From: Manuel <manuel.luque27@gmail.com>
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/?p=pst-eqdf.git;a=commitdiff_plain;h=0747313425c353e89ef3195c3b04ab229fadd780

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 0.385018 
+0.230232 0.391709 
+0.214187 0.397781 
+0.197802 0.403213 
+0.181098 0.407987 
+0.164097 0.412085 
+0.146824 0.415488 
+0.129302 0.418179 
+0.111558 0.42014 
+0.0936185 0.421356 
+0.0755126 0.421811 
+0.0572699 0.421491 
+0.0389216 0.420382 
+0.0205003 0.41847 
+0.00203988 0.415747 
+-0.0164244 0.4122 
+-0.034856 0.407823 
+-0.0532168 0.402608 
+-0.0714679 0.396551 
+-0.0895686 0.389648 
+-0.107477 0.381899 
+-0.125152 0.373305 
+-0.142548 0.363869 
+-0.159621 0.353599 
+-0.176327 0.342502 
+-0.192619 0.330591 
+-0.208451 0.317881 
+-0.223777 0.304388 
+-0.238551 0.290135 
+-0.252726 0.275146 
+-0.266257 0.259447 
+-0.2791 0.24307 
+-0.29121 0.226049 
+-0.302547 0.208421 
+-0.313068 0.190226 
+-0.322737 0.17151 
+-0.331518 0.152317 
+-0.339376 0.132697 
+-0.346281 0.112703 
+-0.352208 0.0923881 
+-0.357132 0.071809 
+-0.361033 0.0510235 
+-0.363895 0.0300908 
+-0.365708 0.00907085 
+-0.366463 -0.0119755 
+-0.366158 -0.0329875 
+-0.364793 -0.0539044 
+-0.362375 -0.0746662 
+-0.358912 -0.0952139 
+-0.35442 -0.11549 
+-0.348917 -0.135438 
+-0.342423 -0.155005 
+-0.334965 -0.174138 
+-0.326572 -0.192789 
+-0.317276 -0.210911 
+-0.307111 -0.228462 
+-0.296115 -0.245401 
+-0.284328 -0.261691 
+-0.27179 -0.277298 
+-0.258545 -0.292193 
+-0.244637 -0.306347 
+-0.230111 -0.319738 
+-0.215014 -0.332344 
+-0.19939 -0.344149 
+-0.183287 -0.355138 
+-0.166751 -0.365299 
+-0.149827 -0.374624 
+-0.132562 -0.383108 
+-0.114999 -0.390746 
+-0.097184 -0.397537 
+-0.079159 -0.403483 
+-0.0609661 -0.408588 
+-0.0426464 -0.412855 
+-0.0242395 -0.416292 
+-0.00578405 -0.418909 
+0.0126829 -0.420713 
+0.0311255 -0.421718 
+0.0495093 -0.421935 
+0.0678011 -0.421379 
+0.0859691 -0.420064 
+0.103983 -0.418005 
+0.121814 -0.41522 
+0.139433 -0.411724 
+0.156815 -0.407536 
+0.173935 -0.402673 
+0.190768 -0.397155 
+0.207291 -0.391001 
+0.223483 -0.384229 
+0.239324 -0.37686 
+0.254794 -0.368913 
+0.269874 -0.360409 
+0.284548 -0.351367 
+0.298799 -0.341808 
+0.312611 -0.331752 
+0.32597 -0.32122 
+0.338863 -0.310233 
+0.351276 -0.29881 
+0.363198 -0.286973 
+0.374617 -0.274741 
+0.385522 -0.262136 
+0.395905 -0.249178 
+0.405755 -0.235887 
+0.415064 -0.222284 
+0.423824 -0.208389 
+0.432029 -0.194222 
+0.439671 -0.179804 
+0.446744 -0.165154 
+0.453243 -0.150292 
+0.459162 -0.13524 
+0.464497 -0.120016 
+0.469245 -0.104641 
+0.473401 -0.089134 
+0.476962 -0.0735157 
+0.479925 -0.0578055 
+0.48229 -0.0420234 
+0.484053 -0.026189 
+0.485214 -0.0103222 
+0.485771 0.00555738 
+0.485725 0.0214299 
+0.485074 0.0372758 
+0.483821 0.0530751 
+0.481966 0.0688081 
+0.479509 0.0844551 
+0.476454 0.0999963 
+0.472801 0.115412 
+0.468554 0.130682 
+0.463716 0.145786 
+0.458291 0.160705 
+0.452282 0.175418 
+0.445695 0.189906 
+0.438534 0.204148 
+0.430806 0.218124 
+0.422515 0.231814 
+0.41367 0.245197 
+0.404277 0.258254 
+0.394345 0.270964 
+0.383882 0.283306 
+0.372897 0.295259 
+0.3614 0.306804 
+0.349402 0.31792 
+0.336915 0.328587 
+0.32395 0.338783 
+0.31052 0.348488 
+0.29664 0.357682 
+0.282323 0.366345 
+0.267586 0.374456 
+0.252445 0.381995 
+0.236917 0.388942 
+0.221021 0.395277 
+0.204777 0.400982 
+0.188205 0.406037 
+0.171327 0.410423 
+0.154165 0.414121 
+0.136745 0.417115 
+0.119092 0.419387 
+0.101231 0.420919 
+0.0831916 0.421697 
+0.0650026 0.421706 
+0.0466947 0.420931 
+0.0282997 0.41936 
+0.00985115 0.416981 
+-0.0086164 0.413782 
+-0.0270669 0.409757 
+-0.0454629 0.404896 
+-0.0637657 0.399194 
+-0.0819355 0.392648 
+-0.0999312 0.385256 
+-0.11771 0.377018 
+-0.13523 0.367936 
+-0.152446 0.358016 
+-0.169313 0.347266 
+-0.185786 0.335697 
+-0.201818 0.323321 
+-0.217364 0.310155 
+-0.232377 0.29622 
+-0.246811 0.281537 
+-0.26062 0.266133 
+-0.273759 0.250037 
+-0.286184 0.233282 
+-0.297852 0.215904 
+-0.308722 0.197942 
+-0.318756 0.179439 
+-0.327915 0.16044 
+-0.336166 0.140993 
+-0.343477 0.121149 
+-0.349819 0.100961 
+-0.355168 0.0804858 
+-0.359502 0.0597792 
+-0.362803 0.0389003 
+-0.365059 0.0179089 
+-0.36626 -0.00313456 
+-0.366402 -0.0241691 
+-0.365482 -0.0451341 
+-0.363506 -0.065969 
+-0.360482 -0.0866144 
+-0.356421 -0.107012 
+-0.351341 -0.127105 
+-0.345261 -0.146839 
+-0.338205 -0.166161 
+-0.330202 -0.185021 
+-0.321281 -0.203372 
+-0.311477 -0.221168 
+-0.300826 -0.238369 
+-0.289367 -0.254936 
+-0.27714 -0.270835 
+-0.264187 -0.286032 
+-0.250553 -0.300501 
+-0.236282 -0.314215 
+-0.221419 -0.327154 
+-0.206011 -0.339298 
+-0.190105 -0.350631 
+-0.173745 -0.361141 
+-0.156979 -0.370819 
+-0.139853 -0.379657 
+-0.12241 -0.38765 
+-0.104697 -0.394798 
+-0.0867554 -0.401099 
+-0.0686287 -0.406557 
+-0.050358 -0.411175 
+-0.0319837 -0.414961 
+-0.0135447 -0.417921 
+0.00492123 -0.420066 
+0.0233777 -0.421405 
+0.0417897 -0.421952 
+0.0601235 -0.42172 
+0.0783467 -0.420722 
+0.0964285 -0.418974 
+0.114339 -0.416492 
+0.13205 -0.413293 
+0.149535 -0.409394 
+0.166767 -0.404813 
+0.183723 -0.399569 
+0.200379 -0.39368 
