From: Manuel Date: Thu, 12 Jul 2012 04:19:09 +0000 (+0200) Subject: Kepler-16b, une planète tournant autour de deux soleils. Les trajectoires avec les... X-Git-Url: https://melusine.eu.org/syracuse/G/git/?a=commitdiff_plain;h=0747313425c353e89ef3195c3b04ab229fadd780;p=pst-eqdf.git Kepler-16b, une planète tournant autour de deux soleils. Les trajectoires avec les données de la NASA. Des calculs avec PSTricks, la résolution des équations avec pst-eqdf et l'animation avec animate. --- diff --git a/gravitation/Kepler16.pdf b/gravitation/Kepler16.pdf new file mode 100644 index 0000000..097be2f Binary files /dev/null and b/gravitation/Kepler16.pdf differ diff --git a/gravitation/Kepler16.tex b/gravitation/Kepler16.tex new file mode 100644 index 0000000..a55e126 --- /dev/null +++ b/gravitation/Kepler16.tex @@ -0,0 +1,594 @@ + +\documentclass{article} +\usepackage[a4paper,margin=2cm]{geometry} +\usepackage[T1]{fontenc} +\usepackage[latin1]{inputenc}% +\usepackage[garamond]{mathdesign} +\usepackage{pst-eqdf,pst-node,pst-tools} +\usepackage{array,amsmath} +\usepackage{animate} +\usepackage{wasysym} +\newpsstyle{vecteurA}{arrowinset=0.05,arrowsize=0.1,linecolor={[rgb]{1 0.5 0}}} +\newpsstyle{vecteurB}{arrowinset=0.05,arrowsize=0.1,linecolor={[rgb]{0 0.5 1}}} +\newpsstyle{vecteurC}{arrowinset=0.1,arrowsize=0.2,linecolor={[rgb]{1 0 0}}} +\makeatletter +%% adapté de \psRandom du package pstricks-add +%% pour rendre aléatoire la taille des étoiles +%% Manuel Luque +\newdimen\pssizeStar +\def\psset@sizeStar#1{\pssetlength\pssizeStar{#1}} +\psset@sizeStar{1pt} +\define@key[psset]{pst-eqd}{randomPoints}[1000]{\def\psk@randomPoints{#1}} +\psset[pst-eqd]{randomPoints=1000} +\define@boolkey[psset]{pst-eqd}[Pst@]{color}[true]{} +\psset[pst-eqd]{color=false} +\def\psRandomStar{\pst@object{psRandomStar}}% +\def\psRandomStar@i{\@ifnextchar({\psRandomStar@ii}{\psRandomStar@iii(0,0)(1,1)}} +\def\psRandomStar@ii(#1){\@ifnextchar({\psRandomStar@iii(#1)}{\psRandomStar@iii(0,0)(#1)}} +\def\psRandomStar@iii(#1)(#2)#3{% + \def\pst@tempA{#3}% + \ifx\pst@tempA\pst@empty\psclip{\psframe(#2)}\else\psclip{#3}\fi + \pst@getcoor{#1}\pst@tempA + \pst@getcoor{#2}\pst@tempB + \begin@SpecialObj + \addto@pscode{ + \pst@tempA\space /yMin exch def + /xMin exch def + \pst@tempB\space /yMax exch def + /xMax exch def + /dy yMax yMin sub def + /dx xMax xMin sub def + rrand srand % initializes the random generator + /getRandReal { rand 2147483647 div } def + \psk@randomPoints { + /DS \pst@number\pssizeStar\space getRandReal mul def + \@nameuse{psds@\psk@dotstyle} + \ifPst@color getRandReal 1 1 sethsbcolor \fi + getRandReal dx mul xMin add + getRandReal dy mul yMin add + Dot + \ifx\psk@fillstyle\psfs@solid fill \fi stroke + } repeat + }% + \end@SpecialObj + \endpsclip + \ignorespaces +} +\makeatother +%%%%%%%%%%%%%%%%%% +%timeline +\begin{filecontents}{kepler16.dat} +::0x0 +::1 +::2 +::3 +::4 +::5 +::6 +::7 +::8 +::9 +::10 +::11 +::12 +::13 +::14 +::15 +::16 +::17 +::18 +::19 +::20 +::21 +::22 +::23 +::24 +::25 +::26 +::27 +::28 +::29 +::30 +::31 +::32 +::33 +::34 +::35 +::36 +::37 +::38 +::39 +::40 +::41 +::42 +::43 +::44 +::45 +::46 +::47 +::48 +::49 +::50 +::51 +::52 +::53 +::54 +::55 +::56 +::57 +::58 +::59 +::60 +::61 +::62 +::63 +::64 +::65 +::66 +::67 +::68 +::69 +::70 +::71 +::72 +::73 +::74 +::75 +::76 +::77 +::78 +::79 +::80 +::81 +::82 +::83 +::84 +::85 +::86 +::87 +::88 +::89 +::90 +::91 +::92 +::93 +::94 +::95 +::96 +::97 +::98 +::99 +::100 +::101 +::102 +::103 +::104 +::105 +::106 +::107 +::108 +::109 +::110 +::111 +::112 +::113 +::114 +::115 +::116 +::117 +::118 +::119 +::120 +::121 +::122 +::123 +::124 +::125 +::126 +::127 +::128 +::129 +::130 +::131 +::132 +::133 +::134 +::135 +::136 +::137 +::138 +::139 +::140 +::141 +::142 +::143 +::144 +::145 +::146 +::147 +::148 +::149 +::150 +::151 +::152 +::153 +::154 +::155 +::156 +::157 +::158 +::159 +::160 +::161 +::162 +::163 +::164 +::165 +::166 +::167 +::168 +::169 +::170 +::171 +::172 +::173 +::174 +::175 +::176 +::177 +::178 +::179 +::180 +::181 +::182 +::183 +::184 +::185 +::186 +::187 +::188 +::189 +::190 +::191 +::192 +::193 +::194 +::195 +::196 +::197 +::198 +::199 +::200 +\end{filecontents} +%%%%%%%%%%%%%%%%% +\title{Gravitation : une planète à deux soleils comme Tatooine celle de Luke Skywalker dans \textit{La Guerre des étoiles}} +\date{10 juillet 2\,012} +\begin{document} +\maketitle +\section{La représentation avec les données de la NASA} +Ceci est une tentative pour essayer de schématiser une planète orbitant autour d'une étoile binaire, comme Kepler-16b. On parle dans ce cas-là d'une planète \textit{circumbinaire}. +Le site de la NASA dédié à cette planète\footnote{http://kepler.nasa.gov/Mission/discoveries/kepler16b/}, fournit un grand nombre de renseignements sur les étoiles et la planète, ce qui permet de reconstituer leurs trajectoires respectives. Voici les caractéristiques utiles pour le schéma et l'animation. +\begin{center} +\begin{tabular}{|ll|} +\hline +\textbf{ Paramètres}&\textbf{Valeurs}\\ \hline + \textit{Étoile A}&\\ \hline + Masse, $M_A(M_{\astrosun})$&0.6897\\ + Rayon, $R_A(R_{\astrosun})$&0.6489\\ \hline + \textit{Étoile B}&\\ \hline + Masse, $M_B(M_{\astrosun})$&0.20255\\ + Rayon, $R_B(R_{\astrosun})$&0.22623\\ \hline + \textit{Planète b}&\\ \hline + Masse, $M_b(M_{\jupiter})$&0.333\\ + Rayon, $R_b(R_{\jupiter})$&0.7538\\ \hline + \textit{Orbite de l'étoile binaire}&\\ \hline + Période(jours)&41.076\\ + Demi-grand axe(ua) $\mathrm{a_1}$&0.22431\\ + Excentricité $\mathrm{e_1}$&0.15944\\ + Argument du périastre(deg) $\omega_1$&263.464\\ \hline + \textit{Orbite de la planète circumbinaire} &\\ \hline + Période(jours)&228.776\\ + Demi-grand axe(ua)$\mathrm{a_2}$&0.7048\\ + Excentricité $\mathrm{e_2}$&0.0069\\ + Argument du périastre(deg) $\omega_2$&318\\ \hline +\end{tabular} +\end{center} + +\begin{center} +\begin{pspicture}(-5,-5)(5,5) +\psgrid[subgriddiv=0,gridcolor=lightgray,griddots=10,gridlabels=0pt]% +\pstVerb{% pour le système binaire d'étoiles + /a1 0.22431 def % semi-major axis + /e1 0.15944 def % eccentricity + /w1 263.464 def % argument of periaspe + /MA 0.6897 def % masse of star A + /MB 0.20255 def % masse of star B + /Mt MA MB add def % masse totale + /P1 41.076 def % period (day) + % pour la planète + /Mb 0.3333 def % masse of planet b (M_Jupiter) + /a2 0.7048 def % semi-major axis + /e2 0.0069 def % eccentricity + /w2 318 def % argument of periaspe + /P2 228.776 def % period (day) +% on en déduit le paramètre de chacune des ellipses + /p1 a1 1 e1 dup mul add mul def + /p2 a2 1 e2 dup mul add mul def + }% +\pnode(!