From e4a4cc8cf85944433b7d6c344b664aa30daa4047 Mon Sep 17 00:00:00 2001 From: guyotv Date: Wed, 8 Jan 2025 22:40:30 +0100 Subject: [PATCH] =?UTF-8?q?R=C3=A9solution=20des=20probl=C3=A8mes=20de=20n?= =?UTF-8?q?otes=20...=20mais=20pas=20pour=20l'ent=C3=AAte.?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- Annexe-Energies/Annexe-Energies.tex | 8 +- Annexe-MRUA/Annexe-MRUA.tex | 2 +- Annexe-Maree/Annexe-Maree.tex | 2 +- .../Annexe-MesuresDistances.tex | 6 +- Annexe-Rotations/Annexe-Rotations.tex | 6 +- Annexe-Satellites/Annexe-Satellites.tex | 2 +- .../Annexe-Thermodynamique.tex | 2 +- Cinematique/Cinematique.tex | 12 +- CoursMecaniqueOSDF.bcf | 121 ++++++++---------- CoursMecaniqueOSDF.blg | 30 ++--- CoursMecaniqueOSDF.out | 2 +- CoursMecaniqueOSDF.pdf | Bin 13431521 -> 13458523 bytes CoursMecaniqueOSDF.run.xml | 4 +- CoursMecaniqueOSDF.tex | 5 +- CoursMecaniqueOSDF.tex.bak | 2 + Dynamique/Dynamique.tex | 6 +- Energie/Energie.tex | 22 ++-- Energie/Energie.tex.bak | 32 ++--- Introduction/Introduction.tex | 18 +-- Introduction/Introduction.tex.bak | 44 +++---- PhysiqueTheorique/PhysiqueTheorique.tex | 2 +- Preambule.tex | 2 + Preambule.tex.bak | 7 +- Thermodynamique/Thermodynamique.tex | 4 +- ThermodynamiqueOS/ThermodynamiqueOS.tex | 2 +- 25 files changed, 166 insertions(+), 177 deletions(-) diff --git a/Annexe-Energies/Annexe-Energies.tex b/Annexe-Energies/Annexe-Energies.tex index f7445fd..8d5fa77 100644 --- a/Annexe-Energies/Annexe-Energies.tex +++ b/Annexe-Energies/Annexe-Energies.tex @@ -107,14 +107,14 @@ Cela constitue la limite de Betz\index{limite de Betz}. \subsection{Éoliennes\index{eolienne@éolienne}} \subsubsection{Éolienne de Collonges-Dorénaz} -Il ne s'agit pas ici de se substituer aux multiples informations qui se trouvent sur internet\endnote{Voir le site de RhônEole~: \url=http://www.rhoneole.ch/=}. Il s'agit simplement d'illustrer la théorie à travers l'exemple concret de la plus grande éolienne de Suisse pour permettre une comparaison avec un barrage comme celui du Châtelot (voir paragraphe \ref{barrageduchatelot}). +Il ne s'agit pas ici de se substituer aux multiples informations qui se trouvent sur internet\endnote{Voir le site de RhônEole~: \url{http://www.rhoneole.ch/}}. Il s'agit simplement d'illustrer la théorie à travers l'exemple concret de la plus grande éolienne de Suisse pour permettre une comparaison avec un barrage comme celui du Châtelot (voir paragraphe \ref{barrageduchatelot}). Le mât\index{mat@mât} fait pratiquement \SI{100}{\metre} de haut et la longueur des pales\index{pale} est de \SI{33}{\metre}. Le rendement est très proche de la limite de Betz\index{limite de Betz} puisqu'iut 56\%. La puissance maximale est de \SI{2000}{\kilo\watt}, mais la production annuelle est de \SI{3,5}{\giga\watt\hour}. Si la consommation électrique annuelle moyenne d'un ménage est d'environ \SI{2000}{\kilo\watt\hour}, le nombre \(n\) de ménages qui peuvent être alimentés par cette éolienne vaut~: \[n=\frac{3,5\cdot 10^6}{2000}=1750\,\text{ménages}\] Comparé au \num{74000} ménages alimentés par le barrage\index{barrage} du Châtelot (parties suisse et française ensemble), cela peut paraître bien peu. Encore faut-il comparer le coût du barrage aux quatre millions d'investissement pour cette éolienne. Et aussi comparer les deux impacts écologiques, les possibilités et le coût de démontage, les risques d'accidents~\dots\ Une juste comparaison nécessite de prendre en compte un nombre de paramètres assez grand pour qu'il ne soit pas possible ici de poursuivre plus avant la comparaison. \subsubsection{Éoliennes du Mont Soleil (Jura suisse)} -A nouveau l'information se trouve sur internet\endnote{Voir le site de Juvent~: \url=http://www.juvent.ch/=}. +A nouveau l'information se trouve sur internet\endnote{Voir le site de Juvent~: \url{http://www.juvent.ch/}}. Il faut savoir que cette centrale est constituée de huit éoliennes\index{eolienne@éolienne} d'une puissance allant de 600 à \SI{1750}{\kilo\watt}. Elles ont une hauteur de mât\index{mat@mât} de 45 à \SI{67}{\metre} et des pales\index{pale} de 22 à \SI{33}{\metre}. L'ensemble a produit en 2006 une énergie de \SI{9,176}{\giga\watt\hour}. Cela représente 4588 ménages (à \SI{2000}{\kilo\watt\hour\per\year}). Une fois encore c'est bien peu comparé au barrage\index{barrage} du Châtelot. Mais les remarques faites précédemment restent valables. @@ -128,14 +128,14 @@ Au total, la centrale de Collonges-Dorénaz et celle du Mont Soleil alimentent e %Si on évoque souvent le faible rendement d'environ 15\% des cellules solaires électriques, on ignore aussi trop souvent les paramètres nécessaires pour envisager son utilisation pour des habitations privées. \section{Géothermie\index{geothermie@géothermie}}\label{riehen} -Il existe en Suisse une centrale géothermique qui permet un chauffage urbain, à l'instar de Cridor à La Chaux-de-Fonds. Il s'agit de la centrale de Riehen près de Bâle. Elle est constituée de deux pompes à chaleur qui exploitent la chaleur d'une eau à \SI{65}{\degree} provenant d'un forage\index{forage} à \SI{1547}{\metre} (un second forage, distant de \SI{1}{\kilo\metre} du premier, réinjecte de l'eau froide à \SI{1247}{\metre}, avec un débit de \SI{18}{\litre\per\second}). Elle permet d'approvisionner 180 immeubles à Riehen et de nouvelles constructions en Allemagne. L'énergie annuellement produite est de \SI{22,8}{\giga\watt\hour}\endnote{Voir les sites de Géothermie~: \url=http://www.geothermal-energy.ch/= et \url=http://www.ader.ch/energieaufutur/energies/geothermie/index2.php=}. À raison d'environ \SI{20}{\mega\watt\hour\per an} pour une famille de trois personnes, on a une couverture en terme de chauffage à distance (chauffage et eau chaude sanitaire) de~: +Il existe en Suisse une centrale géothermique qui permet un chauffage urbain, à l'instar de Cridor à La Chaux-de-Fonds. Il s'agit de la