$$\frac{d^2r}{d\lambda^2} = -\frac{GM}{r^2} + \frac{L^2}{r^3}$$
where $\eta^{im}$ is the Minkowski metric. moore general relativity workbook solutions
Consider a particle moving in a curved spacetime with metric moore general relativity workbook solutions
where $L$ is the conserved angular momentum. moore general relativity workbook solutions
After some calculations, we find that the geodesic equation becomes