/radius p1 1 e1 w1 w1 sub cos mul add div def + /radius1 radius MB Mt div mul neg def + radius1 w1 cos mul 5 mul + radius1 w1 sin mul 5 mul){MA0} +\parametricplot[plotpoints=360,unit=5,linecolor=red]{0}{360}{ + /radius p1 1 e1 t w1 sub cos mul add div def + /radius1 radius MB Mt div mul neg def + radius1 t cos mul + radius1 t sin mul} +\pscircle[fillstyle=solid,fillcolor=yellow!50](MA0){0.3} +\parametricplot[plotpoints=360,unit=5,linecolor=green]{0}{360}{ + /radius p1 1 e1 t w1 sub cos mul add div def + /radius2 radius MA Mt div mul def + radius2 t cos mul + radius2 t sin mul} +\pnode(!/radius p1 1 e1 w1 w1 sub cos mul add div def + /radius1 radius MA Mt div mul def + radius1 w1 cos mul 5 mul + radius1 w1 sin mul 5 mul){MB0} +\pscircle[fillstyle=solid,fillcolor=red](MB0){0.15} +\parametricplot[plotpoints=360,unit=5,linecolor=blue]{0}{360}{ + /radius p2 1 e2 t w2 sub cos mul add div def + radius t cos mul + radius t sin mul} +\pnode(!/radius p2 1 e2 w2 w2 sub cos mul add div def + radius w2 cos mul 5 mul + radius w2 sin mul 5 mul){Mb0} +\pscircle[fillstyle=solid,fillcolor=blue](Mb0){0.07} +\end{pspicture} +\end{center} +\section{La simulation avec PSTricks} +\begin{center} +\begin{pspicture}(-3,-1)(6,7) +\psgrid[subgriddiv=0,gridcolor=lightgray,griddots=10,gridlabels=0pt]% +\pstVerb{/x01 -3 def /y01 0 def + /x02 5 def /y02 0 def + /xr012 x02 x01 sub def + /yr012 y02 y01 sub def + /x0 2 def /y0 5 def + /xr002 x02 x0 sub def + /yr002 y02 y0 sub def + /xr001 x01 x0 sub def + /yr001 y01 y0 sub def + /M0 0.2 def + /M1 0.07 def + /M2 3.2e-4 def + /Mt M1 M2 add def + /xG012 x01 M1 mul x02 M2 mul add Mt div def + /yG012 y01 M1 mul y02 M2 mul add Mt div def + }% +\pnode(0,0){O} +\pnode(!x01 y01){M1} +\pnode(!x02 y02){M2} +\pnode(!x0 y0){M0} +\pnode(!xG012 yG012){C12} % centre de masse de M1 et M2 +\pscircle[fillstyle=solid,fillcolor=yellow!50](M2){0.21} +\pscircle[fillstyle=solid,fillcolor=red!50](M1){0.5} +\pscircle[fillstyle=solid,fillcolor=blue!50](M0){0.07} +\psline[linestyle=dotted](M1)(M2) +\psline[linestyle=dashed](M2)(M0)(M1) +\psline{<->}(6,0)(0,0)(0,7) +\uput[u](M0){$M_0$} +\uput[r](0,6.8){$y$} +\uput[u](5.8,0){$x$} +\uput[l](0,6.8){$\mathcal{R}$} +\uput{0.6}[d](M1){$M_1$} +\uput{0.25}[d](M2){$M_2$} +\rput(M1){\psline[style=vecteurC]{->}(!xr012 3 div yr012 3 div)\uput[d](!xr012 3 div yr012 3 div){$\overrightarrow{F}_{2/1}$} + \psline[style=vecteurC]{->}(!xr001 5 div neg yr001 5 div neg)\uput[r](!xr001 5 div neg yr001 5 div neg){$\overrightarrow{F}_{0/1}$}} +\rput(M2){\psline[style=vecteurC]{->}(!xr012 3 div neg yr012 3 div neg)\uput[d](!xr012 3 div neg yr012 3 div