centrale de Riehen près de Bâle. Elle est constituée de deux pompes à chaleur qui exploitent la chaleur d'une eau à \SI{65}{\degree} provenant d'un forage\index{forage} à \SI{1547}{\metre} (un second forage, distant de \SI{1}{\kilo\metre} du premier, réinjecte de l'eau froide à \SI{1247}{\metre}, avec un débit de \SI{18}{\litre\per\second}). Elle permet d'approvisionner 180 immeubles à Riehen et de nouvelles constructions en Allemagne. L'énergie annuellement produite est de \SI{22,8}{\giga\watt\hour}\endnote{Voir les sites de Géothermie~: \url{http://www.geothermal-energy.ch/} et \url{http://www.ader.ch/energieaufutur/energies/geothermie/index2.php}}. À raison d'environ \SI{20}{\mega\watt\hour\per an} pour une famille de trois personnes, on a une couverture en terme de chauffage à distance (chauffage et eau chaude sanitaire) de~: \[n=\frac{22'800}{20}=1'140\,\text{ménages}\] Ce qui représente environ \num{3500} personnes. \section{Énergie de combustion des déchets\index{energie@énergie!de combustion!des déchets}} Nous allons prendre pour exemple de ce type de production énergétique la centrale de chauffage à distance de Cridor à La Chaux-de-Fonds dans le Jura suisse. L'objectif est d'avoir un exemple concret de ce qui se fait déjà dans un domaine concernant les énergies renouvelables qui passe souvent trop inaperçu. -La production\endnote{voir dépliant ``Nos déchets = notre énergie'' sur le site~: \url=http://www.cridor.ch/content/doc/brochures.php=} totale d'énergie par cette usine d'incinération est de \SI{85000}{\mega\watt\hour\per\year}. Par comparaison, rappelons que la production du barrage\index{barrage} du Châtelot est de \SI{150000}{\mega\watt\hour\per an} (voir équation \ref{prodchatelot}), soit environ le double. +La production\endnote{voir dépliant ``Nos déchets = notre énergie'' sur le site~: \url{http://www.cridor.ch/content/doc/brochures.php}} totale d'énergie par cette usine d'incinération est de \SI{85000}{\mega\watt\hour\per\year}. Par comparaison, rappelons que la production du barrage\index{barrage} du Châtelot est de \SI{150000}{\mega\watt\hour\per an} (voir équation \ref{prodchatelot}), soit environ le double. Cette énergie se partage en \SI{60000}{\mega\watt\hour\per\year} pour le chauffage à distance (chauffage des habitations) et \SI{25000}{\mega\watt\hour\per\year} produit par une turbine sous forme électrique, dont \SI{19000}{\mega\watt\hour\per\year} sont vendus. Cela représente \SI{55000}{\tonne\per\year} de déchets incinérés. Le nombre de ménages fournis en énergie électrique est donc de~: \[n=\frac{19'000\cdot 10^6}{2000\cdot 10^3}=9500\,\text{ménages}\] diff --git a/Annexe-MRUA/Annexe-MRUA.tex b/Annexe-MRUA/Annexe-MRUA.tex index 7d6232c..f335128 100644 --- a/Annexe-MRUA/Annexe-MRUA.tex +++ b/Annexe-MRUA/Annexe-MRUA.tex @@ -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 (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~: +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 a5eb641..c51d94e 100644 --- a/Annexe-Maree/Annexe-Maree.tex +++ b/Annexe-Maree/Annexe-Maree.tex @@ -2,7 +2,7 @@ \chapter{Marées\index{maree@marée}}\label{chapmarees} \section{Introduction} -\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. +\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. diff --git a/Annexe-MesuresDistances/Annexe-MesuresDistances.tex b/Annexe-MesuresDistances/Annexe-MesuresDistances.tex index cbf647c..e711426 100644 --- a/Annexe-MesuresDistances/Annexe-MesuresDistances.tex +++ b/Annexe-MesuresDistances/Annexe-MesuresDistances.tex @@ -54,7 +54,7 @@ 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}\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 \(60/28,9=2,1\). +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 @@ -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 ee21d85..81b2efd 100644 --- a/Annexe-Rotations/Annexe-Rotations.tex +++ b/Annexe-Rotations/Annexe-Rotations.tex @@ -66,13 +66,13 @@ Le second problème tient dans la cinématique des planètes du système solaire \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}\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. +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}\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. +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 @@ -108,7 +108,7 @@ v&=\frac{d}{t}=\frac{2\cdot \pi\cdot R_{S\rightarrow G}}{T_s}\\ \end{align*} Cette vitesse est incroyable. Nous ne la ressentons à nouveau pas ou peu toujours à cause de l'inertie\index{inertie}. -Notons que cette vitesse est la même pour toutes les étoiles proches du Soleil qui participent au mouvement de rotation autour du centre de la galaxie. Mais le Soleil a aussi un mouvement propre, c'est-à-dire qu'une partie de sa vitesse ne correspond pas à sa vitesse de rotation autour du centre de la galaxie. Cette composante vaut environ \SI{20}{\kilo\metre\per\second}.\endnote{Voir le site \url=http://www.dil.univ-mrs.fr/~gispert/enseignement/astronomie/5eme\_partie/voieLactee.php=} +Notons que cette vitesse est la même pour toutes les étoiles proches du Soleil qui participent au mouvement de rotation autour du centre de la galaxie. Mais le Soleil a aussi un mouvement propre, c'est-à-dire qu'une partie de sa vitesse ne correspond pas à sa vitesse de rotation autour du centre de la galaxie. Cette composante vaut environ \SI{20}{\kilo\metre\per\second}.