# Manev potencial and some problems with it [closed]

Given the Manev potential by the equation below

$$\ V_M(r) = - \frac{-mMG}{r} \left(1 + \frac{\gamma MG}{c^2r}\right)$$

in which: M is the Sun's mass; m is the planet's mass; G is Newton's constant; c is speed of light; $$\gamma$$ is adimensional number in which the $$\frac{-\gamma M^2 G^2}{c^2r^2}$$ term is a relativistic correction.

I need to find the effective potential $$V_{ef}$$ corresponding for a body with angular momentum L, then the conditions over $$V_{ef}$$ in which this potencial admits stable orbits and last, considering a theory with the attractive potencial $$V = - \frac {K}{r^n}$$, I have to proof that only for $$n>2$$ this theory can admit stable orbits for any L values.

I need to solve this using the harmonic oscillator stuff. Any help?