_Bruno.jpg=}}} +\raggedleft{\footnotesize{Portrait de Giordano Bruno tiré de Wikipedia\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://en.wikipedia.org/wiki/Image:Giordano\_Bruno.jpg=}}} \end{minipage} \hfill \parbox[b]{6cm}{\includegraphics[width=6cm]{Giordano_Bruno.eps}} @@ -59,7 +60,7 @@ Giordano Bruno fut brûlé vif en 1600, pour avoir, sur la base d'une analyse du \begin{figure*}[t] \centering -\caption[L'évolution du Soleil]{L'évolution du soleil\label{evosol} \par \scriptsize{Vers une nébuleuse planétaire\endnote{Voir le site de l'encyclopédie wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Vie_du_soleil.jpg=}}} +\caption[L'évolution du Soleil]{L'évolution du soleil\label{evosol} \par \scriptsize{Vers une nébuleuse planétaire}} \includegraphics[width=14cm]{Vie_du_soleil.eps} \end{figure*} @@ -70,44 +71,44 @@ En réalité, les choses sont plus complexes encore, puisqu'aujourd'hui les phys \subsection{Les amas de galaxies} \begin{figure}[t] \centering -\caption[Groupe local]{Groupe local\label{localesgalaxies} \par \scriptsize{Les galaxies proches\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://fr.wikipedia.org/wiki/Accueil= notamment pour le copyright de l'image. Remerciements à son auteur Greg Goebel.}}} +\caption[Groupe local]{Groupe local\label{localesgalaxies} \par \scriptsize{Les galaxies proches}} \includegraphics[width=6cm]{Groupelocal.eps} \end{figure} Viennent ensuite les amas de galaxies\index{amas@amas!de galaxies}. Leur nombre dans l'univers est estimé à \num{25} milliards. La répartition de ces amas de galaxies n'est pas homogène, contrairement à celle des super-amas de galaxies. Cette répartition est celle de filaments qui laissent apparaître des zones plus ou moins denses d'amas de galaxies. -Cette répartition est complexe et encore sujette à de nombreuses discussions. En particulier elle est l'objet d'études approfondies en relation avec la naissance de l'univers\index{univers@univers}. En effet, il est difficile d'expliquer comment, à partir des conditions homogènes propres au big-bang\index{big@big!bang}, sont nées des structures aussi particulières. La figure \ref{universprofond} montre ce que l'on peut voir au-delà des étoiles de notre galaxie. Sur la photo de cette \og petite\fg{} partie de l'espace ne figurent que des galaxies. Leur nombre et leur diversité sont saisissants. La figure \ref{localesgalaxies} montre quant à elle le groupe local dans lequel se trouve notre galaxie la Voie Lactée. Il s'agit d'un amas de galaxies. +Cette répartition est complexe et encore sujette à de nombreuses discussions. En particulier elle est l'objet d'études approfondies en relation avec la naissance de l'univers\index{univers@univers}. En effet, il est difficile d'expliquer comment, à partir des conditions homogènes propres au big-bang\index{big@big!bang}, sont nées des structures aussi particulières. La figure \ref{universprofond} montre ce que l'on peut voir au-delà des étoiles de notre galaxie. Sur la photo de cette \og petite\fg{} partie de l'espace ne figurent que des galaxies. Leur nombre et leur diversité sont saisissants. La figure \ref{localesgalaxies}\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://fr.wikipedia.org/wiki/Accueil= notamment pour le copyright de l'image. Remerciements à son auteur Greg Goebel.} montre quant à elle le groupe local dans lequel se trouve notre galaxie la Voie Lactée. Il s'agit d'un amas de galaxies. \subsection{Les galaxies\index{galaxie@galaxie}} \begin{figure}[t] \centering -\caption[Galaxie du Sombrero]{Galaxie du Sombrero\label{galaxies} \par \scriptsize{Image du télescope spatial Hubble\endnote{Voir le site du télescope spatial Hubble~: op cit. Remerciements à la NASA.}}} +\caption[Galaxie du Sombrero]{Galaxie du Sombrero\label{galaxies} \par \scriptsize{Image du télescope spatial Hubble}} \includegraphics[width=6cm]{Sombrero.eps} \end{figure} -Au nombre d'environ trois cent cinquante milliards dans l'univers, les galaxies\index{galaxie@galaxie} sont des structures composées de centaines de milliards d'étoiles\index{etoile@étoile} qui se regroupent sous l'effet de la force de gravitation\index{gravitation@gravitation}. Dans l'espace interstellaire\index{espace@espace!interstellaire} constituant le \og vide\fg{} autour des étoiles se trouvent aussi des nuages de poussières et de gaz (des nébuleuses\index{nebuleuse@nébuleuse}). +Au nombre d'environ trois cent cinquante milliards dans l'univers, les galaxies\index{galaxie@galaxie} sont des structures composées de centaines de milliards d'étoiles\index{etoile@étoile} qui se regroupent sous l'effet de la force de gravitation\index{gravitation@gravitation}(voir figure \ref{galaxies}\endnote{Voir le site du télescope spatial Hubble~: op cit. Remerciements à la NASA.