Retrograde Motion

T = 2.59;
r = 1.524;
stars = Partition[
   Riffle[RandomReal[{-2, 2}, 20], RandomReal[{2.5, 3.5}, 20]], 2];
Project[{ax_, ay_}, {bx_, by_}] :=
  Module[{\[Lambda] = (3 - ay)/(
     by - ay)}, {ax + \[Lambda] bx - \[Lambda] ax, 3}];
mars[t_] := r {Sin[2 Pi t/T], Cos[2 Pi t/T]};
earth[t_] := {Sin[2 Pi t], Cos[2 Pi t]};
Manipulate[
 Show[Graphics[Join[
    { RGBColor[1, 0.2, 0], Disk[mars[t], 0.05],
     RGBColor[0, 0.6, 1],
     Disk[earth[t], 0.05],
     If[Abs[t] <= 0.38,
      Line[{earth[t], Project[earth[t], mars[t]] + {0, t}}],
      Opacity[1]],
     Blend[{Yellow, Orange}, 0.2],
      Disk[{0, 0}, 0.1], White, Point[stars]}
    ], PlotRange -> {{-2, 2}, {-2, 4}}],
  ParametricPlot[{Project[earth[t], mars[t]][[1]], t + 3}, {t, -0.38,
    0.38}, Axes -> None, PlotStyle -> RGBColor[1, 0.2, 0]]
  , Background -> Black]
 , {t, -1, 1 }]