+0.216712 -0.387166 
+0.232703 -0.380046 
+0.248331 -0.37234 
+0.263577 -0.364068 
+0.278423 -0.355249 
+0.292854 -0.345906 
+0.306852 -0.336057 
+0.320404 -0.325723 
+0.333494 -0.314925 
+0.346111 -0.303683 
+0.358241 -0.292017 
+0.369872 -0.27995 
+0.380995 -0.267499 
+0.391599 -0.254688 
+0.401674 -0.241534 
+0.411212 -0.22806 
+0.420205 -0.214286 
+0.428645 -0.200231 
+0.436524 -0.185916 
+0.443838 -0.171361 
+0.450579 -0.156586 
+0.456743 -0.141611 
+0.462326 -0.126457 
+0.467321 -0.111143 
+0.471727 -0.0956893 
+0.475539 -0.0801155 
+0.478755 -0.0644415 
+0.481373 -0.0486873 
+0.48339 -0.0328724 
+0.484805 -0.0170168 
+0.485617 -0.0011401 
+0.485825 0.0147379 
+0.48543 0.0305975 
+0.484432 0.0464189 
+0.48283 0.0621823 
+0.480627 0.0778681 
+0.477825 0.0934563 
+0.474424 0.108927 
+0.470428 0.124261 
+0.46584 0.139438 
+0.460662 0.154437 
+0.4549 0.16924 
+0.448557 0.183825 
+0.441638 0.198173 
+0.434149 0.212264 
+0.426095 0.226077 
+0.417484 0.239592 
+0.408322 0.25279 
+0.398618 0.265648 
+0.388378 0.278148 
+0.377613 0.290268 
+0.366332 0.301988 
+0.354546 0.313288 
+0.342264 0.324146 
+0.3295 0.334544 
+0.316266 0.344459 
+0.302576 0.353871 
+0.288442 0.362761 
+0.273882 0.371108 
+0.258911 0.378891 
+0.243545 0.386091 
+0.227804 0.392688 
+0.211705 0.398662 
+0.19527 0.403994 
+0.17852 0.408665 
+0.161477 0.412657 
+0.144164 0.415951 
+0.126607 0.418531 
+0.108832 0.420379 
+0.0908661 0.421478 
+0.0727378 0.421815 
+0.0544775 0.421374 
+0.0361165 0.420142 
+0.0176875 0.418106 
+-0.000775394 0.415257 
+-0.0192366 0.411583 
+-0.0376594 0.407077 
+-0.0560056 0.401733 
+-0.074236 0.395546 
+-0.0923097 0.388513 
+-0.110185 0.380633 
+-0.12782 0.371909 
+-0.145169 0.362345 
+-0.162189 0.351946 
+-0.178834 0.340723 
+-0.195058 0.328688 
+-0.210816 0.315855 
+-0.22606 0.302244 
+-0.240745 0.287875 
+-0.254824 0.272774 
+-0.268253 0.256968 
+-0.280986 0.240489 
+-0.29298 0.223371 
+-0.304194 0.205651 
+-0.314587 0.187373 
+-0.324122 0.168578 
+-0.332762 0.149315 
+-0.340475 0.129632 
+-0.347232 0.109584 
+-0.353005 0.089223 
+-0.357772 0.0686067 
+-0.361513 0.047793 
+-0.364214 0.0268412 
+-0.365864 0.00581159 
+-0.366455 -0.0152351 
+-0.365985 -0.0362379 
+-0.364456 -0.0571362 
+-0.361875 -0.0778702 
+-0.358251 -0.098381 
+-0.3536 -0.118611 
+-0.347941 -0.138505 
+-0.341295 -0.158009 
+-0.333689 -0.177072 
+-0.325152 -0.195645 
+-0.315718 -0.213682 
+-0.30542 -0.231141 
+-0.294297 -0.247983 
+-0.282389 -0.264169 
+-0.269738 -0.279668 
+-0.256385 -0.294449 
+-0.242377 -0.308487 
+-0.227758 -0.321757 
+-0.212574 -0.33424 
+-0.196872 -0.345918 
+-0.180697 -0.356778 
+-0.164097 -0.36681 
+-0.147116 -0.376004 
+-0.1298 -0.384355 
+-0.112195 -0.39186 
+-0.0943436 -0.398519 
+-0.076289 -0.404333 
+-0.0580732 -0.409306 
+-0.0397369 -0.413443 
+-0.0213196 -0.416751 
+-0.00285969 -0.419239 
+0.015606 -0.420917 
+0.0340417 -0.421797 
+0.0524132 -0.421892 
+0.0706876 -0.421216 
+0.0888334 -0.419782 
+0.10682 -0.417608 
+0.124619 -0.41471 
+0.142203 -0.411104 
+0.159546 -0.406808 
+0.176621 -0.401841 
+0.193406 -0.396222 
+0.209879 -0.389969 
+0.226017 -0.383102 
+0.2418 -0.37564 
+0.257209 -0.367604 
+0.272227 -0.359014 
+0.286834 -0.349889 
+0.301017 -0.340251 
+0.314758 -0.330119 
+0.328045 -0.319514 
+0.340862 -0.308456 
+0.353198 -0.296967 
+0.365041 -0.285066 
+0.37638 -0.272775 
+0.387203 -0.260113 
+0.397502 -0.247101 
+0.407267 -0.23376 
+0.41649 -0.22011 
+0.425163 -0.20617 
+0.433279 -0.191962 
+0.440831 -0.177506 
+0.447814 -0.162822 
+0.454222 -0.147929 
+0.460049 -0.132848 
+0.465292 -0.117599 
+0.469946 -0.102202 
+0.474008 -0.0866762 
+0.477475 -0.0710421 
+0.480344 -0.0553193 
+0.482614 -0.0395277 
+0.484282 -0.0236869 
+0.485348 -0.0078167 
+0.48581 0.00806309 
+0.485669 0.0239328 
+0.484923 0.0397726 
+0.483575 0.0555629 
+0.481625 0.0712837 
+0.479074 0.0869154 
+0.475924 0.102438 
+0.472178 0.117832 
+0.467838 0.133077 
+0.462908 0.148154 
+0.457391 0.163042 
+0.451291 0.177721 
+0.444613 0.192172 
+0.437363 0.206373 
+0.429546 0.220306 
+0.421168 0.233949 
+0.412237 0.247283 
+0.402759 0.260287 
+0.392743 0.27294 
+0.382198 0.285222 
+0.371133 0.297114 
+0.359557 0.308593 
+0.347482 0.31964 
+0.334919 0.330234 
+0.321881 0.340355 
+0.308381 0.349981 
+0.294432 0.359094 
+0.280049 0.367672 
+0.265248 0.375695 
+0.250046 0.383143 
+0.23446 0.389996 
+0.218509 0.396235 
+0.202213 0.40184 
+0.185593 0.406791 
+0.16867 0.411072 
+0.151468 0.414662 
+0.134011 0.417545 
+0.116324 0.419703 
+0.098435 0.421119 
+0.0803715 0.421779 
+0.0621632 0.421668 
+0.0438408 0.42077 
+0.0254366 0.419075 
+0.006984 0.41657 
+-0.011482 0.413245 
+-0.0299252 0.409091 
+-0.048308 0.404101 
+-0.0665915 0.39827 
+-0.0847358 0.391594 
+-0.102699 0.384071 
+-0.12044 0.375703 
+-0.137914 0.366493 
+-0.155078 0.356446 
+-0.171886 0.34557 
+-0.188293 0.333876 
+-0.204252 0.321379 
+-0.219718 0.308094 
+-0.234643 0.294043 
+-0.248983 0.279249 
+-0.262691 0.263738 
+-0.275722 0.24754 
+-0.288033 0.230688 
+-0.29958 0.213219 
+-0.310324 0.195173 
+-0.320225 0.176592 
+-0.329247 0.157522 
+-0.337356 0.138012 
+-0.344519 0.118113 
+-0.350711 0.097879 