}). Dans l'espace interstellaire\index{espace@espace!interstellaire} constituant le \og vide\fg{} autour des étoiles se trouvent aussi des nuages de poussières et de gaz (des nébuleuses\index{nebuleuse@nébuleuse}). A cette échelle, les mouvements des galaxies sont perceptibles. Presque toutes s'éloignent de nous. Ce phénomène est appelé \og expansion\index{expansion@expansion}\fg. Il est interprété comme un mouvement dû au \og gonflement\fg{} de l'univers\index{univers@univers} lui-même. Le mouvement local des galaxies\index{galaxie@galaxie} étant faible par rapport à celui général de l'expansion\index{expansion@expansion} de l'univers, il est rare de voir des galaxies se rapprocher de nous. Pourtant, cela est le cas de la très fameuse (parce qu'observable à l'\oe il nu et la plus proche galaxie massive (autre que naine) de nous) galaxie d'Andromède\index{Andromede@Andromède}. \begin{figure*}[t] \centering -\caption[Interaction de deux galaxies]{Interaction de deux galaxies\label{choc} \par \scriptsize{Image du télescope spatial Hubble\endnote{Voir le site du télescope spatial Hubble~: ibid. Remerciements à la NASA.}}} +\caption[Interaction de deux galaxies]{Interaction de deux galaxies\label{choc} \par \scriptsize{Image du télescope spatial Hubble}} \includegraphics[width=14cm]{HubbleChienChasse.eps} \end{figure*} -Les mouvements locaux des galaxies entre elles donnent lieu à des \og chocs\fg{}\index{choc@choc!galactique} spectaculaires entre galaxies. Le résultat est par exemple le système des deux galaxies dites des \og Chiens de chasse\fg{} ou sur la figure \ref{choc} \og la grande spirale NGC 2207\fg{} (à gauche), située à 114 millions d'années-lumière de la terre, étendant et disloquant sur plusieurs centaines de milliers d'années-lumière la \og petite IC2163\fg{} en longs filaments de \og gaz et de poussières\fg{}. +Les mouvements locaux des galaxies entre elles donnent lieu à des \og chocs\fg{}\index{choc@choc!galactique} spectaculaires entre galaxies. Le résultat est par exemple le système des deux galaxies dites des \og Chiens de chasse\fg{} ou sur la figure \ref{choc}\endnote{Voir le site du télescope spatial Hubble~: ibid. Remerciements à la NASA.} \og la grande spirale NGC 2207\fg{} (à gauche), située à 114 millions d'années-lumière de la terre, étendant et disloquant sur plusieurs centaines de milliers d'années-lumière la \og petite IC2163\fg{} en longs filaments de \og gaz et de poussières\fg{}. \subsection{Les étoiles\index{etoile@étoile}} 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{}. +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}\endnote{Voir le site de l'encyclopédie wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Vie\_du\_soleil.jpg=}) 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}\endnote{Voir le site du télescope spatial Hubble~: ibid. Remerciements à la NASA.}) 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 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}. \begin{figure} \centering -\caption[Nébuleuse planétaire]{Nébuleuse planétaire\label{planetaire} \par \scriptsize{Image du télescope spatial Hubble\endnote{Voir le site du télescope spatial Hubble~: ibid. Remerciements à la NASA.}}} +\caption[Nébuleuse planétaire]{Nébuleuse planétaire\label{planetaire} \par \scriptsize{Image du télescope spatial Hubble}} \includegraphics[width=6cm]{NebuleusePlanetaire.eps} \end{figure} @@ -121,34 +122,34 @@ La première exoplanète découverte l'a été en 1995 par l'observatoire de Gen \begin{figure}[t] \centering -\caption[Première exoplanète]{Première image d'une exoplanète\label{2M1207} \par \scriptsize{Il s'agit d'une image dans le proche infrarouge. La planète est en bas à droite. Image de Hubble\endnote{Voir le site de Hubble~: \url=http://hubblesite.org/newscenter/archive/releases/2005/03/image/a/=}}} +\caption[Première exoplanète]{Première image d'une exoplanète\label{2M1207} \par \scriptsize{Il s'agit d'une image dans le proche infrarouge. La planète est en bas à droite. Image de Hubble}} \includegraphics[width=6cm]{2M1207.eps} \end{figure} -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. +En 2005, soit dix ans après, la première image d'une exoplanète (voir figure \ref{2M1207}\endnote{Voir le site de Hubble~: \url=http://hubblesite.org/newscenter/archive/releases/2005/03/image/a/=}) 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. \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. +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}\endnote{Voir le site de l'encyclopédie wikipedia~: \url=http://fr.wikipedia.org/wiki/Image:Solar\_sys.jpg= Remerciements à la NASA.} présente le système solaire sans respecter les ordres de grandeurs. \begin{figure*}[t] \centering -\caption[Système solaire]{Système solaire\label{systemesolaire} \par \scriptsize{Image de la Nasa\endnote{Voir le site de l'encyclopédie wikipedia~: \url=http://fr.wikipedia.org/wiki/Image:Solar_sys.jpg= Remerciements à la NASA.