Message Boards Message Boards

Traveling around Jupiter and Saturn

Figure 2 Figure 3

Since we have historical conjunction of Jupiter and Saturn I have prepared code with visualization planet Jupiter and Saturn with moons. First code also published here. Visualization of planet Jupiter:

JSP = QuantityMagnitude[
   UnitConvert[
     PlanetaryMoonData[{"Io", "Europa", "Ganymede", 
       "Callisto"}, {"OrbitPeriod", "SemimajorAxis", "Radius"}], 
     "SI"] /. 
    q : Quantity[_, "Days" | "Hours"] :> UnitConvert[q, "Seconds"]];
a = Pi*RandomReal[{0, 2}, Length[JSP]];
b = 31557600*
   QuantityMagnitude[Entity["Planet", "Jupiter"]["OrbitPeriod"]]*
   Table[1/JSP[[i, 1]], {i, 1, 4}];
R = Table[JSP[[i, 2]], {i, 1, 4}];
c = Table[JSP[[i, 3]], {i, 1, 4}];
k = 3;
radius = QuantityMagnitude[
   Entity["Planet", "Jupiter"]["EquatorialRadius"], "Kilometers"];
radius1 = 
  QuantityMagnitude[Entity["Planet", "Jupiter"]["PolarRadius"], 
   "Kilometers"];
Xoblateness = Entity["Planet", "Jupiter"]["Oblateness"];
Xobliquity = Entity["Planet", "Jupiter"]["Obliquity"];
distanse = 
  QuantityMagnitude[
   Entity["Planet", "Jupiter"]["AverageOrbitDistance"], "Kilometers"];
angularvelocity = 
  Entity["Planet", "Jupiter"]["EquatorialAngularVelocity"];
texture = 
  ImageReflect[
   EntityValue[Entity["Planet", "Jupiter"], 
    "CylindricalEquidistantTexture"], Bottom];

planet = ParametricPlot3D[{radius Cos[t] Sin[p], 
   radius Sin[t] Sin[p], (1 - Xoblateness) radius Cos[p]}, {t, 0, 
   2 Pi}, {p, 0, \[Pi]}, Mesh -> None, PlotStyle -> Texture[texture], 
  Lighting -> "Neutral", Boxed -> False, Axes -> False, 
  PlotPoints -> 100]

Visualization of travelling orbit (we solve restricted 3 body problem)

M1 = QuantityMagnitude[Entity["Planet", "Jupiter"]["Mass"]];
M2 = QuantityMagnitude[Entity["Star", "Sun"]["Mass"]];
Ra = QuantityMagnitude[
    Entity["Planet", "Jupiter"]["EquatorialRadius"]]*10^3;
S = QuantityMagnitude[Entity["Planet", "Jupiter"]["SemimajorAxis"]];
ar = Ra/(S*149597870700);
m = M1/M2;
G = 6.67384*10^(-11); vS = 
 Sqrt[G*M1/Ra]; u0 = 16000; {ux, uy, 
  uz} = {0.28309789428056364`, -2.269693660804425`, 
  0.24765897137821516`}; tm = 2*0.007188414157797473;
{x0, y0, z0} = {0.9987450742768228`, -0.00006988474848081634`, \
-0.000015444353758731164`};
eq = {x''[t] == 
    2*y'[t] + x[t] - (
     m (-1 + m + x[t]))/((-1 + m + x[t])^2 + y[t]^2 + z[t]^2)^(
     3/2) - ((1 - m) (m + x[t]))/((m + x[t])^2 + y[t]^2 + z[t]^2)^(
     3/2), y''[t] == -2*x'[t] + y[t] - (
     m y[t])/((-1 + m + x[t])^2 + y[t]^2 + z[t]^2)^(
     3/2) - ((1 - m) y[t])/((m + x[t])^2 + y[t]^2 + z[t]^2)^(3/2), 
   z''[t] == -((m z[t])/((-1 + m + x[t])^2 + y[t]^2 + z[t]^2)^(
      3/2)) - ((1 - m) z[t])/((m + x[t])^2 + y[t]^2 + z[t]^2)^(3/2), 
   x[0.] == x0, y[0.] == y0, x'[0.] == ux, y'[0.] == uy, z'[0.] == uz,
    z[0.] == z0};
{xfun, yfun, zfun} = NDSolveValue[eq, {x, y, z}, {t, 0, tm}];
rt = RotationTransform[Xobliquity, {1, 0, 0}]; V = 
 rt[S*149597870.700*{xfun[t] - 1 + m, yfun[t], zfun[t]}];

{Orbit = ParametricPlot3D[V, {t, 0, tm}], Plot[Norm[V], {t, 0, tm}]}

Show[{Graphics3D[Orbit[[1]], Boxed -> False], planet}]

We have this picture with Jupiter and orbit around Figure 1

Now we combine orbit, planet and moons in one scene, and export it as a gif (or animate).

Th = tm*31557600*
   QuantityMagnitude[
      Entity["Planet", "Jupiter"]["OrbitPeriod"]]/(3600)/(2*Pi);

frames = Table[
   Show[{Graphics3D[
      Rotate[planet[[1]], 2*Pi*Th*t/9.841666666666667/tm, {0, 0, 1}], 
      Boxed -> False, Axes -> False, ImageSize -> .25 {1920, 1080}], 
     Table[Graphics3D[{White, 
        Sphere[{R[[i]]*Cos[a[[i]] + b[[i]]*t], 
          R[[i]]*Sin[a[[i]] + b1[[i]]*t], 0}, k*c[[i]]]}, 
       Background -> Black, Boxed -> False, PlotRange -> All], {i, 1, 
       4}]}, Background -> Black, SphericalRegion -> True, 
    ViewAngle -> Pi/4, PlotRange -> All, 
    Lighting -> {{"Ambient", GrayLevel[0.05]}, {"Point", 
       White, {20 radius, 0, 0}}}, ViewVector -> {V, {0, 0, 0}}], {t, 
    0, (1 - .0025)*tm, .0025*tm}];
Export["C:\\...\\Jupiter.gif", frames, AnimationRepetitions -> Infinity]

Figure 2

Second code with visualization of Saturn and moons "Mimas", "Enceladus", "Tethys", "Dione", "Rhea", "Titan" is differ from above since we need to show rings and also orbit around Saturn is not like orbit around Jupiter. The code is in notebook attached. And animation looks like this one

Figure 3

Attachments:

enter image description here -- you have earned Featured Contributor Badge enter image description here

Your exceptional post has been selected for our editorial column Staff Picks http://wolfr.am/StaffPicks and Your Profile is now distinguished by a Featured Contributor Badge and is displayed on the Featured Contributor Board. Thank you!

POSTED BY: EDITORIAL BOARD
Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Reply Preview
Attachments
Remove
or Discard

Group Abstract Group Abstract