+-0.355905 0.0773652 
+-0.360082 0.0566292 
+-0.363225 0.0357299 
+-0.36532 0.0147272 
+-0.366359 -0.00631829 
+-0.366338 -0.0273457 
+-0.365257 -0.0482944 
+-0.36312 -0.069104 
+-0.359937 -0.0897152 
+-0.355719 -0.11007 
+-0.350484 -0.130112 
+-0.344253 -0.149787 
+-0.337051 -0.169041 
+-0.328905 -0.187827 
+-0.319847 -0.206096 
+-0.309911 -0.223805 
+-0.299133 -0.240912 
+-0.287553 -0.257379 
+-0.275212 -0.273173 
+-0.262152 -0.288262 
+-0.248416 -0.302617 
+-0.234051 -0.316215 
+-0.219101 -0.329034 
+-0.203613 -0.341055 
+-0.187633 -0.352263 
+-0.171207 -0.362647 
+-0.154382 -0.372197 
+-0.137202 -0.380906 
+-0.119714 -0.38877 
+-0.101962 -0.395788 
+-0.0839877 -0.40196 
+-0.0658348 -0.407289 
+-0.0475442 -0.411779 
+-0.0291561 -0.415438 
+-0.0107091 -0.418272 
+0.0077591 -0.420292 
+0.0262124 -0.42151 
+0.0446159 -0.421936 
+0.0629361 -0.421584 
+0.0811408 -0.42047 
+0.0991994 -0.418608 
+0.117082 -0.416014 
+0.134761 -0.412705 
+0.15221 -0.4087 
+0.169402 -0.404015 
+0.186314 -0.39867 
+0.202923 -0.392682 
+0.219206 -0.386073 
+0.235143 -0.378861 
+0.250713 -0.371065 
+0.2659 -0.362707 
+0.280684 -0.353805 
+0.295049 -0.344382 
+0.30898 -0.334456 
+0.322461 -0.324048 
+0.33548 -0.31318 
+0.348022 -0.30187 
+0.360076 -0.290141 
+0.371629 -0.278012 
+0.382673 -0.265504 
+0.393195 -0.252638 
+0.403188 -0.239433 
+0.412642 -0.22591 
+0.421549 -0.21209 
+0.429902 -0.197993 
+0.437694 -0.18364 
+0.444919 -0.169049 
+0.451571 -0.154241 
+0.457645 -0.139237 
+0.463136 -0.124057 
+0.46804 -0.10872 
+0.472353 -0.0932457 
+0.476072 -0.0776549 
+0.479195 -0.061967 
+0.481719 -0.0462019 
+0.483641 -0.0303793 
+0.484962 -0.0145191 
+0.48568 0.00135918 
+0.485794 0.0172356 
+0.485304 0.0330905 
+0.484211 0.0489042 
+0.482515 0.0646568 
+0.480218 0.0803286 
+0.477321 0.0958998 
+0.473827 0.11135 
+0.469737 0.126661 
+0.465056 0.141811 
+0.459786 0.156781 
+0.453932 0.171551 
+0.447498 0.1861 
+0.440489 0.200409 
+0.432911 0.214458 
+0.424769 0.228226 
+0.416071 0.241692 
+0.406823 0.254838 
+0.397033 0.267641 
+0.38671 0.280083 
+0.375863 0.292141 
+0.364501 0.303797 
+0.352636 0.315029 
+0.340277 0.325816 
+0.327438 0.336139 
+0.314131 0.345976 
+0.300369 0.355308 
+0.286167 0.364114 
+0.271541 0.372373 
+0.256506 0.380066 
+0.241079 0.387172 
+0.22528 0.393672 
+0.209127 0.399547 
+0.19264 0.404776 
+0.175842 0.409341 
+0.158754 0.413224 
+0.141401 0.416407 
+0.123807 0.418873 
+0.105999 0.420604 
+0.0880055 0.421584 
+0.069854 0.421799 
+0.0515752 0.421234 
+0.0332008 0.419876 
+0.0147638 0.417713 
+-0.0037015 0.414735 
+-0.0221595 0.41093 
+-0.0405731 0.406293 
+-0.0589039 0.400816 
+-0.0771125 0.394496 
+-0.095158 0.38733 
+-0.112999 0.379317 
+-0.130591 0.370461 
+-0.147892 0.360764 
+-0.164856 0.350236 
+-0.181438 0.338884 
+-0.197592 0.326723 
+-0.213271 0.313767 
+-0.22843 0.300035 
+-0.243023 0.28555 
+-0.257003 0.270337 
+-0.270324 0.254423 
+-0.282944 0.237842 
+-0.294818 0.220627 
+-0.305905 0.202818 
+-0.316166 0.184457 
+-0.325562 0.165586 
+-0.334059 0.146255 
+-0.341624 0.126513 
+-0.348228 0.106413 
+-0.353845 0.0860095 
+-0.358452 0.0653597 
+-0.362032 0.0445218 
+-0.364569 0.0235553 
+-0.366053 0.00252043 
+-0.366478 -0.0185219 
+-0.365843 -0.0395109 
+-0.364149 -0.0603861 
+-0.361405 -0.0810876 
+-0.35762 -0.101557 
+-0.352811 -0.121737 
+-0.346997 -0.141572 
+-0.3402 -0.161009 
+-0.332448 -0.179998 
+-0.32377 -0.198489 
+-0.314199 -0.216438 
+-0.303772 -0.233802 
+-0.292525 -0.250543 
+-0.280499 -0.266624 
+-0.267737 -0.282012 
+-0.254281 -0.296679 
+-0.240176 -0.310598 
+-0.225467 -0.323747 
+-0.2102 -0.336105 
+-0.194422 -0.347657 
+-0.178179 -0.358389 
+-0.161517 -0.368291 
+-0.144483 -0.377354 
+-0.12712 -0.385574 
+-0.109474 -0.392948 
+-0.091589 -0.399476 
+-0.0735072 -0.40516 
+-0.0552705 -0.410002 
+-0.0369194 -0.41401 
+-0.0184933 -0.417191 
+-3.02915e-05 -0.419553 
+0.0184329 -0.421107 
+0.0368608 -0.421865 
+0.0552195 -0.421839 
+0.0734761 -0.421045 
+0.0915994 -0.419496 
+0.109559 -0.417208 
+0.127327 -0.414199 
+0.144876 -0.410486 
+0.162179 -0.406085 
+0.179211 -0.401016 
+0.19595 -0.395297 
+0.212373 -0.388948 
+0.228457 -0.381988 
+0.244185 -0.374436 
+0.259535 -0.366313 
+0.274491 -0.357638 
+0.289034 -0.348432 
+0.30315 -0.338716 
+0.316823 -0.328509 
+0.330038 -0.317833 
+0.342783 -0.306707 
+0.355044 -0.295152 
+0.366811 -0.28319 
+0.378071 -0.270839 
+0.388814 -0.258121 
+0.399032 -0.245057 
+0.408714 -0.231666 
+0.417853 -0.217969 
+0.426441 -0.203987 
+0.434471 -0.189739 
+0.441936 -0.175245 
+0.448831 -0.160527 
+0.45515 -0.145604 
+0.460887 -0.130495 
+0.46604 -0.115221 
+0.470603 -0.0998025 
+0.474574 -0.0842585 
+0.477949 -0.068609 
+0.480726 -0.052874 
+0.482903 -0.0370731 
+0.484479 -0.0212262 
+0.485451 -0.00535294 
+0.48582 0.0105268 
+0.485586 0.0263934 
+0.484748 0.0422271 
+0.483307 0.0580081 
+0.481264 0.0737166 
+0.47862 0.0893329 
+0.475378 0.104837 
+0.47154 0.120209 
+0.467109 0.13543 
+0.462088 0.150479 
+0.456481 0.165336 
+0.450291 0.179981 
+0.443525 0.194394 
+0.436187 0.208555 
+0.428283 0.222444 
+0.419819 0.236041 
+0.410803 0.249325 
+0.401241 0.262275 
+0.391143 0.274872 
+0.380517 0.287095 