}}} +\caption[Système solaire]{Système solaire\label{systemesolaire} \par \scriptsize{Image de la Nasa}} \includegraphics[width=14cm]{Systemesolaire.eps} \end{figure*} -La rotation des planètes se fait dans un seul plan que l'on nomme le plan de l'écliptique\index{ecliptique@écliptique}. Relativement à la Terre, ce plan est décrit par l'orbite du soleil. La nuit, c'est donc le long de la trajectoire du Soleil qu'on peut voir certaines planètes\index{planete@planète}. Car, si certaines sont visibles en pleine nuit, d'autres ne le seront jamais. C'est le cas, par exemple, de Vénus\index{Venus@Vénus}. C'est une planète qui tourne près du Soleil. Elle tourne aussi à l'intérieur du cercle (en réalité c'est une ellipse\index{ellipse@ellipse} quasiment circulaire) que décrit la Terre sur sa trajectoire\index{trajectoire@trajectoire} (on parle de l'orbite\index{orbite@orbite} de la Terre et on parle de planète interne). C'est pourquoi, depuis la Terre, nous ne la verrons que dans le voisinage du Soleil. Ainsi, on peut la voir le matin avant que le soleil se lève (on l'appelle alors l'Étoile du matin\index{etoile@étoile!du matin}) ou le soir, peu de temps après que le Soleil se soit couché (elle porte alors le nom d'Étoile du soir\index{etoile@étoile!du soir}), mais pas au cours de la nuit. Les planètes se divisent en trois groupes~: les quatre planètes dites telluriques\index{planete@planète!tellurique} sont celles qui sont le plus proche du soleil. Elles sont petites, solides et relativement semblables à la Terre. Les quatre planètes dites joviennes\index{planete@planète!jovienne} sont, à l'image de Jupiter\index{Jupiter@Jupiter}, très grosses et gazeuses. Enfin, à partir de Pluton\index{Pluton@Pluton}, les corps sont très petits, très éloignés et ne sont plus considérés comme des planètes (même si on parle de planètes naines). La figure \ref{lesplanetes} présente les planètes en respectant les ordres de grandeurs de leurs tailles respectives. +La rotation des planètes se fait dans un seul plan que l'on nomme le plan de l'écliptique\index{ecliptique@écliptique}. Relativement à la Terre, ce plan est décrit par l'orbite du soleil. La nuit, c'est donc le long de la trajectoire du Soleil qu'on peut voir certaines planètes\index{planete@planète}. Car, si certaines sont visibles en pleine nuit, d'autres ne le seront jamais. C'est le cas, par exemple, de Vénus\index{Venus@Vénus}. C'est une planète qui tourne près du Soleil. Elle tourne aussi à l'intérieur du cercle (en réalité c'est une ellipse\index{ellipse@ellipse} quasiment circulaire) que décrit la Terre sur sa trajectoire\index{trajectoire@trajectoire} (on parle de l'orbite\index{orbite@orbite} de la Terre et on parle de planète interne). C'est pourquoi, depuis la Terre, nous ne la verrons que dans le voisinage du Soleil. Ainsi, on peut la voir le matin avant que le soleil se lève (on l'appelle alors l'Étoile du matin\index{etoile@étoile!du matin}) ou le soir, peu de temps après que le Soleil se soit couché (elle porte alors le nom d'Étoile du soir\index{etoile@étoile!du soir}), mais pas au cours de la nuit. Les planètes se divisent en trois groupes~: les quatre planètes dites telluriques\index{planete@planète!tellurique} sont celles qui sont le plus proche du soleil. Elles sont petites, solides et relativement semblables à la Terre. Les quatre planètes dites joviennes\index{planete@planète!jovienne} sont, à l'image de Jupiter\index{Jupiter@Jupiter}, très grosses et gazeuses. Enfin, à partir de Pluton\index{Pluton@Pluton}, les corps sont très petits, très éloignés et ne sont plus considérés comme des planètes (même si on parle de planètes naines). La figure \ref{lesplanetes}\endnote{Voir le site de l'encyclopédie~: \planete{} Remerciements à la NASA.} présente les planètes en respectant les ordres de grandeurs de leurs tailles respectives. % la commande ci-dessous est nécessaire car on a des % dans l'url \urldef\planete\url{http://fr.wikipedia.org/wiki/Image:Portrait_de_famille_%281_px_%3D_1000_km%29.jpg} \begin{figure*}[t] \centering -\caption[La taille des planètes]{La taille des planètes\label{lesplanetes} \par \scriptsize{Image de la Nasa\endnote{Voir le site de l'encyclopédie~: \planete{} Remerciements à la NASA.}}} +\caption[La taille des planètes]{La taille des planètes\label{lesplanetes} \par \scriptsize{Image de la Nasa}} \includegraphics[width=14cm]{Lesplanetes.eps} \end{figure*} -Il existe encore d'autres corps importants dans le système solaire~: les \emph{comètes}\index{comete@comète} (voir figure \ref{comete}). Ce sont de très petits corps (quelques dizaines de kilomètres de diamètre) qui viennent de régions très éloignées du système solaire (le nuage de Oort\index{nuage@nuage!de Oort}~: \og il s'agirait d'une vaste enveloppe de corps orbitant entre \SI{40000}{\astronomicalunit} et \SI{150000}{\astronomicalunit} (\SI{0,73}{pc}) de distance du Soleil, et donc située bien au-delà de l'orbite des planètes et de la ceinture de Kuiper\fg{}\endnote{voir~: \url=http://fr.wikipedia.org/wiki/Nuage_de_Oort=}) et qui, pour ainsi dire, tombent sur le Soleil selon une trajectoire très elliptique\index{elliptique@elliptique}. +Il existe encore d'autres corps importants dans le système solaire~: les \emph{comètes}\index{comete@comète} (voir figure \ref{comete}\endnote{Voir le site du télescope spatial Hubble~: ibid. Remerciements à la NASA.