A particle moving in a plane is attracted towards a point (fixed) by a force zr^-5. The particle is projected from an apse at distance a with speed SQRT(z/(2a^4)).
Show that the orbit is r=acos(theta)
Using the Orbit Eq: d^2 u/dC^2 + u = za^-5/(hu)^2
h = angular momentum, or r(speed) in this case, u = 1/r
I get down to (du/dC)^2 + u^2 = -4/[(a^3)u] + A
where C = theta, A = integration constant.
Am I correct so far?