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Inverse-square force

Repulsive inverse-square force

Laplace-Runge-Lenz vector

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

Polar equation of a repulsive inverse-square orbit

Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 3 / 8B / Solution

Polar equation of a repulsive inverse-square orbit

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Polar equation of a repulsive inverse-square orbit

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