}). Ce sont de très petits corps (quelques dizaines de kilomètres de diamètre) qui viennent de régions très éloignées du système solaire (le nuage de Oort\index{nuage@nuage!de Oort}~: \og il s'agirait d'une vaste enveloppe de corps orbitant entre \SI{40000}{\astronomicalunit} et \SI{150000}{\astronomicalunit} (\SI{0,73}{pc}) de distance du Soleil, et donc située bien au-delà de l'orbite des planètes et de la ceinture de Kuiper\fg{}\endnote{voir~: \url=http://fr.wikipedia.org/wiki/Nuage\_de\_Oort=}) et qui, pour ainsi dire, tombent sur le Soleil selon une trajectoire très elliptique\index{elliptique@elliptique}. En passant elles laissent sur leur orbite\index{orbite@orbite} une traînée de poussières qui se manifeste sous la forme d'une magnifique queue. Celle-ci est produite par le vent solaire qui emporte les éléments à la surface de la comète. La direction de la queue est donc toujours à l'opposé du soleil et peu être perpendiculaire à la trajectoire de la comète. La figure \ref{billetcomete} présente pourtant un billet de banque suisse sur lequel est représenté une comète dont la queue ne pointe pas à tort vers le soleil. @@ -158,17 +159,17 @@ 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}\endnote{Voir le site de l'encyclopédie wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Leonid\_Meteor\_Storm\_1833.jpg=} 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 -\caption[Une comète]{Une comète\label{comete} \par \scriptsize{Image du télescope spatial Hubble\endnote{Voir le site du télescope spatial Hubble~: ibid. Remerciements à la NASA.}}} +\caption[Une comète]{Une comète\label{comete} \par \scriptsize{Image du télescope spatial Hubble}} \includegraphics[width=6cm]{comete.eps} \end{figure} \begin{figure} \centering -\caption[Étoiles filantes]{Pluie d'étoiles filantes des Léonides\label{Leonides} \par \scriptsize{Leonid Meteor Strom, as seen over North America in the night of November 12./13., 1833.\endnote{Voir le site de l'encyclopédie wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Leonid_Meteor_Storm_1833.jpg=}}} +\caption[Étoiles filantes]{Pluie d'étoiles filantes des Léonides\label{Leonides} \par \scriptsize{Leonid Meteor Strom, as seen over North America in the night of November 12./13., 1833.}} \includegraphics[width=6cm]{Leonid_Meteor_Storm_1833.eps} \end{figure} @@ -201,12 +202,12 @@ De plus, on ne peut comprendre que les saison\index{saison@saison} soient diffé \begin{figure}[t] \centering -\caption[La terre et la lune]{La terre et la lune\label{terrelune} \par \scriptsize{Image de la Nasa\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Moon_Earth_Comparison.png=. Remerciements à la NASA.}}} +\caption[La terre et la lune]{La terre et la lune\label{terrelune} \par \scriptsize{Image de la Nasa}} \includegraphics[width=6cm]{Terrelune.eps} \end{figure} \subsubsection{La Lune} -Finissons ce petit voyage dans le monde céleste en parlant de la Lune. La figure \ref{terrelune} montre le rapport de taille entre la Lune et la Terre, ainsi que les différences d'aspect de leur surface. +Finissons ce petit voyage dans le monde céleste en parlant de la Lune. La figure \ref{terrelune}\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Moon\_Earth\_Comparison.png=. Remerciements à la NASA.} montre le rapport de taille entre la Lune et la Terre, ainsi que les différences d'aspect de leur surface. Il peut sembler au premier abord que le mouvement de la Lune est simple. En effet, elle gravite sur une ellipse (on la voit donc parfois un peu plus grosse et parfois un peu plus petite~: au périgée\index{perigee@périgée} où la distance terre-lune est de \SI{3,654e8}{\metre}, son diamètre apparent\index{diametre@diamètre!apparent} est de \ang{;33,5;} et à l'apogée\index{apogee@apogée} où la distance vaut \SI{4,067e8}{,metre}, son diamètre apparent vaut \ang{;29,3;}, soit \(\sim\) 10\% de la distance moyenne) en un mois environ. La variation apparente de sa taille, ainsi que de celle du soleil due à la trajectoire elliptique que suit la terre et qui oscille entre \ang{;31,5;} et \ang{;32,5;}, expliquent l'allure des différentes éclipses de Soleil. Quand la Lune est éloignée de la Terre, elle ne cache pas tout le disque solaire et l'éclipse présente un anneau de lumière autour de la Lune, on parle alors d'éclipse annulaire\index{eclipse@éclipse!annulaire}. Par contre, quand la Lune est proche de la Terre, son diamètre apparent est plus grand et la Lune couvre tout le disque solaire. On parle alors d'éclipse totale\index{eclipse@éclipse!totale}. @@ -220,11 +221,11 @@ Quand la Lune ne nous présente plus que sa partie éclairée, elle est alors \o Enfin, la Lune se présente une nouvelle fois en demi-Lune, c'est-à-dire qu'on en voit que l'autre quart. C'est le Dernier Quartier. -La figure \ref{phasesdelalune} résume la situation décrite ci-dessus. +La figure \ref{phasesdelalune}\endnote{Voir le site de l'encyclopédie~: \url=http://commons.wikimedia.org/wiki/Image:TerreOrbiteLuneEtPhases.png=} résume la situation décrite ci-dessus. \begin{figure*}[t] \centering -\caption[Les phases de la lune]{Les phases de la lune\label{phasesdelalune} \par \scriptsize{Ce n'est pas l'ombre de la terre\endnote{Voir le site de l'encyclopédie~: \url=http://commons.wikimedia.org/wiki/Image:TerreOrbiteLuneEtPhases.png=}}} +\caption[Les phases de la lune]{Les phases de la lune\label{phasesdelalune} \par \scriptsize{Ce n'est pas l'ombre de la