Keplerian Orbits

Click to focus on the app, then click again to add a particle, and click again to set its velocity.

$p = \frac{M^{2}}{k}$ $e = \sqrt{1 + \frac{2 E M^{2}}{k^{2}}}$ $r (φ) = \frac{p}{1 + e \cos (φ - φ_{0})}$ $\dot{φ} = \frac{M}{r^{2}}$ $φ_{0} = φ - ArcTanFull (\frac{\dot{r} p}{M e}, (\frac{p}{r} - 1) \frac{1}{e})$

for a unit mass particle at angle

ϕ

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