### Comet in a parabolic trajectory

A comet in a parabolic orbit around the sun has a least distance of kR, k < 1. Show that the time during which the comets distance is less than R is: (1/3*pi)[2(1-k)]^1/2 * (1+2k) years I have derived the following expression for t as a function of r: t = the integral from r to ro of [2/m (E - u(r) - l^2/2mr^2)]^-1/2 dr