\endnote{Voir le site \url{http://www.dil.univ-mrs.fr/~gispert/enseignement/astronomie/5eme\_partie/voieLactee.php}} Relevons enfin une règle bien pratique pour la transformation d'unité entre les \si{\metre\per\second} et les \si{\kilo\metre\per\hour}. On a en effet~: \[\SI{1}{\kilo\metre\per\hour}=\frac{1\,km}{1\,h}=\frac{1000\,m}{3600\,s}=1 / 3,6\unit{\metre\per\second}\] diff --git a/Annexe-Satellites/Annexe-Satellites.tex b/Annexe-Satellites/Annexe-Satellites.tex index f670c05..493169e 100644 --- a/Annexe-Satellites/Annexe-Satellites.tex +++ b/Annexe-Satellites/Annexe-Satellites.tex @@ -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 (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. +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/Annexe-Thermodynamique/Annexe-Thermodynamique.tex b/Annexe-Thermodynamique/Annexe-Thermodynamique.tex index 2a6b000..e663235 100644 --- a/Annexe-Thermodynamique/Annexe-Thermodynamique.tex +++ b/Annexe-Thermodynamique/Annexe-Thermodynamique.tex @@ -1132,7 +1132,7 @@ 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}\endnote{Voir Wikipedia~: \url{http://fr.wikipedia.org/wiki/Fichier:4-Stroke-Engine.gif}}} \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}~: diff --git a/Cinematique/Cinematique.tex b/Cinematique/Cinematique.tex index 31e10f3..6695134 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 (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~: +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. @@ -267,7 +267,7 @@ La vitesse moyenne est donc de~: \smallskip{} En réalité le mouvement de la capsule est loin d'être un MRU\index{MRU@MRU}. En effet, la Terre et la Lune exercent leurs attractions respectives. Ainsi, si la vitesse initiale de rotation de la capsule\index{capsule@capsule} autour de la Terre était de \SI{28000}{\kilo\metre\per\hour}, celle-ci était augmentée par la propulsion pour se dégager de la Terre jusqu'à une valeur de \SI{38000}{\kilo\metre\per\hour}. -Ensuite, l'attraction\index{attraction@attraction} de la terre freinait constamment le vaisseau. \og Sa vitesse tombait ainsi à près de \SI{5000}{\kilo\metre\per\hour} au point d'équigravité\index{equigravite@équigravité} (gravité équivalente entre la Terre et la Lune) qui se situe à environ \SI{300000}{\kilo\metre} de notre planète (sur une distance moyenne Terre-Lune de \SI{380000}{\kilo\metre}), pour accélérer à nouveau compte tenu de l'attraction\index{attraction@attraction} lunaire. Au voisinage de notre satellite\index{satellite@satellite}, le vaisseau Apollo\index{Apollo@Apollo} arrivait à une vitesse de \SI{8000}{\kilo\metre\per\hour}, mais encore bien trop rapide pour devenir captif de la gravité\index{gravite@gravité} lunaire. Aussi, l'engin devait effectuer une rotation de \(180^{\circ}\) (l'arrière vers l'avant) puis, grâce à la mise à feu du propulseur auxiliaire libérant une poussée de 10 tonnes (pendant 4 minutes et demie), ralentissait juste ce qu'il fallait pour être pris dans le champ de la gravité\index{gravite@gravité} lunaire.\fg{}~\endnote{Les missions Apollo~: \url=http://perso.wanadoo.fr/alexandre.schwenk/index.htm=} +Ensuite, l'attraction\index{attraction@attraction} de la terre freinait constamment le vaisseau. \og Sa vitesse tombait ainsi à près de \SI{5000}{\kilo\metre\per\hour} au point d'équigravité\index{equigravite@équigravité} (gravité équivalente entre la Terre et la Lune) qui se situe à environ \SI{300000}{\kilo\metre} de notre planète (sur une distance moyenne Terre-Lune de \SI{380000}{\kilo\metre}), pour accélérer à nouveau compte tenu de l'attraction\index{attraction@attraction} lunaire. Au voisinage de notre satellite\index{satellite@satellite}, le vaisseau Apollo\index{Apollo@Apollo} arrivait à une vitesse de \SI{8000}{\kilo\metre\per\hour}, mais encore bien trop rapide pour devenir captif de la gravité\index{gravite@gravité} lunaire. Aussi, l'engin devait effectuer une rotation de \(180^{\circ}\) (l'arrière vers l'avant) puis, grâce à la mise à feu du propulseur auxiliaire libérant une poussée de 10 tonnes (pendant 4 minutes et demie), ralentissait juste ce qu'il fallait pour être pris dans le champ de la gravité\index{gravite@gravité} lunaire.\fg{}~\endnote{Les missions Apollo~: \url{http://perso.wanadoo.fr/alexandre.schwenk/index.htm}} On voit ainsi que le mouvement des engins spatiaux est loin d'être un mouvement aussi simple qu'on pourrait le penser étant donné le vide dans lequel ils se trouvent. En particulier, il est loin d'être rectiligne et de se faire à vitesse constante. @@ -282,7 +282,7 @@ Contrairement à la plupart des galaxies\index{galaxie@galaxie} qui s'éloignent \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}\endnote{Voir le site de Wikicommon (notamment pour le copyright~: sans copyright)~: \url=http://commons.wikimedia.org/wiki/Image:Andromeda\_collision.jpg=}). +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} @@ -366,7 +366,7 @@ Galilée\index{Galilee@Galilée} est parfois considéré comme le père de la ph On peut considérer Galilée\index{Galilee@Galilée} comme le \og père\fg{} de l'équation horaire de la position d'un objet en chute libre. Le théorème II proposition II des \og Discours et démonstrations mathématiques concernant deux sciences nouvelles\fg{} dit~: \smallskip -\raggedleft{\footnotesize{Portrait de Galilée tiré de Wikipedia\endnote{Voir \url=http://fr.wikipedia.org/wiki/Image:Galilee.jpg=}}} +\raggedleft{\footnotesize{Portrait de Galilée tiré de Wikipedia\endnote{Voir \url{http://fr.wikipedia.org/wiki/Image:Galilee.jpg}}}} \end{minipage} \hfill \begin{minipage}[b]{6.5cm} @@ -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} @@ -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}\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. +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/CoursMecaniqueOSDF.bcf b/CoursMecaniqueOSDF.bcf index aa7072f..3486e96 100644 --- a/CoursMecaniqueOSDF.bcf +++ b/CoursMecaniqueOSDF.bcf @@ -1,5 +1,5 @@ - + @@ -137,6 +137,10 @@ nosortothers 0 + + pluralothers + 0 + singletitle 0 @@ -372,11 +376,11 @@ 0 - skiplab + skipbiblist 0 - skipbiblist + skiplab 0 @@ -599,6 +603,7 @@ labeltitle labeltitleyear labeldateparts + pluralothers nohashothers nosortothers noroman @@ -1043,7 +1048,7 @@ given - + prefix family @@ -2344,72 +2349,48 @@ Bibliographies/BiblioCoursOS.bib - HNHR08 - JR00 - FC05 - SV06 - FB05 - SV06 - JL06 - SH03 - SH03 - EL99 - EL99 - GSJ05 - SH03 - BM85 - BM85 - BM85 - SH03 - OG04 - BS07 - GC88 - GC88 - LJ04 - HRaFL03 - OP06 - HRaFL03 - HRaFL03 - SV06 - HRaFL03 - SU03 - SU03 - AK05 - AS06 - AS02 - JJD21 - JL96 - GG92 - JR07 - GC88 - JR00 - GC88 - GC88 - BS07 - HNHR08 - JR00 - FC05 - SV06 - FB05 - JL06 - SH03 - EL99 - GSJ05 - BM85 - OG04 - BS07 - GC88 - LJ04 - HRaFL03 - OP06 - SU03 - AK05 - AS06 - AS02 - JJD21 - JL96 - GG92 - JR07 + HNHR08 + JR00 + FC05 + SV06 + FB05 + SV06 + JL06 + SH03 + SH03 + EL99 + EL99 + GSJ05 + SH03 + BM85 + BM85 + BM85 + SH03 + OG04 + BS07 + GC88 + GC88 + LJ04 + HRaFL03 + OP06 + HRaFL03 + HRaFL03 + SV06 + HRaFL03 + SU03 + SU03 + AK05 + AS06 + AS02 + JJD21 + JL96 + GG92 + JR07 + GC88 + JR00 + GC88 + GC88 + BS07 diff --git a/CoursMecaniqueOSDF.blg b/CoursMecaniqueOSDF.blg index 7a0e234..f5bf47a 100644 --- a/CoursMecaniqueOSDF.blg +++ b/CoursMecaniqueOSDF.blg @@ -1,15 +1,15 @@ -[0] Config.pm:307> INFO - This is Biber 2.17 -[0] Config.pm:310> INFO - Logfile is 'CoursMecaniqueOSDF.blg' -[59] biber:340> INFO - === mer jan 8, 2025, 09:20:17 -[69] Biber.pm:418> INFO - Reading 'CoursMecaniqueOSDF.bcf' -[123] Biber.pm:972> INFO - Found 24 citekeys in bib section 0 -[133] Biber.pm:4383> INFO - Processing section 0 -[140] Biber.pm:4574> INFO - Looking for bibtex file 'Bibliographies/BiblioCoursOS.bib' for section 0 -[142] bibtex.pm:1713> INFO - LaTeX decoding ... -[175] bibtex.pm:1518> INFO - Found BibTeX data source 'Bibliographies/BiblioCoursOS.bib' -[277] UCollate.pm:68> INFO - Overriding locale 'fr-FR' defaults 'variable = shifted' with 'variable = non-ignorable' -[277] UCollate.pm:68> INFO - Overriding locale 'fr-FR' defaults 'normalization = NFD' with 'normalization = prenormalized' -[277] Biber.pm:4203> INFO - Sorting list 'nty/global//global/global' of type 'entry' with template 'nty' and locale 'fr-FR' -[277] Biber.pm:4209> INFO - No sort tailoring available for locale 'fr-FR' -[291] bbl.pm:654> INFO - Writing 'CoursMecaniqueOSDF.bbl' with encoding 'UTF-8' -[297] bbl.pm:757> INFO - Output to CoursMecaniqueOSDF.bbl +[0] Config.pm:306> INFO - This is Biber 2.18 +[0] Config.pm:309> INFO - Logfile is 'CoursMecaniqueOSDF.blg' +[103] biber:340> INFO - === mer jan 8, 2025, 22:32:07 +[122] Biber.pm:418> INFO - Reading 'CoursMecaniqueOSDF.bcf' +[205] Biber.pm:978> INFO - Found 24 citekeys in bib section 0 +[221] Biber.pm:4401> INFO - Processing section 0 +[232] Biber.pm:4592> INFO - Looking for bibtex file 'Bibliographies/BiblioCoursOS.bib' for section 0 +[235] bibtex.pm:1713> INFO - LaTeX decoding ... +[278] bibtex.pm:1518> INFO - Found BibTeX data source 'Bibliographies/BiblioCoursOS.bib' +[429] UCollate.pm:68> INFO - Overriding locale 'fr-FR' defaults 'variable = shifted' with 'variable = non-ignorable' +[429] UCollate.pm:68> INFO - Overriding locale 'fr-FR' defaults 'normalization = NFD' with 'normalization = prenormalized' +[429] Biber.pm:4221> INFO - Sorting list 'nty/global//global/global' of type 'entry' with template 'nty' and locale 'fr-FR' +[429] Biber.pm:4227> INFO - No sort tailoring available for locale 'fr-FR' +[450] bbl.pm:654> INFO - Writing 'CoursMecaniqueOSDF.bbl' with encoding 'UTF-8' +[460] bbl.pm:757> INFO - Output to CoursMecaniqueOSDF.bbl diff --git a/CoursMecaniqueOSDF.out b/CoursMecaniqueOSDF.out index 01aa3f0..b0336e9 100644 --- a/CoursMecaniqueOSDF.out +++ b/CoursMecaniqueOSDF.out @@ -421,5 +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 [2][-]{subsection.M.3.7}{\376\377\000R\000e\000p\000r\000\351\000s\000e\000n\000t\000a\000t\000i\000o\000n\000\040\000g\000r\000a\000p\000h\000i\000q\000u\000e}{section.M.3}% 423 -\BOOKMARK [0][-]{section*.302}{\376\377\000R\000e\000m\000a\000r\000q\000u\000e\000s}{}% 424 +\BOOKMARK [0][-]{section*.302}{\376\377\000N\000o\000t\000e\000s}{}% 424 \BOOKMARK [0][-]{appendix*.304}{\376\377\000B\000i\000b\000l\000i\000o\000g\000r\000a\000p\000h\000i\000e}{}% 425 diff --git a/CoursMecaniqueOSDF.pdf 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zJe(E?vLoHR0%_biaV^IJalu8(jc!wAe{AH(SK#6nC7UiMHUBahz!}M6FLequDxjGr zkL1Pv189{aQeoK>2-wm6sAx~?N~dq}fScumkZHA9@85m>kAI$j{POX`Uy#Fc{@<66 zAAd#D#=D0%hc~b9A0Dn>zkR^yK*Ahf9p1cpb$I>o^7FU ]> - + latex CoursMecaniqueOSDF.bcf @@ -61,7 +61,7 @@ english.lbx - + biber biber diff --git a/CoursMecaniqueOSDF.tex b/CoursMecaniqueOSDF.tex index 1c0ce0c..b08aa1a 100644 --- a/CoursMecaniqueOSDF.tex +++ b/CoursMecaniqueOSDF.tex @@ -157,9 +157,10 @@ % inclusion de l'annexe Incertitudes (OS) \opt{OS}{\include{Annexe-Incertitudes/Annexe-Incertitudes}} %-------------------------------------------------------------- -\newpage + +\myclearpage + \printendnotes -%\theendnotes \myclearpage diff --git a/CoursMecaniqueOSDF.tex.bak b/CoursMecaniqueOSDF.tex.bak index 53709ca..b299eea 100644 --- a/CoursMecaniqueOSDF.tex.bak +++ b/CoursMecaniqueOSDF.tex.bak @@ -158,6 +158,8 @@ \opt{OS}{\include{Annexe-Incertitudes/Annexe-Incertitudes}} %-------------------------------------------------------------- +\newpage +\myclearpage \printendnotes %\theendnotes diff --git a/Dynamique/Dynamique.tex b/Dynamique/Dynamique.tex index 3b0a709..dd305af 100644 --- a/Dynamique/Dynamique.tex +++ b/Dynamique/Dynamique.tex @@ -44,7 +44,7 @@ Un homme du IV\up{e} siècle av. J.-C., qui représentera la connaissance classi \end{quotation} Un homme, ou plutôt une doctrine à laquelle les Bruno\index{Bruno@Bruno!Giordano} et Galilée\index{Galilee@Galilée} s'opposeront pour faire émerger l'idée d'une physique universelle. -\raggedleft{\footnotesize{Aristote peint par Raphaël, tiré de Wikipedia\endnote{Voir \url=http://fr.wikipedia.org/wiki/Image:Aristotle\_by\_Raphael.jpg=}}} +\raggedleft{\footnotesize{Aristote peint par Raphaël, tiré de Wikipedia\endnote{Voir \url{http://fr.wikipedia.org/wiki/Image:Aristotle\_by\_Raphael.jpg}}}} \end{minipage} \hfill \parbox[b]{6cm}{\includegraphics[width=6cm]{Aristotle_by_Raphael.eps}} @@ -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. 