+0.369372 0.298924 
+0.357718 0.310337 
+0.345567 0.321315 
+0.33293 0.331837 
+0.31982 0.341882 
+0.306249 0.35143 
+0.292232 0.360461 
+0.277783 0.368954 
+0.262919 0.376889 
+0.247657 0.384246 
+0.232013 0.391004 
+0.216008 0.397146 
+0.19966 0.40265 
+0.182991 0.407499 
+0.166023 0.411673 
+0.14878 0.415154 
+0.131285 0.417925 
+0.113566 0.419969 
+0.0956474 0.421269 
+0.0775594 0.421809 
+0.0593312 0.421576 
+0.0409938 0.420555 
+0.0225796 0.418734 
+0.00412238 0.416102 
+-0.0143427 0.412648 
+-0.0327793 0.408364 
+-0.0511496 0.403243 
+-0.0694145 0.39728 
+-0.0875337 0.390472 
+-0.105466 0.382817 
+-0.123168 0.374317 
+-0.140598 0.364975 
+-0.157709 0.354798 
+-0.174458 0.343793 
+-0.190799 0.331972 
+-0.206685 0.31935 
+-0.22207 0.305944 
+-0.236908 0.291774 
+-0.251152 0.276865 
+-0.264758 0.261244 
+-0.27768 0.24494 
+-0.289874 0.227989 
+-0.3013 0.210426 
+-0.311915 0.192292 
+-0.321681 0.17363 
+-0.330562 0.154487 
+-0.338525 0.134912 
+-0.345539 0.114956 
+-0.351576 0.0946729 
+-0.356613 0.0741194 
+-0.360628 0.0533529 
+-0.363608 0.0324324 
+-0.365538 0.0114181 
+-0.366411 -0.00962955 
+-0.366223 -0.0306495 
+-0.364976 -0.051581 
+-0.362674 -0.0723642 
+-0.359327 -0.0929396 
+-0.354948 -0.11325 
+-0.349556 -0.133238 
+-0.34317 -0.15285 
+-0.335818 -0.172035 
+-0.327526 -0.190743 
+-0.318328 -0.208927 
+-0.308257 -0.226544 
+-0.297351 -0.243553 
+-0.285648 -0.259917 
+-0.273191 -0.275602 
+-0.260022 -0.290577 
+-0.246184 -0.304815 
+-0.231724 -0.318291 
+-0.216687 -0.330985 
+-0.201118 -0.34288 
+-0.185065 -0.353959 
+-0.168574 -0.364212 
+-0.151691 -0.37363 
+-0.13446 -0.382206 
+-0.116928 -0.389937 
+-0.0991384 -0.396822 
+-0.0811341 -0.402861 
+-0.0629575 -0.408058 
+-0.0446496 -0.412417 
+-0.0262503 -0.415945 
+-0.00779822 -0.418651 
+0.0106693 -0.420544 
+0.0291164 -0.421636 
+0.0475083 -0.421939 
+0.0658117 -0.421466 
+0.0839948 -0.420234 
+0.102027 -0.418255 
+0.119879 -0.415548 
+0.137523 -0.412129 
+0.154932 -0.408016 
+0.172082 -0.403226 
+0.188947 -0.397779 
+0.205505 -0.391693 
+0.221734 -0.384988 
+0.237614 -0.377683 
+0.253126 -0.369798 
+0.268249 -0.361353 
+0.282968 -0.352369 
+0.297266 -0.342865 
+0.311127 -0.332862 
+0.324536 -0.322381 
+0.33748 -0.311442 
+0.349947 -0.300066 
+0.361922 -0.288273 
+0.373397 -0.276083 
+0.384359 -0.263518 
+0.394799 -0.250597 
+0.404707 -0.237341 
+0.414076 -0.223771 
+0.422896 -0.209906 
+0.431162 -0.195768 
+0.438866 -0.181375 
+0.446001 -0.166749 
+0.452563 -0.15191 
+0.458545 -0.136877 
+0.463945 -0.12167 
+0.468756 -0.10631 
+0.472977 -0.0908167 
+0.476603 -0.0752093 
+0.479632 -0.0595079 
+0.482062 -0.0437324 
+0.483891 -0.0279025 
+0.485117 -0.0120379 
+0.48574 0.00384146 
+0.48576 0.019716 
+0.485176 0.0355659 
+0.483989 0.0513715 
+0.482199 0.067113 
+0.479808 0.0827706 
+0.476818 0.0983245 
+0.47323 0.113755 
+0.469049 0.129042 
+0.464275 0.144165 
+0.458914 0.159105 
+0.452969 0.173842 
+0.446445 0.188356 
+0.439347 0.202626 
+0.431681 0.216632 
+0.423452 0.230354 
+0.414668 0.243773 
+0.405335 0.256866 
+0.395462 0.269615 
+0.385057 0.281998 
+0.374129 0.293995 
+0.362689 0.305586 
+0.350746 0.31675 
+0.338312 0.327467 
+0.3254 0.337715 
+0.312021 0.347476 
+0.29819 0.356727 
+0.283922 0.365449 
+0.269231 0.373622 
+0.254134 0.381225 
+0.238649 0.388238 
+0.222794 0.394642 
+0.206588 0.400418 
+0.190052 0.405545 
+0.173208 0.410006 
+0.156078 0.413782 
+0.138687 0.416855 
+0.121059 0.419207 
+0.103221 0.420823 
+0.0852016 0.421686 
+0.0670291 0.421781 
+0.0487342 0.421094 
+0.0303488 0.419612 
+0.0119059 0.417324 
+-0.00655982 0.414218 
+-0.0250125 0.410285 
+-0.043415 0.405519 
+-0.0617287 0.399912 
+-0.0799139 0.393461 
+-0.0979296 0.386164 
+-0.115734 0.378021 
+-0.133283 0.369035 
+-0.150534 0.35921 
+-0.167441 0.348553 
+-0.183959 0.337076 
+-0.200042 0.324791 
+-0.215644 0.311714 
+-0.230718 0.297865 
+-0.245218 0.283266 
+-0.259099 0.267943 
+-0.272314 0.251925 
+-0.284821 0.235243 
+-0.296576 0.217935 
+-0.307538 0.200038 
+-0.317667 0.181595 
+-0.326927 0.16265 
+-0.335281 0.143252 
+-0.3427 0.123451 
+-0.349153 0.1033 
+-0.354615 0.0828551 
+-0.359064 0.0621722 
+-0.362484 0.0413101 
+-0.364858 0.0203286 
+-0.366179 -0.000711799 
+-0.36644 -0.0217505 
+-0.365641 -0.0427264 
+-0.363784 -0.0635793 
+-0.360878 -0.0842494 
+-0.356934 -0.104679 
+-0.351968 -0.124809 
+-0.345999 -0.144587 
+-0.339053 -0.163959 
+-0.331155 -0.182875 
+-0.322336 -0.201286 
+-0.31263 -0.219148 
+-0.302072 -0.236419 
+-0.290701 -0.253061 
+-0.278558 -0.269037 
+-0.265685 -0.284316 
+-0.252124 -0.29887 
+-0.237921 -0.312671 
+-0.223122 -0.325699 
+-0.207773 -0.337934 
+-0.191919 -0.34936 
+-0.175607 -0.359964 
+-0.158883 -0.369737 
+-0.141793 -0.37867 
+-0.124383 -0.386759 
+-0.106696 -0.394002 
+-0.0887769 -0.400399 
+-0.0706674 -0.405952 
+-0.0524095 -0.410664 
+-0.0340435 -0.414543 
+-0.0156084 -0.417596 
+0.00285766 -0.419831 
+0.0213183 -0.421261 
+0.0397382 -0.421896 
+0.0580837 -0.42175 
+0.076322 -0.420837 
+0.0944223 -0.419172 
+0.112354 -0.416771 
+0.13009 -0.413651 
+0.147602 -0.409829 
+0.164865 -0.405323 
+0.181854 -0.400151 
+0.198545 -0.394333 
+0.214916 -0.387887 
