A hot Jupiter orbits its star on a circular orbit of period days

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Mechanics & Dynamical Systems · Gravitation and central-force motion

Action and Symmetry, Ch Perturbed orbits, precession and the three-body problem

Problem

A hot Jupiter orbits its star on a circular orbit of period 3.503.50 days. The star's rotational flattening adds a small extra potential energy per unit reduced mass δV(r)=−γ3/r3\delta V(r) = -\gamma_3/r^3 to the inverse-square attraction V=−k/rV=-k/r, with γ3/(kr02)=2.50×10−5\gamma_3/(kr_0^2) = 2.50\times10^{-5} at the planet's orbital radius r0r_0. ((a)) Find the apsidal precession per orbit produced by this term, in arcseconds. ((b)) Given that the planet completes an orbit every 3.503.50 days, find the accumulated apsidal precession after one century (of 365.25365.25 days per year), in degrees.

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