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. +\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}} @@ -474,7 +474,7 @@ Une des nombreuses applications intéressantes de la loi de la gravitation unive \includegraphics[width=6cm]{MCU2.eps} \end{figure} -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. +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 ba9aad2..5519a6c 100644 --- a/Energie/Energie.tex +++ b/Energie/Energie.tex @@ -39,7 +39,7 @@ Remarquons finalement que la définition du travail donnée ci-dessus n'est vala \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}\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~: +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{\(\displaystyle P=\frac{A}{t}\)} @@ -101,7 +101,7 @@ 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 ! Voir figure \ref{encinpotcirc}\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Mozaic-garden009.jpg=}). +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 @@ -193,7 +193,7 @@ 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 (voir figure \ref{Emosson}\endnote{Voir le site~: \url=http://www.emosson-lac.ch/barrage.htm=}). +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 @@ -257,7 +257,7 @@ Différents types de turbines correspondent à différentes plages d'utilisation \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}\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}. +\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\%. @@ -442,7 +442,7 @@ 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}\endnote{Voir le site de l'encyclopédie~: \url=http://fr.wikipedia.org/wiki/Image:Photoelectric\_effect.png=}). +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 @@ -450,7 +450,7 @@ Le principe de base est celui découvert par Heinrich Rudolf Hertz en 1887 et ex \includegraphics[width=6cm]{Photoelectric_effect.eps} \end{figure} -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~: +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] @@ -463,9 +463,9 @@ Ce qui représente plus de \SI{10}{\metre\squared} de surface et est important. \medskip -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~: +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. @@ -479,7 +479,7 @@ 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}\endnote{Voir le site de l'encyclopédie~: \url=http://fr.wikipedia.org/wiki/Image:Tableau-lindal.jpg=}. +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 @@ -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} @@ -592,7 +592,7 @@ 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}\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}. +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 diff --git a/Energie/Energie.tex.bak b/Energie/Energie.tex.bak index ba67f0c..d48bc39 100644 --- a/Energie/Energie.tex.bak +++ b/Energie/Energie.tex.bak @@ -39,7 +39,7 @@ Remarquons finalement que la définition du travail donnée ci-dessus n'est vala \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}\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~: +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{\(\displaystyle P=\frac{A}{t}\)} @@ -101,7 +101,7 @@ 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 ! Voir figure \ref{encinpotcirc}\endnote{Voir le site de l'encyclopédie Wikipedia~: \url=http://commons.wikimedia.org/wiki/Image:Mozaic-garden009.jpg=}). +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 @@ -193,7 +193,7 @@ 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 (voir figure \ref{Emosson}\endnote{Voir le site~: \url=http://www.emosson-lac.ch/barrage.htm=}). +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 @@ -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} @@ -463,9 +463,9 @@ Ce qui représente plus de \SI{10}{\metre\squared} de surface et est important. \medskip -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~: +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. @@ -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*} @@ -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} @@ -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/Introduction/Introduction.tex b/Introduction/Introduction.tex index 0fb6189..afed306 100644 --- a/Introduction/Introduction.tex +++ b/Introduction/Introduction.tex @@ -20,7 +20,7 @@ Qui dit périodes dit donc mouvement et, plus précisément, mouvement répétit \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.} +%\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. @@ -50,7 +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}} @@ -101,7 +101,7 @@ Les mouvements locaux des galaxies entre elles donnent lieu à des \og chocs\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}\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{}. +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}. @@ -159,7 +159,7 @@ En passant elles laissent sur leur orbite\index{orbite@orbite} une traînée de \includegraphics[width=6cm]{Billet10FrsComete.eps} \end{figure} -Ce sont ces traînées de poussières que la Terre rencontre sur son orbite\index{orbite@orbite} en donnant lieu aux fameuses pluies d'étoiles filantes\index{etoile@étoile!filante} (voir la figure \ref{Leonides}\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}. +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 @@ -221,7 +221,7 @@ 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}\endnote{Voir le site de l'encyclopédie~: \url=http://commons.wikimedia.org/wiki/Image:TerreOrbiteLuneEtPhases.png=} 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 @@ -237,7 +237,7 @@ La question se pose alors de la différence entre éclipse de Soleil\index{eclip \includegraphics[width=6cm]{Orbite-lune-soleil.eps} \end{figure} -Comme ces plans ne coïncident pas, tant que la Lune n'est pas dans