Tidal Effects

Clear[soln];
soln[ymax_] :=
 soln[ymax] =
  NDSolve[{y''[t] == -9/y[t]^2, y[0] == ymax, y'[0] == 0},
   y[t], {t, 0, 19}];
y[\[Tau]_, ymax_] := First[y[t] /. soln[ymax] /. {t -> \[Tau]}];
Manipulate[
 Show[
  ContourPlot[10/y^2, {x, -1.7, 1.7}, {y, 9, 16}, Frame -> None,
   Contours -> 10, ColorFunction -> "ThermometerColors",
   AspectRatio -> Automatic],
  Graphics[{Thick, Arrowheads[0.1],
    Table[{Darker@Red,
      Disk[{Cos[\[Theta]], y[\[Tau], 15 + Sin[\[Theta]]]}, 0.1], Blue,
      Arrow[{{Cos[\[Theta]],
         y[\[Tau], 15 + Sin[\[Theta]]]}, {Cos[\[Theta]],
          y[\[Tau], 15 + Sin[\[Theta]]]} - {0, 400/
          y[\[Tau], 15 + Sin[\[Theta]]]^2}}]
      }, {\[Theta], 0, 2 Pi, Pi/10}]
    }, PlotRange -> {{-1.1, 1.1}, {0, 11}}]
  ]

 , {\[Tau], 0, 19}]