gravitation/Kepler16_animation_Nasa.tex

   1
   2 \documentclass{article}
   3 \usepackage[a4paper,margin=2cm]{geometry}
   4 \usepackage[T1]{fontenc}
   5 \usepackage[latin1]{inputenc}%
   6 \usepackage[garamond]{mathdesign}
   7 \usepackage{pst-eqdf,pst-node}
   8 %\usepackage{array,amsmath}
   9 \usepackage{animate}
  10 \usepackage{pst-grad}
  11 %\usepackage{wasysym}
  12 %\usepackage{url}
  13 \newpsstyle{vecteurA}{arrowinset=0.05,arrowsize=0.1,linecolor={[rgb]{1 0.5 0}}}
  14 \newpsstyle{vecteurB}{arrowinset=0.05,arrowsize=0.1,linecolor={[rgb]{0 0.5 1}}}
  15 \newpsstyle{vecteurC}{arrowinset=0.1,arrowsize=0.2,linecolor={[rgb]{1 0 0}}}
  16 \makeatletter
  17 %% adapté de \psRandom du package pstricks-add
  18 %% pour rendre aléatoire la taille des étoiles
  19 %% Manuel Luque
  20 \newdimen\pssizeStar
  21 \def\psset@sizeStar#1{\pssetlength\pssizeStar{#1}}
  22 \psset@sizeStar{1pt}
  23 \define@key[psset]{pst-eqd}{randomPoints}[1000]{\def\psk@randomPoints{#1}}
  24 \psset[pst-eqd]{randomPoints=1000}
  25 \define@boolkey[psset]{pst-eqd}[Pst@]{color}[true]{}
  26 \psset[pst-eqd]{color=false}
  27 \def\psRandomStar{\pst@object{psRandomStar}}%
  28 \def\psRandomStar@i{\@ifnextchar({\psRandomStar@ii}{\psRandomStar@iii(0,0)(1,1)}}
  29 \def\psRandomStar@ii(#1){\@ifnextchar({\psRandomStar@iii(#1)}{\psRandomStar@iii(0,0)(#1)}}
  30 \def\psRandomStar@iii(#1)(#2)#3{%
  31   \def\pst@tempA{#3}%
  32   \ifx\pst@tempA\pst@empty\psclip{\psframe(#2)}\else\psclip{#3}\fi
  33   \pst@getcoor{#1}\pst@tempA
  34   \pst@getcoor{#2}\pst@tempB
  35   \begin@SpecialObj
  36   \addto@pscode{
  37     \pst@tempA\space /yMin exch def
  38     /xMin exch def
  39     \pst@tempB\space /yMax exch def
  40     /xMax exch def
  41     /dy yMax yMin sub def
  42     /dx xMax xMin sub def
  43     rrand srand                 % initializes the random generator
  44     /getRandReal { rand 2147483647 div } def
  45      \psk@randomPoints {
  46     /DS \pst@number\pssizeStar\space getRandReal mul def
  47     \@nameuse{psds@\psk@dotstyle}
  48      \ifPst@color getRandReal 1 1 sethsbcolor \fi
  49      getRandReal dx mul xMin add
  50      getRandReal dy mul yMin add
  51      Dot
  52      \ifx\psk@fillstyle\psfs@solid fill \fi stroke
  53     } repeat
  54   }%
  55   \end@SpecialObj
  56   \endpsclip
  57   \ignorespaces
  58 }
  59 \makeatother
  60 %%%%%%%%%%%%%%%%%%
  61 %timeline
  62 \begin{filecontents}{kepler16Nasa.dat}
  63 ::0x0
  64 ::1
  65 ::2
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 295 \end{filecontents}
 296 \title{Gravitation : une planète à deux soleils - animation \textsc{Nasa}}
 297 \date{17 juillet 2\,012}
 298 \begin{document}
 299 %\section{L'animation à partir des données de la \textsc{Nasa}}
 300 \maketitle
 301 \begin{center}
 302 \def\nFrames{230}% 230 images (229 jours)
 303 \begin{animateinline}[controls,timeline=kepler16Nasa.dat,loop,%
 304                      begin={\begin{pspicture}(-8,-8)(8,8)},
 305                      end={\end{pspicture}}]{10}% 10 images/s
 306 \pstVerb{%
 307 /Pi 3.14159265359 def
 308 /2Pi 6.28318530718 def
 309 % les angles doivent être en degrés
 310 % pour calculer les sinus, cosinus
 311 % en postscript
 312 /rad2deg { 180 mul Pi div } bind def % radians -> degrés
 313 /deg2rad { 180 div Pi mul } bind def %  degrés -> radians
