Potential Energy using effective potential

1. Oct 7, 2013

derrickb

1. The problem statement, all variables and given/known data
For a given angular momentum L, find the potential energy function U(r) that leads to a spiral path of the form r=r0θk. Choose the total energy E to be zero. Hint: obtain an expression for r' that is only a function of r, not θ, and then use the energy equation with effective potential

2. Relevant equations
E=.5μ(r')2+(L2/2μr2)+U(r)
r=r0θk

3. The attempt at a solution
I can't seem to figure out where to start. I don't want a full solution, but if someone could point me in the right direction, I will try to solve it from there.