Valentines card-ioid

point[p0_, t_] :=
  RotationMatrix[-4 Pi t, {0, 0, 1}].p0 +
   RotationMatrix[-2 Pi t, {0, 0, 1}].{0, 2, 0};
d\[Theta] = Pi/3;
p0s = Table[u = RandomReal[{0, 2 Pi}];
   v = RandomReal[{0, Pi}]; {Sin[u] Cos[v], Sin[u] Sin[v],
    Cos[u]}, {i, 20}];
AppendTo[p0s, {0, -1, 0}];
p0fns = Table[point[p0, \[Tau]], {p0, p0s}];
frame[t_] :=
  Show[
   Graphics3D[
    {
     Opacity[0.9],
     Sphere[{0, 0, 0}, 1],
     Sphere[2 {Sin[2 Pi t ], Cos[2 Pi t ], 0}, 1],
     Point[Table[p0fn /. {\[Tau] -> t}, {p0fn, p0fns[[;; -2]]}]],
     PointSize[Medium], Red, Point[p0fns[[-1]] /. {\[Tau] -> t}]
     }
    , PlotRange -> 3, Boxed -> False],
   ParametricPlot3D[Table[
     p0fn,
     {p0fn, p0fns[[;; -2]]}
     ], {\[Tau], Max[0, t - 1], Min[t, 1]},
    PlotStyle -> Directive[Thin, Blue, Opacity[0.7]]],
   ParametricPlot3D[
    p0fns[[-1]], {\[Tau], Max[0, t - 1], Min[t, 1]},
    PlotStyle -> Directive[Thick, Red]]
   , ViewPoint -> {-5, -5, 10}, ImageSize -> 300];
Manipulate[frame[t], {t, 0.001, 1.999, 2/80.1}]