neg){$\overrightarrow{F}_{1/2}$} + \psline[style=vecteurC]{->}(!xr002 3 div neg yr002 3 div neg)\uput[r](!xr002 3 div neg yr002 3 div neg){$\overrightarrow{F}_{0/2}$}} +\rput(M0){\psline[style=vecteurC]{->}(!xr002 3 div yr002 3 div)\uput[r](!xr002 3 div yr002 3 div){$\overrightarrow{F}_{2/0}$}} +\rput(M0){\psline[style=vecteurC]{->}(!xr001 5 div yr001 5 div)\uput[r](!xr001 5 div yr001 5 div){$\overrightarrow{F}_{1/0}$}} +\end{pspicture} +\end{center} +Pour cela, on considère un système de trois corps en interaction gravitationnelle : l'étoile $M_1$ de masse $m_1$, l'étoile $M_2$ de masse $m_2$ constituant l'étoile binaire et une planète $P$ notée $M_0$, de masse $m$ orbitant autour de cette étoile double. + +Avec : $\overrightarrow{r_{01}}=\overrightarrow{M_0M_1}$, $\overrightarrow{r_{02}}=\overrightarrow{M_0M_2}$ et $\overrightarrow{r_{12}}=\overrightarrow{M_1M_2}$ on pose : +\begin{itemize} + \item $\overrightarrow{r}_{01}=\overrightarrow{r}_1-\overrightarrow{r}_0$ + \item $\overrightarrow{r}_{02}=\overrightarrow{r}_2-\overrightarrow{r}_0$ + \item $\overrightarrow{r}_{12}=\overrightarrow{r}_2-\overrightarrow{r}_1$ +\end{itemize} +Chacune des forces s'exprime par : +\[ +\left\{ +\begin{array}[m]{l} +\overrightarrow{F}_{1/0}=\mathcal{G}\dfrac{m_1m_0}{r_{10}^3}\overrightarrow{r_{01}}=-\overrightarrow{F}_{0/1}\\[1em] +\overrightarrow{F}_{2/0}=\mathcal{G}\dfrac{m_2m_0}{r_{20}^3}\overrightarrow{r_{02}}=-\overrightarrow{F}_{0/2}\\[1em] +\overrightarrow{F}_{2/1}=\mathcal{G}\dfrac{m_1m_2}{r_{12}^3}\overrightarrow{r_{12}}=-\overrightarrow{F}_{1/2} +\end{array} +\right. +\] +L'application de la loi de Newton à chacun des corps donne : +\[ +\left\{ +\begin{array}[m]{l} +m_0\dfrac{\mathrm{d^2}\overrightarrow{r_0}}{\mathrm{d}t^2}=\hphantom{-}\mathcal{G}\dfrac{m_1m_0}{r_{10}^3}\overrightarrow{r_{01}}+ + \mathcal{G}\dfrac{m_2m_0}{r_{20}^3}\overrightarrow{r_{02}}\\[1em] +m_1\dfrac{\mathrm{d^2}\overrightarrow{r_1}}{\mathrm{d}t^2}=-\mathcal{G}\dfrac{m_0m_1}{r_{10}^3}\overrightarrow{r_{01}}+ + \mathcal{G}\dfrac{m_1m_2}{r_{12}^3}\overrightarrow{r_{12}}\\[1em] +m_2\dfrac{\mathrm{d^2}\overrightarrow{r_2}}{\mathrm{d}t^2}=-\mathcal{G}\dfrac{m_0m_2}{r_{20}^3}\overrightarrow{r_{02}}- + \mathcal{G}\dfrac{m_1m_2}{r_{12}^3}\overrightarrow{r_{12}} +\end{array} +\right. +\] +Ce qui conduit à un système de 6 équations différentielles : +\[ +\left\{ +\begin{array}[m]{l} +\ddot{x_0}=\hphantom{-}\mathcal{G}\dfrac{m_1}{r_{10}^3}(x_1-x_0)+\mathcal{G}\dfrac{m_2}{r_{20}^3}(x_2-x_0)\\[1em] +\ddot{y_0}=\hphantom{-}\mathcal{G}\dfrac{m_1}{r_{10}^3}(y_1-y_0)+\mathcal{G}\dfrac{m_2}{r_{20}^3}(y_2-y_0)\\[1em] +\ddot{x_1}=-\mathcal{G}\dfrac{m_0}{r_{10}^3}(x_1-x_0)+\mathcal{G}\dfrac{m_2}{r_{12}^3}(x_2-x_1)\\[1em] +\ddot{y_1}=-\mathcal{G}\dfrac{m_0}{r_{10}^3}(y_1-y_0)+\mathcal{G}\dfrac{m_2}{r_{12}^3}(y_2-y_1)\\[1em] +\ddot{x_2}=-\mathcal{G}\dfrac{m_0}{r_{10}^3}(x_2-x_0)-\mathcal{G}\dfrac{m_1}{r_{12}^3}(x_2-x_1)\\[1em] +\ddot{y_2}=-\mathcal{G}\dfrac{m_0}{r_{02}^3}(y_2-y_0)-\mathcal{G}\dfrac{m_1}{r_{12}^3}(y_2-y_1) +\end{array} +\right. +\] + +\begin{verbatim} +% 0 1 2 3 4 5 6 7 8 9 10 11 +% y[0] y[1] y[2] y[3] y[4] y[5] y[6] y[7] y[8] y[9] y[10] y[11] +% x0 y0 x'0 y'0 x1 y1 x'1 y'1 x2 y2 x'2 y'2 +\def\GravAlgIIIcorps{% + y[2]|y[3]|% + M1*(y[4]-y[0])/((y[4]-y[0])^2+(y[5]-y[1])^2)^1.5+M2*(y[8]-y[0])/((y[8]-y[0])^2+(y[9]-y[1])^2)^1.5|% + M1*(y[5]-y[1])/((y[4]-y[0])^2+(y[5]-y[1])^2)^1.5+M2*(y[9]-y[1])/((y[8]-y[0])^2+(y[9]-y[1])^2)^1.5|% + y[6]|y[7]|% + -M0*(y[4]-y[0])/((y[4]-y[0])^2+(y[5]-y[1])^2)^1.5+M2*(y[8]-y[4])/((y[8]-y[4])^2+(y[9]-y[5])^2)^1.5|% + -M0*(y[5]-y[1])/((y[4]-y[0])^2+(y[5]-y[1])^2)^1.5+M2*(y[9]-y[5])/((y[8]-y[4])^2+(y[9]-y[5])^2)^1.5|% + y[10]|y[11]|% + -M0*(y[8]-y[0])/((y[8]-y[0])^2+(y[9]-y[1])^2)^1.5-M1*(y[8]-y[4])/((y[8]-y[4])^2+(y[9]-y[5])^2)^1.5|% + -M0*(y[9]-y[1])/((y[8]-y[0])^2+(y[9]-y[1])^2)^1.5-M1*(y[9]-y[5])/((y[8]-y[4])^2+(y[9]-y[5])^2)^1.5} +\end{verbatim} + + +\newpage +% y[0] y[1] y[2] y[3] y[4] y[5] y[6] y[7] y[8] y[9] y[10] y[11] +% x0 y0 x'0 y'0 x1 y1 x'1 y'1 x2 y2 x'2 y'2 +\def\GravAlgIIIcorps{% + y[2]|y[3]|% + M1*(y[4]-y[0])/((y[4]-y[0])^2+(y[5]-y[1])^2)^1.5+M2*(y[8]-y[0])/((y[8]-y[0])^2+(y[9]-y[1])^2)^1.5|% + M1*(y[5]-y[1])/((y[4]-y[0])^2+(y[5]-y[1])^2)^1.5+M2*(y[9]-y[1])/((y[8]-y[0])^2+(y[9]-y[1])^2)^1.5|% + y[6]|y[7]|% + -M0*(y[4]-y[0])/((y[4]-y[0])^2+(y[5]-y[1])^2)^1.5+M2*(y[8]-y[4])/((y[8]-y[4])^2+(y[9]-y[5])^2)^1.5|% + -M0*(y[5]-y[1])/((y[4]-y[0])^2+(y[5]-y[1])^2)^1.5+M2*(y[9]-y[5])/((y[8]-y[4])^2+(y[9]-y[5])^2)^1.5|% + y[10]|y[11]|% + -M0*(y[8]-y[0])/((y[8]-y[0])^2+(y[9]-y[1])^2)^1.5-M1*(y[8]-y[4])/((y[8]-y[4])^2+(y[9]-y[5])^2)^1.5|% + -M0*(y[9]-y[1])/((y[8]-y[0])^2+(y[9]-y[1])^2)^1.5-M1*(y[9]-y[5])/((y[8]-y[4])^2+(y[9]-y[5])^2)^1.5} +% + +\begin{center} +\def\InitCond{x00 y00 v0x0 v0y0 x01 y01 v0x1 v0y1 x02 y02 v0x2 v0y2} +\psset{method=rk4} +\begin{pspicture}(-8,-8)(8,8) +\psframe*[linecolor={[cmyk]{1 1 0 0.7}}](-8,-8)(8,8) +\pstVerb{ +/arccos { + dup + dup mul neg 1 add sqrt + exch + atan +} def + /G 1 def + /w2 55 def + /x00 7 w2 cos mul def /y00 7 w2 sin mul def + /x01 0.4962 def + /y01 0 def + /v0x1 0 def + /v0y1 .135 def + /x02 -1.69 def + /y02 0 def + /v0x2 0 def + /v0y2 -.46 def + /v0x0 0.36 w2 sin mul neg def + /v0y0 0.36 w2 cos mul def + /M1 0.7 def + /M2 0.2 def + /M0 3e-4 def + /Mt M1 M2 add def + /xG012 x01 M1 mul x02 M2 mul add Mt div def + /yG012 y01 M1 mul y02 M2 mul add Mt div def + }% +\psgrid[subgriddiv=0,gridcolor=white,griddots=10,gridlabels=0pt](-8,-8)(8,8)% +\psequadiff[plotpoints=1000,algebraic, + plotfuncx=y 4 get + y 4 get M1 mul + y 8 get M2 mul add + M1 M2 add div + sub, + plotfuncy=5 get + dup M1 mul + y 9 get M2 mul add + M1 M2 add div + sub, + tabname=XAYA, + saveData,filename=XAYA.dat +% ]{0}{18}{\InitCond}{\GravAlgIIIcorps} + ]{0}{120}{\InitCond}{\GravAlgIIIcorps} +\listplot[unit=1,linecolor=yellow]{XAYA aload pop} +\psequadiff[plotpoints=1000,algebraic, + plotfuncx=y 8 get + y 4 get M1 mul + y 8 get M2 mul add + M1 M2 add div + sub, + plotfuncy=9 get + dup M2 mul + y 5 get M1 mul add + M1 M2 add div + sub, + tabname=XBYB, + saveData,filename=XBYB.dat +% ]{0}{18}{\InitCond}{\GravAlgIIIcorps} + ]{0}{120}{\InitCond}{\GravAlgIIIcorps} +\listplot[unit=1,linecolor=red]{XBYB