terre}} \includegraphics[width=14cm]{TerreOrbiteLuneEtPhases.eps} \end{figure*} @@ -232,11 +233,11 @@ La question se pose alors de la différence entre éclipse de Soleil\index{eclip \begin{figure} \centering -\caption[Orbites de la lune et du soleil]{Orbites de la lune et du soleil\label{Orbite-lune-soleil} \par \scriptsize{Des plans différents\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://fr.wikipedia.org/wiki/Image:Orbite-lune-soleil.png=}}} +\caption[Orbites de la lune et du soleil]{Orbites de la lune et du soleil\label{Orbite-lune-soleil} \par \scriptsize{Des plans différents}} \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 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}. +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}\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://fr.wikipedia.org/wiki/Image:Orbite-lune-soleil.png=}, 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. @@ -274,7 +275,7 @@ Comme cette force agit seulement à faible distance, c'est-à-dire qu'elle a une \begin{figure} \centering -\caption[La nébuleuse du Crabe]{La nébuleuse du Crabe\label{crabnebula} \par \scriptsize{Les restes d'une supernovae\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://fr.wikipedia.org/wiki/Image:Crab_Nebula.jpg= notamment pour le copyright de l'image.}}} +\caption[La nébuleuse du Crabe]{La nébuleuse du Crabe\label{crabnebula} \par \scriptsize{Les restes d'une supernovae\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://fr.wikipedia.org/wiki/Image:Crab\_Nebula.jpg= notamment pour le copyright de l'image.}}} \includegraphics[width=6cm]{Crab_Nebula.eps} \end{figure} diff --git a/PhysiqueTheorique/PhysiqueTheorique.tex b/PhysiqueTheorique/PhysiqueTheorique.tex index 431e358..cb892e6 100644 --- a/PhysiqueTheorique/PhysiqueTheorique.tex +++ b/PhysiqueTheorique/PhysiqueTheorique.tex @@ -14,7 +14,7 @@ Pour le comprendre, il faut revenir sur les deux formes d'énergie potentielle e \section{Énergie potentielle\index{energie@énergie!potentielle}} Il s'agit d'un concept fondamental au même titre que l'énergie cinétique. \begin{quotation} -Le principe de base - qu'on appelle le \emph{principe de l'énergie potentielle} - déclare que toutes les forces proviennent d'une fonction d'énergie potentielle notée V(x). \citep[p. 106]{SU03} +Le principe de base - qu'on appelle le \emph{principe de l'énergie potentielle} - déclare que toutes les forces proviennent d'une fonction d'énergie potentielle notée V(x). \cite[p. 106]{SU03} \end{quotation} Les équations \ref{fderiveenpot} et \ref{fintenpot}, page \pageref{fintenpot} traduisent mathématiquement ce principe~: \begin{equation}\label{thfderiveenpot} diff --git a/PhysiqueTheorique/PhysiqueTheorique.tex.bak b/PhysiqueTheorique/PhysiqueTheorique.tex.bak index 8cd98a9..cb892e6 100644 --- a/PhysiqueTheorique/PhysiqueTheorique.tex.bak +++ b/PhysiqueTheorique/PhysiqueTheorique.tex.bak @@ -14,7 +14,7 @@ Pour le comprendre, il faut revenir sur les deux formes d'énergie potentielle e \section{Énergie potentielle\index{energie@énergie!potentielle}} Il s'agit d'un concept fondamental au même titre que l'énergie cinétique. \begin{quotation} -Le principe de base - qu'on appelle le \emph{principe de l'énergie potentielle} - déclare que toutes les forces proviennent d'une fonction d'énergie potentielle notée V(x). \citep[p. 106]{SU03} +Le principe de base - qu'on appelle le \emph{principe de l'énergie potentielle} - déclare que toutes les forces proviennent d'une fonction d'énergie potentielle notée V(x). \cite[p. 106]{SU03} \end{quotation} Les équations \ref{fderiveenpot} et \ref{fintenpot}, page \pageref{fintenpot} traduisent mathématiquement ce principe~: \begin{equation}\label{thfderiveenpot} @@ -101,7 +101,7 @@ Chaque parcourt ne va pas transférer son énergie cinétique en énergie potent \textit{En reliant deux points, la trajectoire prise par le corps n'est pas toujours celle qui lui fait dépenser globalement le moins d'énergie car c'est la dépense immédiate (ou plutôt instantanée) d'énergie qui est minimisée (comme si le corps ne percevait que les conditions de son environnement immédiat) et si le chemin parcouru est long, un chemin plus court avec une dépense d'énergie immédiate plus élevée peut permettre une dépense globale inférieure. Une analogie avec la consommation en carburant d'une voiture peut être faite.} -\textit{Dans ce \og résumé \fg, \og énergie\fg{} signifie énergie cinétique, et une \og dépense d'énergie\fg{} signifie que de l'énergie cinétique se transforme en énergie potentielle.}\fg\endnote{Voir Wikipedia : \url|https://fr.wikipedia.org/wiki/Principe_de_moindre_action|} +\textit{Dans ce \og résumé \fg, \og énergie\fg{} signifie énergie cinétique, et une \og dépense d'énergie\fg{} signifie que de l'énergie cinétique se transforme en énergie potentielle.}\fg\endnote{Voir Wikipedia : \url|https://fr.wikipedia.org/wiki/Principe\_de\_moindre\_action|} \end{quotation} \begin{quotation} @@ -114,7 +114,7 @@ Chaque parcourt ne va pas transférer son énergie cinétique en énergie potent \textit{La chute libre d'un corps est l'exemple type de la transformation de l'énergie potentielle (gravitationnelle) en énergie cinétique. Le ralentissement et l'arrêt (avant sa chute) d'un corps lancé verticalement est un exemple de la transformation inverse.