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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?

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