If the planet moves in a nearly circular orbit of radius a

Question

Solar oblateness A planet of mass m moves in the equatorial plane of a star that is a uniform oblate spheroid. The planet experiences a force field of the form

F = -mγ / r² (1+(∈a²/r²))r^{^},

approximately, where γ , a and ∈ are positive constants and ∈ is small. If the planet moves in a nearly circular orbit of radius a, find an approximation to the ‘annual' advance of the perihelion.

[It has been suggested that oblateness of the Sun might contribute significantly to the precession of the planets, thus undermining the success of general relativity. This point has yet to be resolved conclusively.]