Kepler radial energy equation ($\frac{1}{2}{\dot{r}}^2+\frac{L^2}{2r^2}=E+GM/r$)

For unit mass in $\Phi =-GM/r$, conservation of angular momentum splits the velocity norm into ${\dot{r}}^2+L^2/r^2$. Conservation of energy then gives $\frac{1}{2}{\dot{r}}^2+L^2/(2r^2)=E+GM/r$. It separates radial dynamics from the reconstruction of the orbital angle.