} -\textit{Les frottements imposent une transformation plus compliquée car ils engendrent de la chaleur, qui est l'énergie cinétique des molécules des matériaux, mais en négligeant cette forme d'énergie, on peut utiliser le Principe de moindre action en considérant que de l'énergie cinétique se perd (sort du système étudié).} \fg{}\endnote{Voir Wikipedia : \url{https://fr.wikipedia.org/wiki/Principe_de_moindre_action_et_mécanique_classique}} +\textit{Les frottements imposent une transformation plus compliquée car ils engendrent de la chaleur, qui est l'énergie cinétique des molécules des matériaux, mais en négligeant cette forme d'énergie, on peut utiliser le Principe de moindre action en considérant que de l'énergie cinétique se perd (sort du système étudié).} \fg{}\endnote{Voir Wikipedia : \url{https://fr.wikipedia.org/wiki/Principe\_de\_moindre\_action\_et\_mécanique\_classique}} \end{quotation} Ainsi le principe de moindre action se réalise-t-il et il s'écrit pratiquement~: @@ -125,7 +125,7 @@ Mathématiquement cela signifie que toutes les variations sont minimalisées sur \section{Euler-Lagrange} \begin{quotation} -\og \emph{Cette méthode aboutit aux équations d'Euler-Lagrange qui donnent des trajets sur lesquels l'action n'est pas toujours minimale, mais parfois maximale, voire ni l'un ni l'autre mais seulement stationnaire. Dans tous les cas ces trajets respectent les conditions physiques et sont donc réalistes. Mais le long de chacun de ces trajets, si deux points sont assez proches (mesure faite par la longueur du trajet les séparant) alors on peut démontrer qu'entre eux ce trajet minimise l'action dans la méthode variationnelle, ce qui justifie le nom du principe.} \fg{}\endnote{Voir Wikipedia : \url{https://fr.wikipedia.org/wiki/Principe_de_moindre_action_et_mécanique_classique}} +\og \emph{Cette méthode aboutit aux équations d'Euler-Lagrange qui donnent des trajets sur lesquels l'action n'est pas toujours minimale, mais parfois maximale, voire ni l'un ni l'autre mais seulement stationnaire. Dans tous les cas ces trajets respectent les conditions physiques et sont donc réalistes. Mais le long de chacun de ces trajets, si deux points sont assez proches (mesure faite par la longueur du trajet les séparant) alors on peut démontrer qu'entre eux ce trajet minimise l'action dans la méthode variationnelle, ce qui justifie le nom du principe.} \fg{}\endnote{Voir Wikipedia : \url{https://fr.wikipedia.org/wiki/Principe\_de\_moindre\_action\_et\_mécanique\_classique}} \end{quotation} Pour obtenir les équations d'Euler-Lagrange, il faut partir du principe de moindre action~: diff --git a/Preambule.tex b/Preambule.tex index d94881e..def9184 100644 --- a/Preambule.tex +++ b/Preambule.tex @@ -3,7 +3,7 @@ \usepackage{etex} % nécessaire au package xy (pourquoi ????) \usepackage[T1]{fontenc} % écrire avec les accents \usepackage[utf8]{inputenc} % écrire avec les accents -\usepackage{natbib} % à utiliser impérativement avec apalike-fr pour parfaire les entrées +%\usepackage{natbib} % à utiliser impérativement avec apalike-fr pour parfaire les entrées %\usepackage{babel} \usepackage[english,main=french]{babel} % pour le support des documents multilingues. Il vaut mieux mettre french là plutôt que dans le documentclass % pour pouvoir gérer l'anglais ou autres langues. @@ -31,7 +31,8 @@ \usepackage{hhline} % pour faire des filets spéciaux dans les tableaux \usepackage{supertabular} % pour faire des tableaux sur plusieurs pages \usepackage{float} % permet un placement obligatoire -\usepackage{url} % permet une bonne gestion de la césure des url +\usepackage[hyphens]{url} % permet une bonne gestion de la césure des url +\usepackage{xurl} \usepackage{graphicx} % pour charger le module étendu graphicx du module graphics. Pour différents effets graphiques dont l'orientation et le redimentionnement des eps %\usepackage{graphics} % idem que graphicx, mais sans orientation et redimentionnement \usepackage{wrapfig} % pour mettre des figures dans le flot du texte @@ -47,6 +48,9 @@ \usepackage{ifthen} \usepackage{moreverb} \usepackage{tikz} +\usepackage[backend=biber]{biblatex} +%\usepackage[backend=bibtex]{biblatex} + \usepackage{multido} % pour répéter des figures en pstricks %\usepackage[figuresright ou figuresleft]{rotating} % permet de faire tourner des figures \sidewaysfigure ou des textes \rotatebox dans un sens ou un autre @@ -68,11 +72,20 @@ \DeclareCaptionLabelSeparator{endash}{ -- } % pour définir un tiret après le numéro des légentes \captionsetup{labelsep=endash,justification=centering,belowskip=10pt} % pour avoir un petit trait après le no de légende \usepackage{verbatim} % pour faire des commentaires longs \begin{comment} -\usepackage{endnotes} % pour faire des notes de fin +%\usepackage{endnotes} % pour faire des notes de fin %\renewcommand{\theendnote}{\Roman{endnote}} % pour mettre les notes de fin en romain +\usepackage{enotez} +\setenotez{ + reset = true, + backref = true, + totoc = chapter, + %split = chapter, + list-style = itemize +} \renewcommand{\thefootnote}{\alph{footnote}} % pour mettre les notes de bas de page en alphabétique %\usepackage{apalike} % nécessaire pour que le style de bibliographie apalike soit correctement appliqué % attention, le module apalike ne doit être utilisé qu'en anglais. Le titre bibliography est codé en dur à l'intérieur du module + %%% natbib %\usepackage{textcomp} % pour mettre de beaux degrés \usepackage{textcomp} % pour le symbole pourmille~: \textperthousand (! pas en mode math) et pour le symbole de copyleft \textcopyleft @@ -127,4 +140,8 @@ range-phrase = { \translate{to (numerical range)} }, %\selectbiblanguage{french} % sélection de la langue (attention, pour apalike, il faut sélectionner apalike-fr) \usepackage{lettrine} % pour mettre des lettrines \usepackage{listings} % pour mettre du code informatique non interprété -\usepackage{xspace} % pour gérer les expaces nott. entre X et e pour les siècles \ No newline at end of file +\usepackage{xspace} % pour gérer les expaces nott. entre X et e pour les siècles + +% Suivant le cours DF ou OS, choisir ci-dessous +%\bibliography{Bibliographies/BiblioCours} +\bibliography{Bibliographies/BiblioCoursOS} \ No newline at end of file diff --git a/Preambule.tex.bak b/Preambule.tex.bak index a4947e3..def9184 100644 --- a/Preambule.tex.bak +++ b/Preambule.tex.bak @@ -3,7 +3,7 @@ \usepackage{etex} % nécessaire au package xy (pourquoi ????) \usepackage[T1]{fontenc} % écrire avec les accents \usepackage[utf8]{inputenc} % écrire avec les accents -\usepackage{natbib} % à utiliser impérativement avec apalike-fr pour parfaire les entrées +%\usepackage{natbib} % à utiliser impérativement avec apalike-fr pour parfaire les entrées %\usepackage{babel} \usepackage[english,main=french]{babel} % pour le support des documents multilingues. Il vaut mieux mettre french là plutôt que dans le documentclass % pour pouvoir gérer l'anglais ou autres langues. @@ -14,7 +14,7 @@ \setcounter{tocdepth}{5} % pour définir la profondeur de la table des matières \usepackage{makeidx} % pour permettre de construire un index \makeindex % pour construire effectivement l'index -\usepackage{morewrites} +\usepackage{morewrites} % pour permettre la compilation à partir de plus de 20 fichiers \makeatletter % pour faire de @ une lettre simple (et non un caractère associé à une macro interne \usepackage{path} % pour mettre du code non interprété \usepackage{fancybox} % pour faire des boites entourée de différents types de cadres @@ -31,7 +31,8 @@ \usepackage{hhline} % pour faire des filets spéciaux dans les tableaux \usepackage{supertabular} % pour faire des tableaux sur plusieurs pages \usepackage{float} % permet un placement obligatoire -\usepackage{url} % permet une bonne gestion de la césure des url +\usepackage[hyphens]{url} % permet une bonne gestion de la césure des url +\usepackage{xurl} \usepackage{graphicx} % pour charger le module étendu graphicx du module graphics. Pour différents effets graphiques dont l'orientation et le redimentionnement des eps %\usepackage{graphics} % idem que graphicx, mais sans orientation et redimentionnement \usepackage{wrapfig} % pour mettre des figures dans le flot du texte @@ -47,6 +48,9 @@ \usepackage{ifthen} \usepackage{moreverb} \usepackage{tikz} +\usepackage[backend=biber]{biblatex} +%\usepackage[backend=bibtex]{biblatex} + \usepackage{multido} % pour répéter des figures en pstricks %\usepackage[figuresright ou figuresleft]{rotating} % permet de faire tourner des figures \sidewaysfigure ou des textes \rotatebox dans un sens ou un autre @@ -68,11 +72,20 @@ \DeclareCaptionLabelSeparator{endash}{ -- } % pour définir un tiret après le numéro des légentes \captionsetup{labelsep=endash,justification=centering,belowskip=10pt} % pour avoir un petit trait après le no de légende \usepackage{verbatim} % pour faire des commentaires longs \begin{comment} -\usepackage{endnotes} % pour faire des notes de fin +%\usepackage{endnotes} % pour faire des notes de fin %\renewcommand{\theendnote}{\Roman{endnote}} % pour mettre les notes de fin en romain +\usepackage{enotez} +\setenotez{ + reset = true, + backref = true, + totoc = chapter, + %split = chapter, + list-style = itemize +} \renewcommand{\thefootnote}{\alph{footnote}} % pour mettre les notes de bas de page en alphabétique %\usepackage{apalike} % nécessaire pour que le style de bibliographie apalike soit correctement appliqué % attention, le module apalike ne doit être utilisé qu'en anglais. Le titre bibliography est codé en dur à l'intérieur du module + %%% natbib %\usepackage{textcomp} % pour mettre de beaux degrés \usepackage{textcomp} % pour le symbole pourmille~: \textperthousand (! pas en mode math) et pour le symbole de copyleft \textcopyleft @@ -127,4 +140,8 @@ range-phrase = { \translate{to (numerical range)} }, %\selectbiblanguage{french} % sélection de la langue (attention, pour apalike, il faut sélectionner apalike-fr) \usepackage{lettrine} % pour mettre des lettrines \usepackage{listings} % pour mettre du code informatique non interprété -\usepackage{xspace} % pour gérer les expaces