Click to focus on the app, then click again to add a particle, and click again to set its velocity.
$$p=\frac{M^2}{k}$$ $$e=\sqrt{1+\frac{2 E M^2}{k^2}}$$ $$r(\varphi)=\frac{p}{1+e\cos(\varphi-\varphi_0)}$$ $$\dot{\varphi}=\frac{M}{r^2}$$ $$\varphi_0=\varphi-\mbox{ArcTanFull}\left(\frac{\dot{r} p}{M e} ,(\frac{p}{r}-1)\frac{1}{e}\right)$$
for a unit mass particle at angle $\phi$ with respect to some reference axis, angular momentum $M$, distance $r$ from the center, orbital energy $E$, where $p$ and $e$ are the parameter and eccentricity of the ellipse, and the particle is in a potential $-k/r$