Originally Posted by

**kolahalb** Central force **F**=-a**r**/(r^3) & Central potential energy,U=-(a/r)

(not U_eff)

Find the nature of orbits if (i)a>0 and (ii)a<0

If we remember the attractive central force E=E(r) diagram,i.e.the one showing the graph of U_eff,we only need to know E_total=K+U.

Where only PE is given.

We see,

U= -integration[F.dr]=integration[dW]=-integration[dK]=-K

Then K=a/r and U=-(a/r)

So,the E=K+U=0

Then in positive and negative both caes we get a parabolic orbit.

Please check if i am correct.