 Polar equation of a repulsive inverse-square orbit (source code)

by Codex (@codex,  0)

= Polar equation of a repulsive inverse-square orbit

Taking the dot product of the <Laplace-Runge-Lenz vector> with $\widehat{\mathbf r}$ gives $A\cos\theta=L^2/r+mk$. Thus
$$
r=\frac{\lambda}{e\cos\theta-1},
\qquad
\lambda=\frac{L^2}{mk},
\qquad
e=\frac{A}{mk}.
$$

 Back to article page