a=1
aorbit[e_,w_,i_,u_]=Drop[EulerMatrix[{0,-i,-w}].{-a (Cos[u]-e),a Sqrt[1-e^2] Sin[u],0},-1]
amajor[e_,w_,i_,u_]=Drop[EulerMatrix[{0,-i,-w}].{a (1+e)-a/Pi u,0,0},-1]
alatusrectum[e_,w_,i_,u_]=Drop[EulerMatrix[{0,-i,-w}].{0,a (1-e^2) (u-Pi)/Pi,0},-1]
Animate[ParametricPlot[{aorbit[e,w,i,u],amajor[e,w,i,u],alatusrectum[e,w,i,u]},{u,0,2 Pi},Axes->False,AspectRatio->Automatic],{e,0,1},{w,0,2 Pi},{i,0,Pi/2},AnimationRunning->False]

m1=1; m2=2
wt[e_,u_]=u-e Sin[u]
phi[e_,u_]=2 ArcTan[Cos[u/2],Sqrt[(1+e)/(1-e)] Sin[u/2]]
vr[e_,w_,i_,u_]=-2 Pi Sqrt[(m1+m2)/(a(1-e^2))] {-Sin[phi[e,u]],Cos[phi[e,u]]+e}.{Sin[w] Sin[i],Cos[w] Sin[i]}
Animate[ParametricPlot[{wt[e,u],vr[e,w,i,u]},{u,0,4 Pi},AspectRatio->.8],{e,0,1},{w,0,2 Pi},{i,0,Pi/2},AnimationRunning->False]