+0.230947 -0.380833 
+0.246616 -0.373191 
+0.261906 -0.36498 
+0.276799 -0.356221 
+0.291277 -0.346934 
diff --git a/gravitation/XBYB.dat b/gravitation/XBYB.dat
new file mode 100644
index 0000000..fa0d367
--- /dev/null
+++ b/gravitation/XBYB.dat
@@ -0,0 +1,1000 @@
+-1.70038 -0.0126101 
+-1.69932 -0.0681722 
+-1.69615 -0.12365 
+-1.69087 -0.178974 
+-1.68349 -0.234076 
+-1.674 -0.288885 
+-1.66242 -0.343333 
+-1.64876 -0.397351 
+-1.63302 -0.450868 
+-1.61521 -0.503815 
+-1.59536 -0.556122 
+-1.57347 -0.607719 
+-1.54956 -0.658536 
+-1.52365 -0.708502 
+-1.49577 -0.757547 
+-1.46593 -0.8056 
+-1.43416 -0.85259 
+-1.40048 -0.898445 
+-1.36493 -0.943095 
+-1.32753 -0.986467 
+-1.28832 -1.02849 
+-1.24733 -1.06909 
+-1.20461 -1.1082 
+-1.16019 -1.14575 
+-1.11412 -1.18166 
+-1.06644 -1.21586 
+-1.01721 -1.24828 
+-0.966472 -1.27885 
+-0.914287 -1.3075 
+-0.860713 -1.33416 
+-0.805814 -1.35875 
+-0.749654 -1.38122 
+-0.692306 -1.40148 
+-0.633842 -1.41948 
+-0.57434 -1.43515 
+-0.513883 -1.44842 
+-0.452556 -1.45923 
+-0.390452 -1.46752 
+-0.327665 -1.47323 
+-0.264294 -1.47631 
+-0.200445 -1.4767 
+-0.136226 -1.47436 
+-0.0717511 -1.46923 
+-0.00713958 -1.46129 
+0.0574854 -1.45048 
+0.121996 -1.43678 
+0.186259 -1.42016 
+0.250138 -1.4006 
+0.31349 -1.37808 
+0.376171 -1.35261 
+0.438031 -1.32417 
+0.498918 -1.29278 
+0.558675 -1.25845 
+0.617145 -1.22122 
+0.674167 -1.18111 
+0.729579 -1.13817 
+0.78322 -1.09246 
+0.834928 -1.04404 
+0.884541 -0.992999 
+0.9319 -0.93942 
+0.976849 -0.883406 
+1.01924 -0.82507 
+1.05891 -0.764535 
+1.09574 -0.701938 
+1.12958 -0.637426 
+1.16031 -0.571156 
+1.18781 -0.503296 
+1.21199 -0.434022 
+1.23273 -0.36352 
+1.24996 -0.291983 
+1.26361 -0.21961 
+1.27363 -0.146606 
+1.27998 -0.0731803 
+1.28262 0.000456698 
+1.28155 0.0740916 
+1.27678 0.147512 
+1.26831 0.220505 
+1.25619 0.292864 
+1.24047 0.364383 
+1.22121 0.434862 
+1.19848 0.50411 
+1.17238 0.571941 
+1.143 0.638178 
+1.11047 0.702655 
+1.07489 0.765212 
+1.0364 0.825705 
+0.995147 0.883997 
+0.951265 0.939964 
+0.904908 0.993494 
+0.85623 1.04448 
+0.80539 1.09285 
+0.752548 1.1385 
+0.697865 1.18139 
+0.641504 1.22144 
+0.583627 1.25862 
+0.524394 1.29288 
+0.463966 1.32421 
+0.402498 1.35259 
+0.340144 1.37801 
+0.277056 1.40046 
+0.213381 1.41996 
+0.149262 1.43652 
+0.0848384 1.45016 
+0.0202442 1.46091 
+-0.0443902 1.4688 
+-0.108939 1.47387 
+-0.173283 1.47616 
+-0.237304 1.47571 
+-0.300892 1.47257 
+-0.36394 1.46681 
+-0.426348 1.45846 
+-0.488016 1.4476 
+-0.548854 1.43428 
+-0.608772 1.41857 
+-0.667687 1.40052 
+-0.725518 1.38021 
+-0.782191 1.3577 
+-0.837633 1.33306 
+-0.891778 1.30636 
+-0.944559 1.27767 
+-0.995917 1.24706 
+-1.04579 1.2146 
+-1.09414 1.18036 
+-1.1409 1.14442 
+-1.18602 1.10684 
+-1.22947 1.0677 
+-1.27119 1.02706 
+-1.31116 0.98501 
+-1.34933 0.94161 
+-1.38567 0.896934 
+-1.42014 0.851055 
+-1.45272 0.804042 
+-1.48339 0.755968 
+-1.5121 0.706903 
+-1.53885 0.656919 
+-1.5636 0.606085 
+-1.58635 0.554472 
+-1.60707 0.502152 
+-1.62574 0.449192 
+-1.64236 0.395665 
+-1.6569 0.341638 
+-1.66937 0.287182 
+-1.67974 0.232366 
+-1.68801 0.17726 
+-1.69418 0.121933 
+-1.69825 0.0664533 
+-1.7002 0.0108909 
+-1.70004 -0.0446854 
+-1.69776 -0.100206 
+-1.69337 -0.155603 
+-1.68688 -0.210806 
+-1.67828 -0.265747 
+-1.66759 -0.320355 
+-1.6548 -0.374563 
+-1.63994 -0.428299 
+-1.62301 -0.481495 
+-1.60402 -0.53408 
+-1.58299 -0.585985 
+-1.55993 -0.637139 
+-1.53487 -0.687473 
+-1.50782 -0.736915 
+-1.4788 -0.785396 
+-1.44785 -0.832843 
+-1.41497 -0.879186 
+-1.38021 -0.924353 
+-1.34359 -0.968273 
+-1.30514 -1.01088 
+-1.2649 -1.05209 
+-1.22291 -1.09184 
+-1.1792 -1.13005 
+-1.13382 -1.16666 
+-1.08682 -1.20159 
+-1.03824 -1.23477 
+-0.988131 -1.26614 
+-0.936551 -1.29561 
+-0.883557 -1.32311 
+-0.82921 -1.34859 
+-0.773574 -1.37196 
+-0.716719 -1.39316 
+-0.658717 -1.41213 
+-0.599643 -1.42879 
+-0.539579 -1.44307 
+-0.478608 -1.45493 
+-0.41682 -1.46429 
+-0.354309 -1.4711 
+-0.291171 -1.4753 
+-0.227509 -1.47683 
+-0.163431 -1.47565 
+-0.0990491 -1.4717 
+-0.034479 -1.46495 
+0.0301574 -1.45536 
+0.094734 -1.44288 
+0.15912 -1.42749 
+0.22318 -1.40918 
+0.286774 -1.38791 
+0.349759 -1.36368 
+0.411987 -1.33649 
+0.473305 -1.30634 
+0.533561 -1.27325 
+0.592596 -1.23724 
+0.650251 -1.19833 
+0.706364 -1.15658 
+0.760775 -1.11203 
+0.81332 -1.06474 
+0.863838 -1.0148 
+0.912169 -0.962272 
+0.958155 -0.907268 
+1.00164 -0.849893 
+1.04248 -0.790266 
+1.08053 -0.728518 
+1.11564 -0.664791 
+1.1477 -0.599238 
+1.17658 -0.532023 
+1.20217 -0.46332 
+1.22437 -0.393309 
+1.24309 -0.32218 
+1.25826 -0.250132 
+1.26981 -0.177365 
+1.27771 -0.104088 
+1.28191 -0.0305111 
+1.28241 0.0431533 
+1.27919 0.116692 
+1.27227 0.189893 
+1.26169 0.262546 
+1.24747 0.334445 
+1.22969 0.405387 
+1.20841 0.475178 
+1.18372 0.543628 
+1.15571 0.610558 
+1.12448 0.675795 
+1.09017 0.739179 
+1.05289 0.800558 
+1.01278 0.859791 
+0.969989 0.916751 
+0.924655 0.971318 
+0.876935 1.02339 
+0.826986 1.07287 
+0.774967 1.11967 
+0.72104 1.16372 
+0.665366 1.20497 
+0.608108 1.24336 
+0.549428 1.27886 
+0.489485 1.31143 
+0.428437 1.34105 
+0.366439 1.36771 
