consider a star orbitining in the sperically graviational potential Y=(Vc)2 ln(r/r0).
a)use conservation of energy and angular momentum to obtain equation for dr/dt and d(teta)/dt.
b)take the radius and velocity at apogalaction to be ra and va. use these two dimentioned quantities and vc to recast your answer in a) in terms of dimentionless quantities(e.g. you might let z=r/ra and w=(Vc)*t/ra)