Elliptical Orbits

r[a_, e_, θ_] := ((a *(1 - (e^2)))/(1 + e Cos[θ]))

xy[a_, e_, θ_] := r[a, e, θ] {Cos[θ], Sin[θ]}

θf[a_, e_, t_] := Module[{θs, f},
f[tt_] = NDSolveValue[{θ'[tt] == (1/r[a, e, θ[tt]]^2) 2 π Sqrt[a (1 - (e^2))], θ[0] == 0}, θ[tt], {tt, 0, 5}];
f[t]]

Manipulate[
a = 1;
myθ[t_] = θf[a, e, t];
Show[{
Graphics[{Yellow, Disk[{0,0}, 0.1]}],
Graphics[{Blue, Disk[xy[a, e, myθ[t]], 0.04]}],
ParametricPlot[xy[1, e, θ], {θ, 0, 2π}, PlotStyle -> Green]
}, Frame->True, PlotRange -> {{-2.1, 1.2}, {-1.2, 1.2}}, AspectRatio->2.4/3.2],
{{e, 0}, 0, 0.99, 0.02, Appearance -> "Labeled"}, 
{t, 0, 4, 0.01,ControlType -> Animator, Appearance-> "Open",DefaultDuration -> 10, AnimationRunning -> False, AnimationRepetitions -> 1, DisplayAllSteps -> True}]