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 $L$.

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

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