le plan de l'Écliptique\index{ecliptique@écliptique}, c'est-à-dire sur la ligne des n\oe uds\index{ligne@ligne des n\oe uds} présentée dans la figure \ref{Orbite-lune-soleil}\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}. +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. @@ -299,7 +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}\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. +\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. @@ -345,7 +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}\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. +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}} @@ -377,7 +377,7 @@ Il faut noter que le graviton\index{graviton@graviton} est encore hypothétique. \end{itemize} \medskip -Finalement, il faut encore parler des particules très particulières formant l'antimatière\index{antimatiere@antimatière}. On sait de nos jours produire et stocker pendant une courte période (quelques jours\footnote{On crée des anti-protons dans un accélérateur de particules comme le CERN à Genève, on les ralentit et on les piège dans un champ électromagnétique. Voici à ce sujet un commentaire de M. Carlo RUBBIA (Prix Nobel de Physique 1984)~: \begin{quotation}\og \textit{L'antimatière est, comme vous l'avez vu, produite au CERN où une véritable usine de production a été construite. Nous utilisons des protons qui sont accélérés et viennent frapper une cible. Au cours des collisions, il y a production d'un grand nombre de particules ou d'antiparticules et, parmi elles, on trouve des antiprotons. Ces antiprotons sont stockés dans une bouteille magnétique qui, dans le cas particulier, est un anneau de stockage à accumulation. On obtient ainsi une quantité d'antimatière qui n'est pas très petite puisqu'elle atteint un microgramme par jour.}\fg{} \endnote{Voir~: \url=http://cui.unige.ch/isi/ssc/phys/Rubbia-Klapisch.html=}\end{quotation}}) ce type de particules qui interagissent fortement avec la matière ordinaire en disparaissant totalement au profit de lumière. Ce sont des particules qui ont des propriétés inverses des particules de la matière ordinaire. Par exemple, un positron\index{positron@positron}, qui est un anti-électron, a la même masse qu'un électron, mais une charge opposée. Ces particules n'existent pas sur terre ailleurs que dans les accélérateurs de particules où elles sont produites par la collision d'autres particules. Mais on peut envisager qu'il en existe beaucoup ailleurs dans l'univers. Cette question reste cependant débattue. +Finalement, il faut encore parler des particules très particulières formant l'antimatière\index{antimatiere@antimatière}. On sait de nos jours produire et stocker pendant une courte période (quelques jours\footnote{On crée des anti-protons dans un accélérateur de particules comme le CERN à Genève, on les ralentit et on les piège dans un champ électromagnétique. Voici à ce sujet un commentaire de M. Carlo RUBBIA (Prix Nobel de Physique 1984)~: \begin{quotation}\og \textit{L'antimatière est, comme vous l'avez vu, produite au CERN où une véritable usine de production a été construite. Nous utilisons des protons qui sont accélérés et viennent frapper une cible. Au cours des collisions, il y a production d'un grand nombre de particules ou d'antiparticules et, parmi elles, on trouve des antiprotons. Ces antiprotons sont stockés dans une bouteille magnétique qui, dans le cas particulier, est un anneau de stockage à accumulation. On obtient ainsi une quantité d'antimatière qui n'est pas très petite puisqu'elle atteint un microgramme par jour.}\fg{} \endnote{Voir~: \url{http://cui.unige.ch/isi/ssc/phys/Rubbia-Klapisch.html}}\end{quotation}}) ce type de particules qui interagissent fortement avec la matière ordinaire en disparaissant totalement au profit de lumière. Ce sont des particules qui ont des propriétés inverses des particules de la matière ordinaire. Par exemple, un positron\index{positron@positron}, qui est un anti-électron, a la même masse qu'un électron, mais une charge opposée. Ces particules n'existent pas sur terre ailleurs que dans les accélérateurs de particules où elles sont produites par la collision d'autres particules. Mais on peut envisager qu'il en existe beaucoup ailleurs dans l'univers. Cette question reste cependant débattue. \subsubsection{Conclusion} On peut maintenant mieux comprendre pourquoi la compréhension du mouvement est l'un des premiers objectifs du physicien et pourquoi la science qui permet de prévoir le \og destin\fg{} des objets, la mécanique\index{mecanique@mécanique}, commence par une description des mouvements\index{mouvement@mouvement} les plus simples~: la cinématique\index{cinematique@cinématique}. \ No newline at end of file diff --git a/Introduction/Introduction.tex.bak b/Introduction/Introduction.tex.bak index b691992..afed306 100644 --- a/Introduction/Introduction.tex.bak +++ b/Introduction/Introduction.tex.bak @@ -20,7 +20,7 @@ Qui dit périodes dit donc mouvement et, plus précisément, mouvement répétit \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.