Doppler Effect of spinning object

frame[t_, v_] := Graphics[Join[
    {PointSize[Large], ColorData["Rainbow"][0.2],
     Point[{Sin[t], Cos[t]}], RGBColor[0.4, 0.4, 0.5], Thick,
     Line[{{0, 0}, {Sin[t], Cos[t]}}]}
    ,
    Table[{Blend[{GrayLevel[(Max[0, (t - \[Tau])/20])], Green}, 0.1],
      Circle[{Sin[\[Tau]], Cos[\[Tau]]}, (t - \[Tau] ) v]}, {\[Tau],
      0, t, (Sqrt[5] - 1)/2}]
    ], PlotRange -> {{-4, 4}, {-4, 4}}];
frame4[t_] := GraphicsGrid[{
    {frame[t, 0.2], frame[t, 0.8]},
    {frame[t, 1], frame[t, 1.5]}
    }];
Manipulate[frame4[t], {t, 0, 10}]