OK, here's another that might be simpler than it looks but I am about ready to give up. Given the following:
$$U_\mathrm{eff}(r) = - \frac{k}{r}+ \frac{L^2}{2mr^2}$$
$$\frac{U_\mathrm{eff}}{U_0} = -\frac{2}{r / r_0} + \frac {1}{(r/r_0)^2}$$
$$r_0= \frac{L^2}{mk}, \qquad U_0= \frac{k}{2r_0}$$
EDIT - L is angular monentum and k is a constant. m is mass r is radius.
I am supposed to make $U$ dimensionless. But I can't seem to get rid of the $r$ in the denominator. Maybe that isn't what I am supposed to do. The question is "Convert the effective potential to a dimensionless function by scaling to the radius of a circular orbit. " Which makes zero sense to me right now.
One suggestion was to plug in the $r_0$ expression in $U_0$ but I can't seem to see how this is supposed to work. I end up with $U_\mathrm{eff} = \frac{-2L^2}{kmr} + \frac{L^4}{k^2mr^2}$. Maybe that's what is supposed to happen, I don't know.
This isn't even calculus I bet, This should be simple but for some reason I am losing it.
ANyhow, any help is appreciated. thanks.