+0.303644 1.39141 
+0.2402 1.41215 
+0.176253 1.42994 
+0.111943 1.44481 
+0.0474065 1.45677 
+-0.0172243 1.46586 
+-0.081822 1.47211 
+-0.146264 1.47556 
+-0.210432 1.47626 
+-0.274214 1.47425 
+-0.3375 1.46958 
+-0.400187 1.46231 
+-0.462176 1.4525 
+-0.523372 1.44021 
+-0.583685 1.4255 
+-0.64303 1.40842 
+-0.701325 1.38906 
+-0.758493 1.36746 
+-0.81446 1.34371 
+-0.869157 1.31787 
+-0.922519 1.29001 
+-0.974482 1.2602 
+-1.02499 1.22851 
+-1.07398 1.19501 
+-1.12141 1.15978 
+-1.16723 1.12288 
+-1.21139 1.08439 
+-1.25384 1.04437 
+-1.29455 1.00291 
+-1.33348 0.960068 
+-1.3706 0.91592 
+-1.40586 0.870539 
+-1.43924 0.823995 
+-1.47072 0.776359 
+-1.50026 0.727703 
+-1.52783 0.678097 
+-1.55343 0.627612 
+-1.57703 0.576319 
+-1.5986 0.524288 
+-1.61814 0.471589 
+-1.63562 0.418292 
+-1.65104 0.364467 
+-1.66439 0.310183 
+-1.67564 0.255511 
+-1.6848 0.200518 
+-1.69186 0.145276 
+-1.69682 0.0898515 
+-1.69966 0.0343155 
+-1.70039 -0.0212635 
+-1.69901 -0.0768164 
+-1.69551 -0.132274 
+-1.68991 -0.187567 
+-1.6822 -0.242627 
+-1.67239 -0.297384 
+-1.66048 -0.351769 
+-1.6465 -0.405713 
+-1.63044 -0.459145 
+-1.61232 -0.511996 
+-1.59215 -0.564197 
+-1.56995 -0.615676 
+-1.54573 -0.666365 
+-1.51952 -0.716192 
+-1.49133 -0.765087 
+-1.46119 -0.812978 
+-1.42913 -0.859796 
+-1.39516 -0.905468 
+-1.35932 -0.949924 
+-1.32165 -0.993091 
+-1.28216 -1.0349 
+-1.24091 -1.07527 
+-1.19793 -1.11415 
+-1.15325 -1.15144 
+-1.10693 -1.18709 
+-1.05901 -1.22102 
+-1.00955 -1.25316 
+-0.958587 -1.28344 
+-0.906187 -1.31178 
+-0.852408 -1.33813 
+-0.797313 -1.3624 
+-0.740969 -1.38453 
+-0.683446 -1.40444 
+-0.62482 -1.42209 
+-0.565169 -1.43739 
+-0.504575 -1.45028 
+-0.443126 -1.46071 
+-0.380912 -1.4686 
+-0.318031 -1.47391 
+-0.254582 -1.47658 
+-0.190671 -1.47656 
+-0.126408 -1.47379 
+-0.0619061 -1.46823 
+0.00271388 -1.45985 
+0.0673282 -1.4486 
+0.131808 -1.43445 
+0.19602 -1.41738 
+0.259826 -1.39736 
+0.323084 -1.37439 
+0.385648 -1.34846 
+0.447368 -1.31957 
+0.508091 -1.28772 
+0.567661 -1.25294 
+0.625919 -1.21526 
+0.682704 -1.17471 
+0.737856 -1.13134 
+0.791211 -1.08521 
+0.842607 -1.03638 
+0.891885 -0.984942 
+0.938884 -0.930979 
+0.98345 -0.874596 
+1.02543 -0.815909 
+1.06468 -0.755044 
+1.10105 -0.692139 
+1.13443 -0.627341 
+1.16467 -0.56081 
+1.19166 -0.492715 
+1.21531 -0.423235 
+1.23552 -0.352555 
+1.2522 -0.28087 
+1.2653 -0.208381 
+1.27475 -0.135292 
+1.28052 -0.0618138 
+1.28259 0.0118427 
+1.28095 0.085464 
+1.2756 0.158838 
+1.26656 0.231752 
+1.25388 0.303999 
+1.2376 0.375375 
+1.21779 0.445681 
+1.19453 0.514726 
+1.16791 0.582326 
+1.13803 0.648305 
+1.10501 0.712497 
+1.06897 0.774746 
+1.03004 0.834909 
+0.988363 0.89285 
+0.944082 0.948447 
+0.897349 1.00159 
+0.84832 1.05218 
+0.797154 1.10013 
+0.74401 1.14535 
+0.689052 1.1878 
+0.632441 1.22741 
+0.574338 1.26413 
+0.514906 1.29794 
+0.454302 1.32881 
+0.392683 1.35673 
+0.330203 1.38168 
+0.267012 1.40367 
+0.203256 1.42271 
+0.139079 1.43881 
+0.0746187 1.452 
+0.0100089 1.4623 
+-0.0546208 1.46974 
+-0.119146 1.47437 
+-0.183446 1.47622 
+-0.247407 1.47535 
+-0.310917 1.4718 
+-0.373871 1.46562 
+-0.436168 1.45688 
+-0.497711 1.44562 
+-0.558409 1.43192 
+-0.618174 1.41584 
+-0.676923 1.39743 
+-0.734576 1.37677 
+-0.791059 1.35392 
+-0.8463 1.32895 
+-0.900233 1.30193 
+-0.952793 1.27294 
+-1.00392 1.24203 
+-1.05356 1.20929 
+-1.10165 1.17478 
+-1.14816 1.13857 
+-1.19302 1.10074 
+-1.23619 1.06136 
+-1.27764 1.0205 
+-1.31733 0.978227 
+-1.35521 0.934622 
+-1.39126 0.889752 
+-1.42543 0.84369 
+-1.45771 0.796506 
+-1.48807 0.748271 
+-1.51648 0.699057 
+-1.54291 0.648934 
+-1.56735 0.597974 
+-1.58978 0.546246 
+-1.61017 0.49382 
+-1.62852 0.440767 
+-1.64481 0.387156 
+-1.65903 0.333058 
+-1.67116 0.278541 
+-1.68121 0.223675 
+-1.68915 0.16853 
+-1.69499 0.113174 
+-1.69872 0.0576773 
+-1.70034 0.00210826 
+-1.69984 -0.0534637 
+-1.69723 -0.10897 
+-1.69251 -0.16434 
+-1.68569 -0.219507 
+-1.67676 -0.2744 
+-1.66574 -0.328949 
+-1.65262 -0.383087 
+-1.63743 -0.436743 
+-1.62018 -0.489847 
+-1.60087 -0.542331 
+-1.57952 -0.594122 
+-1.55615 -0.645153 
+-1.53077 -0.695351 
+-1.50341 -0.744647 
+-1.47409 -0.79297 
+-1.44283 -0.840248 
+-1.40966 -0.886412 
+-1.3746 -0.931388 
+-1.33769 -0.975107 
+-1.29896 -1.0175 
+-1.25845 -1.05848 
+-1.21619 -1.098 
+-1.17222 -1.13597 
+-1.12658 -1.17232 
+-1.07933 -1.20698 
+-1.03051 -1.23988 
+-0.980171 -1.27095 
+-0.928368 -1.30012 
+-0.875161 -1.32732 
+-0.820611 -1.35247 
+-0.764783 -1.37551 
+-0.707747 -1.39636 
+-0.649576 -1.41497 
+-0.590345 -1.43127 
+-0.530138 -1.44518 
+-0.469037 -1.45665 
+-0.407134 -1.46562 
+-0.344522 -1.47203 
+-0.2813 -1.47582 
+-0.217571 -1.47693 
+-0.153443 -1.47533 
+-0.089028 -1.47095 
+-0.024444 -1.46376 
+0.040187 -1.45372 
+0.104738 -1.4408 
+0.169078 -1.42496 
+0.23307 -1.40619 
+0.296575 -1.38447 
+0.359448 -1.35979 
+0.42154 -1.33214 
+0.4827 -1.30154 
+0.542773 -1.268 
+0.601601 -1.23154 
+0.659025 -1.1922 
+0.714882 -1.15002 
+0.769012 -1.10504 
+0.821252 -1.05735 
+0.871441 -1.007 
+0.919418 -0.954095 
+0.965027 -0.898724 
+1.00811 -0.840999 
+1.04853 -0.781042 
