Animations

Orbite

Un satellite S est en rotation circulaire autour de la terre avec une vitesse v0. À un instant t, on change instantanément l'orientation du vecteur vitesse tout en gardant la même norme que v0. La trajectoire est alors elliptique (v0 est telle que l'énergie mécanique est négative). L'animation montre l'évolution de la trajectoire en fonction de l'angle formé entre le vecteur v0 et le nouveau vecteur vitesse.

Animation flash


orbite.mp
%@AUTEUR: Maxima Chupin
%@DATE: 21 mars 2007
 
verbatimtex
%&latex
\documentclass{article}
\usepackage{amsmath}
\usepackage[mdugm]{mathdesign}
\usepackage[latin1]{inputenc}
\usepackage{color}
\begin{document}
etex
u=2.5cm;
 
for i:= 0 upto 28: 
 beginfig(i+1);
  path droite, droiter, ellipse;
  pair T,S,R,O,F,V;
  numeric a,b,o;
  T:= (0,0);
  fill fullcircle scaled 0.2u withcolor blue;
  a:=1.4u;
  S:=(-a,0);
  draw T--S dashed evenly withcolor green;
  R:=(a*cosd(90+2.5*i),a*sind(90+2.5*i));
  droite := 5[T,R]--5[R,T];
  droiter := droite rotated 90 shifted S;
  draw droite shifted S dashed evenly;
  draw droite shifted T dashed evenly;
  draw droiter dashed evenly;
  O = droite intersectionpoint droiter; 
  b := abs(S-O);
  ellipse = fullcircle xscaled 2a yscaled 2b;
  o:=abs(T-O);
  F:=(2*o*cosd(90+2.5*i),2*o*sind(90+2.5*i));
  draw S--F dashed evenly withcolor green;
  V:= (u*cosd(90+2.5*i),u*sind(90+2.5*i));
 
  pickup pencircle scaled 1pt;
  drawarrow S--(xpart S,u)  withcolor 0.8white;
  draw fullcircle scaled 2a dashed evenly withcolor 0.8white;
  draw ellipse  rotated (90+2.5*i) shifted O withcolor red;
  drawarrow S--(V shifted S);
 
 
  label.ulft(btex $\overrightarrow{v}$ etex, (V shifted S));
  label(btex \textcolor{white}{$T$} etex, T);
  dotlabel.llft(btex $S$ etex,S);
  label.bot(btex $a$ etex,(-(a/2),0));
  if i<>0:
    dotlabel.urt(btex $O$ etex, O);
    dotlabel.ulft(btex $T'$ etex, F);
    label.top(btex $a$ etex,((xpart S + xpart F)/2,(ypart S + ypart F)/2));
    label.urt(btex $b$ etex,((xpart S + xpart O)/2,(ypart S + ypart O)/2));
  fi;
  clip currentpicture to (-3u,-2u)--(2u,-2u)--(2u,3u)--(-3u,3u)--cycle;
 endfig;
endfor;
 
 
for i:= 28 downto 0: 
 beginfig(30 +(28-i));
  path droite, droiter, ellipse;
  pair T,S,R,O,F,V;
  numeric a,b,o;
  T:= (0,0);
  fill fullcircle scaled 0.2u withcolor blue;
  a:=1.4u;
  S:=(-a,0);
  draw T--S dashed evenly withcolor green;
  R:=(a*cosd(90+2.5*i),a*sind(90+2.5*i));
  droite := 5[T,R]--5[R,T];
  droiter := droite rotated 90 shifted S;
  draw droite shifted S dashed evenly;
  draw droite shifted T dashed evenly;
  draw droiter dashed evenly;
  O = droite intersectionpoint droiter;
  b := abs(S-O);
  ellipse = fullcircle xscaled 2a yscaled 2b;
  o:=abs(T-O);
  F:=(2*o*cosd(90+2.5*i),2*o*sind(90+2.5*i));
  draw S--F dashed evenly withcolor green;
  V:= (u*cosd(90+2.5*i),u*sind(90+2.5*i));
 
  pickup pencircle scaled 1pt;
  drawarrow S--(xpart S,u)  withcolor 0.8white;
  draw fullcircle scaled 2a dashed evenly withcolor 0.8white;
  draw ellipse  rotated (90+2.5*i) shifted O withcolor red;
  drawarrow S--(V shifted S);
 
  label.ulft(btex $\overrightarrow{v}$ etex, (V shifted S));
  label(btex \textcolor{white}{$T$} etex, T);
  dotlabel.llft(btex $S$ etex,S);
  label.bot(btex $a$ etex,(-(a/2),0));
  if i<>0:
    dotlabel.urt(btex $O$ etex, O);
    dotlabel.ulft(btex $T'$ etex, F);
    label.top(btex $a$ etex,((xpart S + xpart F)/2,(ypart S + ypart F)/2));
    label.urt(btex $b$ etex,((xpart S + xpart O)/2,(ypart S + ypart O)/2));
  fi;
 
  clip currentpicture to (-3u,-2u)--(2u,-2u)--(2u,3u)--(-3u,3u)--cycle;
 endfig;
endfor;
end.