Ian Jauslin

Kepler orbits

Here, we solve the Kepler problem with a centripetal force: $$ \ddot x=-\frac x{|x|^3}+\frac{g^2x}{|x|^4} $$ with $x\in\mathbb R^2$. This initial condition is specified through the energy $E$ and the angular momentum $L$.

Energy: $E=$-0.5
Angular momentum: $L=$0.75
Centripetal force: $g=$0.

There are two plots below: the first shows the position, and the second shows the velocity.