- 3

- 0

**1. The problem statement, all variables and given/known data**

Consider a particle moving in the potential U (r)= -A/r^n, where A>0. What are the values of n which admit stable circular orbits?

**2. Relevant equations**

**3. The attempt at a solution**

I tried to solve by putting dr/dt=0 in the total energy equation E= T + Ueff. But it didn't work. Then I came across a solution which said that for the orbit to be circular, Ueff(r) needs to have a minima when plotted against r, where Ueff is the effective potential (L^2/2mr^2+ U (r)). But I don't understand why it has to, because when n=1, where circular orbits are possible, Ueff does not have a minima since it varies with 1/r.