Classical Mechanics (Kibble & Berkshire) · Problem 7.11

Non-linear oscillations and phase space — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · nearly-circular-orbits

Problem

Solar oblateness A planet of mass mm moves in the equatorial plane of a star that is a uniform oblate spheroid. The planet experiences a force field of the form F=−mγr2(1+ϵ a2r2)r^,\boldsymbol{F} = -\frac{m\gamma}{r^2}\left(1 + \frac{\epsilon\, a^2}{r^2}\right)\hat{\boldsymbol{r}}, approximately, where γ\gamma, aa and ϵ\epsilon are positive constants and ϵ\epsilon is small. If the planet moves in a nearly circular orbit of radius aa, 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.]

Related theory

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