+1.08614 -0.718985 
+1.12079 -0.654972 
+1.15236 -0.589158 
+1.18074 -0.521707 
+1.20582 -0.452795 
+1.22749 -0.382603 
+1.24567 -0.311324 
+1.26029 -0.239155 
+1.27129 -0.1663 
+1.27862 -0.0929653 
+1.28226 -0.0193629 
+1.28218 0.0542947 
+1.2784 0.127795 
+1.27092 0.200925 
+1.25978 0.273475 
+1.24502 0.345241 
+1.22669 0.41602 
+1.20489 0.485619 
+1.17968 0.55385 
+1.15117 0.620533 
+1.11946 0.685499 
+1.08469 0.748588 
+1.04697 0.80965 
+1.00644 0.868546 
+0.963242 0.92515 
+0.917531 0.979344 
+0.869457 1.03103 
+0.819178 1.0801 
+0.766853 1.12649 
+0.712644 1.17012 
+0.656714 1.21094 
+0.599224 1.24889 
+0.540335 1.28394 
+0.480208 1.31606 
+0.419 1.34523 
+0.356866 1.37144 
+0.293957 1.39469 
+0.230422 1.41498 
+0.166405 1.43232 
+0.102046 1.44674 
+0.0374819 1.45826 
+-0.0271569 1.46691 
+-0.0917434 1.47272 
+-0.156156 1.47575 
+-0.220276 1.47602 
+-0.283993 1.4736 
+-0.347198 1.46853 
+-0.409788 1.46087 
+-0.471665 1.45067 
+-0.532735 1.438 
+-0.592908 1.42292 
+-0.6521 1.40548 
+-0.71023 1.38577 
+-0.76722 1.36384 
+-0.822999 1.33976 
+-0.877497 1.3136 
+-0.930648 1.28543 
+-0.982393 1.25532 
+-1.03267 1.22335 
+-1.08143 1.18958 
+-1.12861 1.15408 
+-1.17418 1.11692 
+-1.21808 1.07819 
+-1.26026 1.03795 
+-1.3007 0.996262 
+-1.33935 0.953212 
+-1.37618 0.908868 
+-1.41116 0.863301 
+-1.44425 0.816581 
+-1.47542 0.768781 
+-1.50466 0.719972 
+-1.53193 0.670224 
+-1.55722 0.619608 
+-1.5805 0.568195 
+-1.60176 0.516055 
+-1.62098 0.463258 
+-1.63814 0.409874 
+-1.65324 0.355972 
+-1.66625 0.301623 
+-1.67718 0.246896 
+-1.68602 0.19186 
+-1.69275 0.136584 
+-1.69737 0.0811382 
+-1.69988 0.0255909 
+-1.70028 -0.0299885 
+-1.69856 -0.0855309 
+-1.69474 -0.140967 
+-1.6888 -0.196229 
+-1.68076 -0.251245 
+-1.67062 -0.305948 
+-1.65839 -0.360269 
+-1.64408 -0.414136 
+-1.6277 -0.467482 
+-1.60925 -0.520236 
+-1.58876 -0.572328 
+-1.56624 -0.623688 
+-1.54171 -0.674246 
+-1.51519 -0.723931 
+-1.48669 -0.772673 
+-1.45625 -0.8204 
+-1.42388 -0.867042 
+-1.38962 -0.912528 
+-1.35348 -0.956786 
+-1.31552 -0.999744 
+-1.27575 -1.04133 
+-1.23423 -1.08147 
+-1.19097 -1.1201 
+-1.14603 -1.15715 
+-1.09946 -1.19253 
+-1.05129 -1.22618 
+-1.00159 -1.25803 
+-0.950393 -1.28801 
+-0.89777 -1.31605 
+-0.843777 -1.34207 
+-0.788479 -1.36601 
+-0.731943 -1.38779 
+-0.67424 -1.40736 
+-0.615445 -1.42463 
+-0.555638 -1.43956 
+-0.494902 -1.45207 
+-0.433325 -1.4621 
+-0.370998 -1.46959 
+-0.308019 -1.47449 
+-0.244489 -1.47674 
+-0.180513 -1.47628 
+-0.116203 -1.47308 
+-0.0516734 -1.46708 
+0.0129552 -1.45824 
+0.0775581 -1.44654 
+0.142006 -1.43193 
+0.206164 -1.41439 
+0.269894 -1.39392 
+0.333053 -1.37048 
+0.395495 -1.34408 
+0.457069 -1.31472 
+0.517621 -1.28242 
+0.576995 -1.24718 
+0.635032 -1.20905 
+0.69157 -1.16805 
+0.746449 -1.12424 
+0.799507 -1.07768 
+0.85058 -1.02844 
+0.899509 -0.976596 
+0.946135 -0.922247 
+0.990304 -0.865497 
+1.03186 -0.806462 
+1.07067 -0.74527 
+1.10658 -0.68206 
+1.13947 -0.616982 
+1.16921 -0.550198 
+1.19568 -0.481878 
+1.2188 -0.4122 
+1.23846 -0.341355 
+1.25458 -0.269535 
+1.26711 -0.196943 
+1.27599 -0.123784 
+1.28118 -0.0502683 
+1.28267 0.0233918 
+1.28045 0.0969834 
+1.27452 0.170294 
+1.26492 0.243113 
+1.25167 0.315232 
+1.23484 0.38645 
+1.21449 0.456567 
+1.1907 0.525394 
+1.16357 0.592747 
+1.1332 0.658454 
+1.0997 0.72235 
+1.0632 0.78428 
+1.02384 0.844102 
+0.981748 0.901683 
+0.937079 0.956903 
+0.889982 1.00965 
+0.840614 1.05983 
+0.789133 1.10736 
+0.735701 1.15216 
+0.680478 1.19417 
+0.623628 1.23333 
+0.565311 1.2696 
+0.505689 1.30296 
+0.44492 1.33337 
+0.38316 1.36083 
+0.320561 1.38532 
+0.257275 1.40685 
+0.193447 1.42544 
+0.129218 1.44108 
+0.0647266 1.45382 
+0.000106021 1.46368 
+-0.0645152 1.47068 
+-0.129013 1.47488 
+-0.193268 1.47631 
+-0.257166 1.47501 
+-0.320598 1.47105 
+-0.383457 1.46448 
+-0.445645 1.45534 
+-0.507065 1.44371 
+-0.567625 1.42963 
+-0.627239 1.41318 
+-0.685825 1.39442 
+-0.743304 1.37342 
+-0.799601 1.35024 
+-0.854646 1.32495 
+-0.908373 1.29762 
+-0.960717 1.26832 
+-1.01162 1.23712 
+-1.06103 1.2041 
+-1.10888 1.16932 
+-1.15513 1.13286 
+-1.19974 1.09478 
+-1.24266 1.05517 
+-1.28384 1.01408 
+-1.32325 0.971602 
+-1.36085 0.927795 
+-1.39661 0.882735 
+-1.4305 0.836493 
+-1.46249 0.78914 
+-1.49254 0.740748 
+-1.52065 0.691388 
+-1.54678 0.641129 
+-1.57091 0.590044 
+-1.59302 0.538202 
+-1.61311 0.485673 
+-1.63114 0.432528 
+-1.64711 0.378836 
+-1.66101 0.324667 
+-1.67282 0.27009 
+-1.68254 0.215176 
+-1.69016 0.159992 
+-1.69567 0.104609 
+-1.69908 0.0490953 
+-1.70037 -0.00647962 
+-1.69955 -0.0620468 
+-1.69662 -0.117537 
+-1.69157 -0.172881 
+-1.68442 -0.228011 
+-1.67517 -0.282855 
+-1.66382 -0.337347 
+-1.65039 -0.391415 
+-1.63488 -0.44499 
+-1.61731 -0.498003 
+-1.59768 -0.550384 
+-1.57602 -0.602062 
+-1.55234 -0.652968 
+-1.52665 -0.703031 
+-1.49899 -0.752181 
+-1.46937 -0.800346 
+-1.43781 -0.847457 
+-1.40434 -0.89344 
+-1.369 -0.938226 
+-1.33181 -0.981743 
+-1.2928 -1.02392 
+-1.25201 -1.06468 
+-1.20949 -1.10396 
+-1.16526 -1.14168 
+-1.11937 -1.17778 
+-1.07187 -1.21217 
+-1.02281 -1.24479 
+-0.972241 -1.27557 
+-0.920217 -1.30444 
