Central force F=-ar/(r^3) & Central potential energy,U=-(a/r)
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.
Then K=a/r and U=-(a/r)
Then in positive and negative both caes we get a parabolic orbit.
Please check if i am correct.
OK,thank you.I got it.
Hence total energy E=K+U= -(1/2)(a/r)
Then,F=+b/r where b=-a>0
K is itrinsically positive.So,total energy positive.
hence hyperbolic trajectory.