aload pop} +\psequadiff[plotpoints=1000,algebraic, + plotfuncx=y 0 get + y 4 get M1 mul + y 8 get M2 mul add + M1 M2 add div + sub, + plotfuncy=1 get + y 5 get M1 mul + y 9 get M2 mul add + M1 M2 add div + sub, + tabname=XbYb, + saveData,filename=XPYP.dat + ]{0}{120}{\InitCond}{\GravAlgIIIcorps} +\listplot[unit=1,linecolor=blue]{XbYb aload pop} +\pnode(!x01 xG012 sub y01 yG012 sub){M01} +\pnode(!x02 xG012 sub y02 yG012 sub){M02} +\pnode(!x00 xG012 sub y00 yG012 sub){M00} +\pscircle*[linecolor=yellow](M01){0.4} +\pscircle*[linecolor=red](M02){0.16} +\pscircle*[linecolor=white](M00){0.07} +%\rput(M01){\psline[unit=2,linecolor=red]{->}(!v0x1 v0y1)} +%\rput(M02){\psline[unit=2,linecolor=blue]{->}(!v0x2 v0y2)} +\psdot(!xG012 yG012) +\end{pspicture} +\end{center} +\section{Animation avec pst-eqdf et animate} +\begin{center} +\def\nFrames{200}% 200 images +\begin{animateinline}[controls,timeline=kepler16.dat,loop,% + begin={\begin{pspicture}(-8,-8)(8,8)}, + end={\end{pspicture}}]{5}% 5 images/s +\pstVerb{/XY1 [(XAYA.dat) run] def + /XY2 [(XBYB.dat) run] def + /XY3 [(XPYP.dat) run] def + }% +\psframe*[linecolor={[cmyk]{1 1 0 0.7}}](-8,-8)(8,8) +\psRandomStar[linecolor={[rgb]{1,1,0.5}}, + randomPoints=1000,sizeStar=1pt](-8,-8)(8,8){\psframe[linestyle=none](-8,-8)(8,8)} +%\listplot[linecolor=gray]{XY1 aload pop} +%\listplot[linecolor=gray]{XY2 aload pop} +%\listplot[linecolor=gray]{XY3 aload pop} +\newframe +\multiframe{\nFrames}{i=0+10}{% 1 point sur 10 +\pstVerb{/X1 XY1 \i\space get def + /Y1 XY1 \i\space 1 add get def + /X2 XY2 \i\space get def + /Y2 XY2 \i\space 1 add get def + /X3 XY3 \i\space get def + /Y3 XY3 \i\space 1 add get def + }% +%\psdot(!X1 Y1) +\pscircle*[linecolor=yellow](!X1 Y1){0.5} +\pscircle*[linecolor=red](!X2 Y2){0.2} +\pscircle*[linecolor=white](!X3 Y3){0.07} +} +\end{animateinline} +\end{center} +\end{document} + diff --git a/gravitation/LISTE.txt b/gravitation/LISTE.txt index 93f2cca..744370b 100644 --- a/gravitation/LISTE.txt +++ b/gravitation/LISTE.txt @@ -39,6 +39,15 @@ IIIXYM1.dat IIIXYM02.dat IIIXYM2.dat IIIXYM12.dat +== Kepler-16b : une planète à deux soleils +Kepler16.pdf +Kepler16.tex +animation_kepler16_pstricks.pdf +animation_kepler16_pstricks.tex +XAYA.dat +XBYB.dat +XPYP.dat +kepler16.dat == Les fichiers du paquet pst-eqdf.tex pst-eqdf.sty @@ -57,3 +66,4 @@ pb_2corps_animation1.png 2corps10.png 3corps1.png 3corps5.png +animation_kepler16_pstricks.png diff --git a/gravitation/XAYA.dat b/gravitation/XAYA.dat new file mode 100644 index 0000000..aee61c0 --- /dev/null +++ b/gravitation/XAYA.dat @@ -0,0 +1,1000 @@ +0.485822 0.0122764 +0.48552 0.0281403 +0.484615 0.0439691 +0.483107 0.0597431 +0.480997 0.0754424 +0.478286 0.0910473 +0.474978 0.106538 +0.471073 0.121895 +0.466576 0.137097 +0.461489 0.152126 +0.455816 0.16696 +0.449562 0.181581 +0.442732 0.195968 +0.43533 0.2101 +0.427363 0.223958 +0.418837 0.237521 +0.409759 0.250769 +0.400137 0.263682 +0.389979 0.276238 +0.379293 0.288419 +0.368091 0.300203 +0.356381 0.311569 +0.344174 0.322497 +0.331483 0.332967 +0.31832 0.342959 +0.304698 0.352451 +0.290631 0.361423 +0.276135 0.369855 +0.261225 0.377726 +0.245918 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b/gravitation/animation_kepler16_pstricks.png new file mode 100644 index 0000000..dd6b32c Binary files /dev/null and b/gravitation/animation_kepler16_pstricks.png differ diff --git a/gravitation/animation_kepler16_pstricks.tex b/gravitation/animation_kepler16_pstricks.tex new file mode 100644 index 0000000..3a8fd5b --- /dev/null +++ b/gravitation/animation_kepler16_pstricks.tex @@ -0,0 +1,297 @@ + +\documentclass{article} +\usepackage[a4paper,margin=2cm]{geometry} +\usepackage[T1]{fontenc} +\usepackage[latin1]{inputenc}% +\usepackage[garamond]{mathdesign} +\usepackage{pstricks,pst-eqdf,pst-node} +\usepackage{animate} +\newpsstyle{vecteurA}{arrowinset=0.05,arrowsize=0.1,linecolor={[rgb]{1 0.5 0}}} +\newpsstyle{vecteurB}{arrowinset=0.05,arrowsize=0.1,linecolor={[rgb]{0 0.5 1}}} +\newpsstyle{vecteurC}{arrowinset=0.1,arrowsize=0.2,linecolor={[rgb]{1 0 0}}} +%timeline +\begin{filecontents}{kepler16.dat} +::0x0 +::1 +::2 +::3 +::4 +::5 +::6 +::7 +::8 +::9 +::10 +::11 +::12 +::13 +::14 +::15 +::16 +::17 +::18 +::19 +::20 +::21 +::22 +::23 +::24 +::25 +::26 +::27 +::28 +::29 +::30 +::31 +::32 +::33 +::34 +::35 +::36 +::37 +::38 +::39 +::40 +::41 +::42 +::43 +::44 +::45 +::46 +::47 +::48 +::49 +::50 +::51 +::52 +::53 +::54 +::55 +::56 +::57 +::58 +::59 +::60 +::61 +::62 +::63 +::64 +::65 +::66 +::67 +::68 +::69 +::70 +::71 +::72 +::73 +::74 +::75 +::76 +::77 +::78 +::79 +::80 +::81 +::82 +::83 +::84 +::85 +::86 +::87 +::88 +::89 +::90 +::91 +::92 +::93 +::94 +::95 +::96 +::97 +::98 +::99 +::100 +::101 +::102 +::103 +::104 +::105 +::106 +::107 +::108 +::109 +::110 +::111 +::112 +::113 +::114 +::115 +::116 +::117 +::118 +::119 +::120 +::121 +::122 +::123 +::124 +::125 +::126 +::127 +::128 +::129 +::130 +::131 +::132 +::133 +::134 +::135 +::136 +::137 +::138 +::139 +::140 +::141 +::142 +::143 +::144 +::145 +::146 +::147 +::148 +::149 +::150 +::151 +::152 +::153 +::154 +::155 +::156 +::157 +::158 +::159 +::160 +::161 +::162 +::163 +::164 +::165 +::166 +::167 +::168 +::169 +::170 +::171 +::172 +::173 +::174 +::175 +::176 +::177 +::178 +::179 +::180 +::181 +::182 +::183 +::184 +::185 +::186 +::187 +::188 +::189 +::190 +::191 +::192 +::193 +::194 +::195 +::196 +::197 +::198 +::199 +::200 +\end{filecontents} +%%%%%%%%%%%%%%%%%% +\makeatletter +%% adapté de \psRandom du package pstricks-add +%% pour rendre aléatoire la taille des étoiles +%% Manuel Luque +\newdimen\pssizeStar +\def\psset@sizeStar#1{\pssetlength\pssizeStar{#1}} +\psset@sizeStar{1pt} +\define@key[psset]{pst-eqd}{randomPoints}[1000]{\def\psk@randomPoints{#1}} +\psset[pst-eqd]{randomPoints=1000} +\define@boolkey[psset]{pst-eqd}[Pst@]{color}[true]{} +\psset[pst-eqd]{color=false} +\def\psRandomStar{\pst@object{psRandomStar}}% +\def\psRandomStar@i{\@ifnextchar({\psRandomStar@ii}{\psRandomStar@iii(0,0)(1,1)}} +\def\psRandomStar@ii(#1){\@ifnextchar({\psRandomStar@iii(#1)}{\psRandomStar@iii(0,0)(#1)}} +\def\psRandomStar@iii(#1)(#2)#3{% + \def\pst@tempA{#3}% + \ifx\pst@tempA\pst@empty\psclip{\psframe(#2)}\else\psclip{#3}\fi + \pst@getcoor{#1}\pst@tempA + \pst@getcoor{#2}\pst@tempB + \begin@SpecialObj + \addto@pscode{ + \pst@tempA\space /yMin exch def + /xMin exch def + \pst@tempB\space /yMax exch def + /xMax exch def + /dy yMax yMin sub def + /dx xMax xMin sub def + rrand srand % initializes the random generator + /getRandReal { rand 2147483647 div } def + \psk@randomPoints { + /DS \pst@number\pssizeStar\space getRandReal mul def + \@nameuse{psds@\psk@dotstyle} + \ifPst@color getRandReal 1 1 sethsbcolor \fi + getRandReal dx mul xMin add + getRandReal dy mul yMin add + Dot + \ifx\psk@fillstyle\psfs@solid fill \fi stroke + } repeat + }% + \end@SpecialObj + \endpsclip + \ignorespaces +} +\makeatother +%%%%%%%%%%%%%%%%%%%%%%% +\title{Gravitation : une planète à deux soleils comme Tatooine celle de Luke Skywalker dans La Guerre des étoiles} +\date{10 juillet 2\,012} +\begin{document} +\begin{center} +\pstVerb{/XY1 [(XAYA.dat) run] def + /XY2 [(XBYB.dat) run] def + /XY3 [(XPYP.dat) run] def + }% +\def\nFrames{200}% 200 images +\begin{animateinline}[controls,timeline=kepler16.dat,loop,% + begin={\begin{pspicture}(-8,-8)(8,8)}, + end={\end{pspicture}}]{5}% 5 images/s +\psframe*[linecolor={[cmyk]{1 1 0 0.7}}](-8,-8)(8,8) +\psRandomStar[linecolor={[rgb]{1,1,0.5}}, + randomPoints=1000,sizeStar=1pt](-8,-8)(8,8){\psframe[linestyle=none](-8,-8)(8,8)} +%\listplot[linecolor=gray]{XY1 aload pop} +%\listplot[linecolor=gray]{XY2 aload pop} +%\listplot[linecolor=gray]{XY3 aload pop} +\newframe +\multiframe{\nFrames}{i=0+10}{% 1 point sur 10 +\pstVerb{/X1 XY1 \i\space get def + /Y1 XY1 \i\space 1 add get def + /X2 XY2 \i\space get def + /Y2 XY2 \i\space 1 add get def + /X3 XY3 \i\space get def + /Y3 XY3 \i\space 1 add get def + }% +%\psdot(!X1 Y1) +\pscircle*[linecolor=yellow](!X1 Y1){0.5} +\pscircle*[linecolor=red](!X2 Y2){0.2} +\pscircle*[linecolor=white](!X3 Y3){0.07} +} +\end{animateinline} +\end{center} +\end{document} + diff --git a/gravitation/kepler16.dat b/gravitation/kepler16.dat new file mode 100644 index 0000000..fa2392b --- /dev/null +++ b/gravitation/kepler16.dat @@ -0,0 +1,205 @@ +%% LaTeX2e file `kepler16.dat' +%% generated by the `filecontents' environment +%% from source `animation_kepler16_pstricks' on 2012/07/11. +%% +::0x0 +::1 +::2 +::3 +::4 +::5 +::6 +::7 +::8 +::9 +::10 +::11 +::12 +::13 +::14 +::15 +::16 +::17 +::18 +::19 +::20 +::21 +::22 +::23 +::24 +::25 +::26 +::27 +::28 +::29 +::30 +::31 +::32 +::33 +::34 +::35 +::36 +::37 +::38 +::39 +::40 +::41 +::42 +::43 +::44 +::45 +::46 +::47 +::48 +::49 +::50 +::51 +::52 +::53 +::54 +::55 +::56 +::57 +::58 +::59 +::60 +::61 +::62 +::63 +::64 +::65 +::66 +::67 +::68 +::69 +::70 +::71 +::72 +::73 +::74 +::75 +::76 +::77 +::78 +::79 +::80 +::81 +::82 +::83 +::84 +::85 +::86 +::87 +::88 +::89 +::90 +::91 +::92 +::93 +::94 +::95 +::96 +::97 +::98 +::99 +::100 +::101 +::102 +::103 +::104 +::105 +::106 +::107 +::108 +::109 +::110 +::111 +::112 +::113 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