+-0.866798 -1.33132 
+-0.812046 -1.35615 
+-0.756027 -1.37885 
+-0.69881 -1.39936 
+-0.640469 -1.41761 
+-0.581082 -1.43354 
+-0.52073 -1.44708 
+-0.459499 -1.45817 
+-0.397479 -1.46674 
+-0.334766 -1.47275 
+-0.271458 -1.47612 
+-0.207659 -1.47682 
+-0.143478 -1.47478 
+-0.0790285 -1.46997 
+-0.0144283 -1.46234 
+0.0501996 -1.45185 
+0.114728 -1.43847 
+0.179024 -1.42218 
+0.242951 -1.40295 
+0.306368 -1.38077 
+0.369131 -1.35562 
+0.431089 -1.32751 
+0.492092 -1.29645 
+0.551983 -1.26245 
+0.610604 -1.22554 
+0.667796 -1.18575 
+0.723397 -1.14312 
+0.777245 -1.09772 
+0.829177 -1.0496 
+0.879032 -0.998846 
+0.926652 -0.945544 
+0.971879 -0.889795 
+1.01456 -0.831709 
+1.05455 -0.771411 
+1.0917 -0.709035 
+1.12588 -0.644726 
+1.15697 -0.578641 
+1.18484 -0.510946 
+1.20939 -0.441818 
+1.23052 -0.37144 
+1.24814 -0.300005 
+1.2622 -0.227711 
+1.27263 -0.154763 
+1.27938 -0.0813692 
+1.28244 -0.00774094 
+1.28178 0.0659089 
+1.27742 0.139368 
+1.26936 0.212423 
+1.25764 0.284866 
+1.24232 0.356492 
+1.22344 0.427101 
+1.2011 0.496498 
+1.17536 0.564499 
+1.14634 0.630924 
+1.11415 0.695607 
+1.0789 0.758387 
+1.04073 0.819118 
+0.999768 0.877662 
+0.956168 0.933894 
+0.910075 0.987701 
+0.861645 1.03898 
+0.811034 1.08764 
+0.758403 1.1336 
+0.703914 1.17679 
+0.647729 1.21716 
+0.590009 1.25465 
+0.530917 1.28924 
+0.470611 1.3209 
+0.409249 1.3496 
+0.346985 1.37535 
+0.283969 1.39813 
+0.220351 1.41795 
+0.156274 1.43483 
+0.0918761 1.4488 
+0.0272938 1.45986 
+-0.0373427 1.46806 
+-0.101907 1.47344 
+-0.166279 1.47603 
+-0.230341 1.47587 
+-0.293982 1.47303 
+-0.357095 1.46755 
+-0.419577 1.45949 
+-0.481331 1.4489 
+-0.542263 1.43584 
+-0.602286 1.42039 
+-0.661314 1.40259 
+-0.719268 1.38252 
+-0.776071 1.36025 
+-0.831651 1.33584 
+-0.88594 1.30936 
+-0.938873 1.28089 
+-0.990389 1.25048 
+-1.04043 1.21822 
+-1.08894 1.18417 
+-1.13588 1.14841 
+-1.18118 1.111 
+-1.22481 1.07203 
+-1.26673 1.03155 
+-1.30689 0.989652 
+-1.34526 0.946395 
+-1.38179 0.901855 
+-1.41647 0.856102 
+-1.44926 0.809209 
+-1.48014 0.761246 
+-1.50907 0.712285 
+-1.53603 0.662396 
+-1.561 0.611651 
+-1.58397 0.560119 
+-1.60491 0.507871 
+-1.62381 0.454977 
+-1.64065 0.401507 
+-1.65542 0.347531 
+-1.66811 0.293117 
+-1.67871 0.238337 
+-1.68722 0.183258 
+-1.69362 0.12795 
+-1.69791 0.0724833 
+-1.70009 0.0169258 
+-1.70016 -0.0386532 
+-1.69812 -0.0941844 
+-1.69396 -0.149599 
+-1.6877 -0.204827 
+-1.67933 -0.2598 
+-1.66886 -0.314449 
+-1.65631 -0.368704 
+-1.64167 -0.422496 
+-1.62496 -0.475754 
+-1.6062 -0.52841 
+-1.58539 -0.580394 
+-1.56256 -0.631634 
+-1.53772 -0.682061 
+-1.51088 -0.731605 
+-1.48208 -0.780194 
+-1.45134 -0.827758 
+-1.41867 -0.874225 
+-1.38412 -0.919525 
+-1.3477 -0.963585 
+-1.30945 -1.00634 
+-1.26941 -1.0477 
+-1.22761 -1.08762 
+-1.18409 -1.126 
+-1.1389 -1.16279 
+-1.09207 -1.19791 
+-1.04367 -1.23129 
+-0.993726 -1.26285 
+-0.942308 -1.29254 
+-0.88947 -1.32026 
+-0.835272 -1.34596 
+-0.779779 -1.36957 
+-0.723059 -1.39102 
+-0.665183 -1.41023 
+-0.606228 -1.42715 
+-0.546273 -1.4417 
+-0.485403 -1.45383 
+-0.423706 -1.46348 
+-0.361274 -1.47057 
+-0.298205 -1.47506 
+-0.234602 -1.47689 
+-0.17057 -1.47602 
+-0.106221 -1.47238 
+-0.0416707 -1.46595 
+0.0229594 -1.45667 
+0.0875438 -1.44452 
+0.151952 -1.42946 
+0.21605 -1.41147 
+0.279699 -1.39054 
+0.342754 -1.36664 
+0.405068 -1.33979 
+0.466491 -1.30997 
+0.526869 -1.27721 
+0.586044 -1.24153 
+0.643857 -1.20295 
+0.700147 -1.16152 
+0.754753 -1.11728 
+0.807512 -1.0703 
+0.858263 -1.02065 
+0.906845 -0.96842 
+0.9531 -0.913695 
+0.996874 -0.856585 
+1.03802 -0.797209 
+1.07638 -0.735697 
+1.11184 -0.672189 
+1.14424 -0.606838 
+1.17348 -0.539805 
+1.19945 -0.471264 
+1.22203 -0.401394 
+1.24115 -0.330384 
+1.25673 -0.258431 
+1.26869 -0.185737 
+1.277 -0.112508 
+1.28163 -0.0389552 
+1.28254 0.0347098 
+1.27974 0.108274 
+1.27325 0.181524 
+1.26307 0.254251 
+1.24927 0.326246 
+1.23189 0.397308 
+1.211 0.467241 
+1.18668 0.535854 
+1.15904 0.602968 
+1.12818 0.668407 
+1.0942 0.732011 
+1.05725 0.793627 
+1.01745 0.853113 
+0.974954 0.910339 
+0.929896 0.965185 
+0.882434 1.01755 
+0.832725 1.06732 
+0.780928 1.11443 
+0.727204 1.15881 
+0.671715 1.20038 
+0.614623 1.2391 
+0.55609 1.27492 
+0.496277 1.30782 
+0.43534 1.33778 
+0.373437 1.36477 
+0.310719 1.38881 
+0.247336 1.40988 
+0.183433 1.42801 
+0.119152 1.4432 
+0.0546296 1.45549 
+-0.0100018 1.4649 
+-0.074614 1.47146 
+-0.139084 1.47522 
+-0.203293 1.47623 
+-0.267127 1.47452 
+-0.330478 1.47014 
+-0.393241 1.46316 
+-0.455316 1.45364 
+-0.516609 1.44162 
+-0.577028 1.42717 
+-0.636488 1.41035 
+-0.694907 1.39124 
+-0.752207 1.36989 
+-0.808313 1.34637 
+-0.863157 1.32076 
+-0.916672 1.29312 
+-0.968796 1.26352 
+-1.01947 1.23203 
diff --git a/gravitation/animation_kepler16_pstricks.pdf b/gravitation/animation_kepler16_pstricks.pdf
new file mode 100644
index 0000000..5070e4b
Binary files /dev/null and b/gravitation/animation_kepler16_pstricks.pdf differ
diff --git a/gravitation/animation_kepler16_pstricks.png 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
+::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