 314 /tan {dup sin exch cos div} def
 315          /arctan {
 316             dup 0 ge
 317             {1 atan}
 318             {neg 1 atan neg}
 319          ifelse
 320         } def
 321 /AV { % anomalie vraie
 322    1 exc add 1 exc sub div sqrt AE rad2deg 2 div tan mul arctan 2 mul
 323   } def
 324 /mA 0.6897 def % masse étoile A
 325 /mB 0.20255 def% masse étoile B
 326 /mt mA mB add def % masse totale
 327 /mP 3e-4 def % masse planète
 328 /a1 0.22431 def % a pour le point réduit
 329 /e1 0.15944 def % excentricité
 330 /p1 a1 1 e1 dup mul sub mul def  % paramètre
 331 /pA p1 mB mul mt div def % paramètre star A
 332 /pB p1 mA mul mt div def % paramètre star B
 333 /e2 0.0069 def % excentricité planète
 334 /a2 0.7048 def % demi-grand axe planète
 335 /w1 263.464 def % arguument
 336 /w2 318 def % arguument planète
 337 /p2 a2 1 e2 dup mul sub mul def  % paramètre planète
 338 % t T e Kepler -> AE
 339 % date periode excentricité -> Kepler -> anomalie excentrique
 340 /Kepler {
 341   /exc exch def
 342   /Ti exch def
 343   /ti exch def
 344   /AM ti 2Pi mul Ti div def % anomalie moyenne à la date t
 345   /AE AM def % valeur initiale de anomalie excentrique
 346     5 {% 5 boucles
 347      /AETemp % anomalie excentrique provisoire
 348       AM exc rad2deg AE sin mul add
 349       def
 350      /AE AETemp def
 351     } repeat
 352     }def
 353 % étoiles A et B
 354 % T=41.076 jours e=0.15944
 355 % planète
 356 % T=228.776 j    e=0.0069
 357 % on calcule sur la periode la planète
 358 % on construit les tableaux des positions
 359 % à 1 jour d'intervalle
 360 /tabStarA [
 361  0 1 229 {/i exch def
 362   i 41.076 e1 Kepler
 363   /radius pA 1 e1 AV cos mul add div neg def
 364    radius AV w1 add cos mul
 365    radius AV w1 add sin mul
 366   } for
 367   ] def
 368 /tabStarB [
 369  0 1 229 {/i exch def
 370   i 41.076 e1 Kepler
 371   /radius pB 1 e1 AV cos mul add div def
 372    radius AV w1 add cos mul
 373    radius AV w1 add sin mul
 374   } for
 375   ] def
 376  /tabPlanet [
 377  0 1 229 {/i exch def
 378   i 228.776 e2 Kepler
 379   /radius p2 1 e2 AV cos mul add div def
 380    radius AV w2 add cos mul
 381    radius AV w2 add sin mul
 382   } for
 383   ] def
 384     }%
 385 \psframe*[linecolor={[cmyk]{1 1 0 0.7}}](-8,-8)(8,8)
 386 \psRandomStar[linecolor={[rgb]{1,1,0.5}},
 387     randomPoints=1000,sizeStar=1pt](-8,-8)(8,8){\psframe[linestyle=none](-8,-8)(8,8)}
 388 %\listplot[unit=10,linecolor=gray]{tabStarA aload pop}
 389 %\listplot[unit=10,linecolor=gray]{tabStarB aload pop}
 390 %\listplot[unit=10,linecolor=gray]{tabPlanet aload pop}
 391 \newframe
 392 \multiframe{\nFrames}{i=0+2}{%
 393 \pstVerb{/i1 \i\space def
 394   /xA tabStarA i1 get 10 mul def
 395   /yA tabStarA i1 1 add get 10 mul def
 396   /xB tabStarB i1 get 10 mul def
 397   /yB tabStarB i1 1 add get 10 mul def
 398   /xP tabPlanet i1 get 10 mul def
 399   /yP tabPlanet i1 1 add get 10 mul def
 400        }%
 401 \pscircle[linestyle=none,fillstyle=gradient,gradmidpoint=0,gradend=yellow,GradientCircle=true,gradbegin=yellow!50!red!50](!xA yA){0.6}
 402 \pscircle[linestyle=none,fillstyle=gradient,gradmidpoint=0,gradend=red,GradientCircle=true,gradbegin=red!50](!xB yB){0.2}
 403 \pscircle*[linecolor=white](!xP yP){0.1}
 404 }
 405 \end{animateinline}
 406 \end{center}
 407 \end{document}
 408