} +%\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. @@ -50,7 +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}} @@ -77,7 +77,7 @@ En réalité, les choses sont plus complexes encore, puisqu'aujourd'hui les phys 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}\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. +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] @@ -101,7 +101,7 @@ Les mouvements locaux des galaxies entre elles donnent lieu à des \og chocs\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}\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{}. +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}. @@ -114,9 +114,9 @@ Le destin et l'évolution des étoiles est donc une chose complexe, d'autant plu \subsection{Le système solaire\index{systeme@système!solaire}} % la commande ci-dessous est nécessaire car on a des % dans l'url -\urldef\extrasol\url{http://fr.wikipedia.org/wiki/Plan%C3%A8tes_extrasolaires} +%\urldef\extrasol\url{http://fr.wikipedia.org/wiki/Plan%C3%A8tes_extrasolaires} -Autour des étoiles qui composent notre galaxie tournent des planètes\index{planete@planète} (actuellement plus de deux cent planètes extra-solaires\index{planete@planète!extrasolaire} ou exoplanètes\index{exoplanete@exoplanète} ont été découvertes\endnote{Voir~: \extrasol{}} ; voir aussi \cite{FC05}). +Autour des étoiles qui composent notre galaxie tournent des planètes\index{planete@planète} (actuellement plus de deux cent planètes extra-solaires\index{planete@planète!extrasolaire} ou exoplanètes\index{exoplanete@exoplanète} ont été découvertes\endnote{Voir~: \url{http://fr.wikipedia.org/wiki/Plan\%C3\%A8tes\_extrasolaires}} ; voir aussi \cite{FC05}). La première exoplanète découverte l'a été en 1995 par l'observatoire de Genève. Elle l'a été par des moyens indirects, comme la plus part de celles qui ont été découvertes par la suite. Essentiellement, il s'agit d'étudier finement la vitesse de déplacement des étoiles autour desquelles les exoplanètes tournent. Si ce déplacement est saccadé, cela traduit la présence d'un corps en rotation autour d'elles. Une autre méthode consiste à observer des variations périodiques de l'intensité lumineuse des étoiles caractéristiques du passage d'une exoplanète devant elles. @@ -126,12 +126,12 @@ La première exoplanète découverte l'a été en 1995 par l'observatoire de Gen \includegraphics[width=6cm]{2M1207.eps} \end{figure} -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. +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}\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. +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 @@ -139,17 +139,17 @@ Autour de notre étoile, le Soleil\index{Soleil@Soleil} tournent huit planètes \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}\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 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~: \url{http://fr.wikipedia.org/wiki/Image:Portrait_de_famille\_\%281\_px\_\%3D\_1000\_km\%29.jpg} 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} +%\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}} \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}\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}. +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. @@ -159,7 +159,7 @@ En passant elles laissent sur leur orbite\index{orbite@orbite} une traînée de \includegraphics[width=6cm]{Billet10FrsComete.eps} \end{figure} -Ce sont ces traînées de poussières que la Terre rencontre sur son orbite\index{orbite@orbite} en donnant lieu aux fameuses pluies d'étoiles filantes\index{etoile@étoile!filante} (voir la figure \ref{Leonides}\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}. +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 @@ -207,7 +207,7 @@ De plus, on ne peut comprendre que les saison\index{saison@saison} soient diffé \end{figure} \subsubsection{La Lune} -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. +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}. @@ -221,7 +221,7 @@ 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}\endnote{Voir le site de l'encyclopédie~: \url=http://commons.wikimedia.org/wiki/Image:TerreOrbiteLuneEtPhases.png=} 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 @@ -237,7 +237,7 @@ La question se pose alors de la différence entre éclipse de Soleil\index{eclip \includegraphics[width=6cm]{Orbite-lune-soleil.eps} \end{figure} -Comme ces plans ne coïncident pas, tant que la Lune n'est pas dans le plan de l'Écliptique\index{ecliptique@écliptique}, c'est-à-dire sur la ligne des n\oe uds\index{ligne@ligne des n\oe uds} présentée dans la figure \ref{Orbite-lune-soleil}\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}. +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. @@ -275,7 +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} @@ -285,7 +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} @@ -299,7 +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. @@ -307,13 +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} @@ -345,7 +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}} @@ -377,7 +377,7 @@ Il faut noter que le graviton\index{graviton@graviton} est encore hypothétique. \end{itemize} \medskip -Finalement, il faut encore parler des particules très particulières formant l'antimatière\index{antimatiere@antimatière}. On sait de nos jours produire et stocker pendant une courte période (quelques jours\footnote{On crée des anti-protons dans un accélérateur de particules comme le CERN à Genève, on les ralentit et on les piège dans un champ électromagnétique. Voici à ce sujet un commentaire de M. Carlo RUBBIA (Prix Nobel de Physique 1984)~: \begin{quotation}\og \textit{L'antimatière est, comme vous l'avez vu, produite au CERN où une véritable usine de production a été construite. Nous utilisons des protons qui sont accélérés et viennent frapper une cible. Au cours des collisions, il y a production d'un grand nombre de particules ou d'antiparticules et, parmi elles, on trouve des antiprotons. Ces antiprotons sont stockés dans une bouteille magnétique qui, dans le cas particulier, est un anneau de stockage à accumulation. On obtient ainsi une quantité d'antimatière qui n'est pas très petite puisqu'elle atteint un microgramme par jour.