Originally Posted by
kolahalb Central force F=-ar/(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.