nott. entre X et e pour les siècles \ No newline at end of file +\usepackage{xspace} % pour gérer les expaces nott. entre X et e pour les siècles + +% Suivant le cours DF ou OS, choisir ci-dessous +%\bibliography{Bibliographies/BiblioCours} +\bibliography{Bibliographies/BiblioCoursOS} \ No newline at end of file diff --git a/Solutions.tex b/Solutions.tex index 54166dc..adbf1b0 100644 --- a/Solutions.tex +++ b/Solutions.tex @@ -180,7 +180,7 @@ \[v=\frac{d}{T}=\frac{9,4e8}{365\cdot 24\cdot 3600}=\SI{29,8}{\kilo\metre\per\second}\] \end{Solution} -\begin{Solution}{16} +\begin{Solution}{71} On a simplement pour le velociraptor~: \[v=\frac{d}{t}=\frac{3,058}{0,284}=\SI{10,8}{\metre\per\second}=\SI{38,8}{\kilo\metre\per\hour}\] Et pour le tyranosaure~: diff --git a/Thermodynamique/Thermodynamique.tex b/Thermodynamique/Thermodynamique.tex index eb4891e..c22f8a8 100644 --- a/Thermodynamique/Thermodynamique.tex +++ b/Thermodynamique/Thermodynamique.tex @@ -21,7 +21,7 @@ Une autre échelle, comportant \SI{180}{\Fahrenheit} entre la fusion de la glace \text{Fusion de la glace}\;&\longleftrightarrow\;\SI{32}{\Fahrenheit}\\ \text{Vaporisation de l'eau}\;&\longleftrightarrow\;\SI{212}{\Fahrenheit} \end{align*} -Cela montre que non seulement la définition du zéro de la température mais aussi celle de l'unité de température sont arbitraire. +Cela montre que non seulement la définition du zéro de la température mais aussi celle de l'unité de température sont arbitraire (voir figure \ref{thermometres}\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Fahrenheit\_Celsius\_scales.jpg= pour l'image de gauche et \url=http://commons.wikimedia.org/wiki/Image:Celsius\_kelvin\_estandar\_1954.png= pour l'image de droite, notamment pour le copyright.}). Il existe bien entendu une correspondance entre les deux échelles qui est donnée par~: \[T_F=\frac{9}{5}\cdot T_C+32\] @@ -49,7 +49,7 @@ v_{O_2}&=\sqrt{\frac{3\cdot k\cdot 293,15}{5,312\cdot 10^{-26}}}=\SI{478}{\metre \centering \subfigure[Fahrenheit\label{celsiusfahrenheit}]{\includegraphics[width=2cm]{Celsius_Fahrenheit.eps}}\qquad \subfigure[Kelvin\label{celsiuskelvin}]{\includegraphics[width=3cm]{Celsius_Kelvin.eps}} -\caption[Thermomètres]{Les échelles de température\label{thermometres}\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Fahrenheit\_Celsius\_scales.jpg= pour l'image de gauche et \url=http://commons.wikimedia.org/wiki/Image:Celsius\_kelvin\_estandar\_1954.png= pour l'image de droite, notamment pour le copyright.}} +\caption[Thermomètres]{Les échelles de température\label{thermometres}} \end{figure} Ces vitesses sont considérables. L'image microscopique de notre environnement est donc plutôt celle d'un ensemble de molécules et d'atomes se déplaçant à grande vitesse sur de courtes distances que celle du monde immobile tel que nous le voyons à échelle macroscopique. diff --git a/ThermodynamiqueOS/ThermodynamiqueOS.tex b/ThermodynamiqueOS/ThermodynamiqueOS.tex index 823f922..1621c00 100644 --- a/ThermodynamiqueOS/ThermodynamiqueOS.tex +++ b/ThermodynamiqueOS/ThermodynamiqueOS.tex @@ -1169,10 +1169,10 @@ Ce bilan permet de déterminer le rendement du moteur. Il s'agit du rapport entr \subfigure[Temps moteur\label{tempsmoteur}]{\includegraphics[height=4.8cm]{TempsMoteur.eps}}\quad \subfigure[Échappement\label{echappement}]{\includegraphics[height=4.8cm]{Echappement.eps}}\quad \subfigure[Évacuation\label{evacuation}]{\includegraphics[height=4.8cm]{Evacuation.eps}} -\caption[Moteur à explosion]{Moteur à explosion\label{motess}\endnote{Voir Wikipedia~: \url=http://fr.wikipedia.org/wiki/Fichier:4-Stroke-Engine.gif=}} +\caption[Moteur à explosion]{Moteur à explosion\label{motess}} \end{figure*} -Un autre exemple de moteur thermique est le moteur à explosion\index{moteur!à explosion} et plus particulièrement celui à essence\index{moteur!à essence}. Si la description qu'on va donner ici reste très théorique, elle présente néanmoins ce moteur dans son principe de fonctionnement en relation avec le cycle thermodynamique dit d'Otto\index{cycle!d'Otto} ou de Beau de Rochas\index{Beau de Rochas} qui le traduit. Il est constitué des six étapes présentées à la figure \ref{motess}~: +Un autre exemple de moteur thermique est le moteur à explosion\index{moteur!à explosion} et plus particulièrement celui à essence\index{moteur!à essence}. Si la description qu'on va donner ici reste très théorique, elle présente néanmoins ce moteur dans son principe de fonctionnement en relation avec le cycle thermodynamique dit d'Otto\index{cycle!d'Otto} ou de Beau de Rochas\index{Beau de Rochas} qui le traduit. Il est constitué des six étapes présentées à la figure \ref{motess}\endnote{Voir Wikipedia~: \url=http://fr.wikipedia.org/wiki/Fichier:4-Stroke-Engine.gif=}~: \begin{description} \item[Admission] (\small{fig. \ref{admission}}) Pendant ce premier temps, la soupape d'admission s'ouvre pour laisser entrer de l'essence et de l'air. Ce mélange est aspiré par l'augmentation du volume dans le cylindre due au déplacement du piston entraîné par l'inertie du mouvement du vilebrequin.

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