}\fg{} \endnote{Voir~: \url=http://cui.unige.ch/isi/ssc/phys/Rubbia-Klapisch.html=}\end{quotation}}) ce type de particules qui interagissent fortement avec la matière ordinaire en disparaissant totalement au profit de lumière. Ce sont des particules qui ont des propriétés inverses des particules de la matière ordinaire. Par exemple, un positron\index{positron@positron}, qui est un anti-électron, a la même masse qu'un électron, mais une charge opposée. Ces particules n'existent pas sur terre ailleurs que dans les accélérateurs de particules où elles sont produites par la collision d'autres particules. Mais on peut envisager qu'il en existe beaucoup ailleurs dans l'univers. Cette question reste cependant débattue. +Finalement, il faut encore parler des particules très particulières formant l'antimatière\index{antimatiere@antimatière}. On sait de nos jours produire et stocker pendant une courte période (quelques jours\footnote{On crée des anti-protons dans un accélérateur de particules comme le CERN à Genève, on les ralentit et on les piège dans un champ électromagnétique. Voici à ce sujet un commentaire de M. Carlo RUBBIA (Prix Nobel de Physique 1984)~: \begin{quotation}\og \textit{L'antimatière est, comme vous l'avez vu, produite au CERN où une véritable usine de production a été construite. Nous utilisons des protons qui sont accélérés et viennent frapper une cible. Au cours des collisions, il y a production d'un grand nombre de particules ou d'antiparticules et, parmi elles, on trouve des antiprotons. Ces antiprotons sont stockés dans une bouteille magnétique qui, dans le cas particulier, est un anneau de stockage à accumulation. On obtient ainsi une quantité d'antimatière qui n'est pas très petite puisqu'elle atteint un microgramme par jour.}\fg{} \endnote{Voir~: \url{http://cui.unige.ch/isi/ssc/phys/Rubbia-Klapisch.html}}\end{quotation}}) ce type de particules qui interagissent fortement avec la matière ordinaire en disparaissant totalement au profit de lumière. Ce sont des particules qui ont des propriétés inverses des particules de la matière ordinaire. Par exemple, un positron\index{positron@positron}, qui est un anti-électron, a la même masse qu'un électron, mais une charge opposée. Ces particules n'existent pas sur terre ailleurs que dans les accélérateurs de particules où elles sont produites par la collision d'autres particules. Mais on peut envisager qu'il en existe beaucoup ailleurs dans l'univers. Cette question reste cependant débattue. \subsubsection{Conclusion} On peut maintenant mieux comprendre pourquoi la compréhension du mouvement est l'un des premiers objectifs du physicien et pourquoi la science qui permet de prévoir le \og destin\fg{} des objets, la mécanique\index{mecanique@mécanique}, commence par une description des mouvements\index{mouvement@mouvement} les plus simples~: la cinématique\index{cinematique@cinématique}. \ No newline at end of file diff --git a/PhysiqueTheorique/PhysiqueTheorique.tex b/PhysiqueTheorique/PhysiqueTheorique.tex index cb892e6..4ba5c38 100644 --- a/PhysiqueTheorique/PhysiqueTheorique.tex +++ b/PhysiqueTheorique/PhysiqueTheorique.tex @@ -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} diff --git a/Preambule.tex b/Preambule.tex index 6a65b13..dd3bd59 100644 --- a/Preambule.tex +++ b/Preambule.tex @@ -5,6 +5,7 @@ \usepackage[utf8]{inputenc} % écrire avec les accents %\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. \usepackage{lmodern} @@ -75,6 +76,7 @@ %\renewcommand{\theendnote}{\Roman{endnote}} % pour mettre les notes de fin en romain \usepackage{enotez} \setenotez{ + list-name = Notes, reset = true, backref = true, totoc = chapter, diff --git a/Preambule.tex.bak b/Preambule.tex.bak index def9184..dd3bd59 100644 --- a/Preambule.tex.bak +++ b/Preambule.tex.bak @@ -5,6 +5,7 @@ \usepackage[utf8]{inputenc} % écrire avec les accents %\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. \usepackage{lmodern} @@ -31,8 +32,7 @@ \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[hyphens]{url} % permet une bonne gestion de la césure des url -\usepackage{xurl} +%\usepackage[hyphens]{url} % permet une bonne gestion de la césure des url \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 @@ -76,6 +76,7 @@ %\renewcommand{\theendnote}{\Roman{endnote}} % pour mettre les notes de fin en romain \usepackage{enotez} \setenotez{ + list-name = Notes, reset = true, backref = true, totoc = chapter, @@ -112,6 +113,8 @@ \usepackage{translator} \usepackage{siunitx} % meilleure gestion des unités que siunits, mais incompatible avec celui-ci ! \ProvidesFile{siunitx.cfg} +\usepackage{breakurl} % Ne fonctionne qu'avec dvips ! +%\usepackage[hyphens]{url} \sisetup{ output-decimal-marker = {,}, per-mode = symbol, diff --git a/Thermodynamique/Thermodynamique.tex b/Thermodynamique/Thermodynamique.tex index c22f8a8..3f9ff47 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 (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.}). +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~: \[T_F=\frac{9}{5}\cdot T_C+32\] @@ -185,7 +185,7 @@ Il ébaucha la première loi de la thermodynamique\index{première loi!de la the \bigskip -\raggedleft{\footnotesize{Nicolas Léonard Sadi Carnot en uniforme de polytechnicien peint par Louis Léopold Boilly, tiré de Wikipedia\endnote{Voir \url=http://fr.wikipedia.org/wiki/Image:Sadi\_Carnot.jpeg=}}} +\raggedleft{\footnotesize{Nicolas Léonard Sadi Carnot en uniforme de polytechnicien peint par Louis Léopold Boilly, tiré de Wikipedia\endnote{Voir \url{http://fr.wikipedia.org/wiki/Image:Sadi\_Carnot.jpeg}}}} \end{minipage} \hfill \parbox[b]{6cm}{\includegraphics[width=6cm]{Sadi_Carnot.eps}} diff --git a/ThermodynamiqueOS/ThermodynamiqueOS.tex b/ThermodynamiqueOS/ThermodynamiqueOS.tex index 1621c00..baa2baa 100644 --- a/ThermodynamiqueOS/ThermodynamiqueOS.tex +++ b/ThermodynamiqueOS/ThermodynamiqueOS.tex @@ -1172,7 +1172,7 @@ Ce bilan permet de déterminer le rendement du moteur. Il s'agit du rapport entr \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}\endnote{Voir Wikipedia~: \url=http://fr.wikipedia.org/wiki/Fichier:4-Stroke-Engine.gif=}~: +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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