Central Force Motion and Kepler Orbit Equation

Two-Body Central Force Problem

The equation of orbit under inverse-square law (r) = -k/r^2$ is: 2497747\frac{d^2 u}{d\theta^2} + u = \frac{m k}{L^2}2497747

Conic section solution: 2497747r(\theta) = \frac{p}{1 + e \cos\theta}2497747