An orbiter circles Mars in a circular orbit at height 400 km above the surface

PHYSICS · Subjective · Fermi University Physics · Mechanics & Dynamical Systems · Gravitation and central-force motion · Gravitation and central-force motion

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

Problem

An orbiter circles Mars in a circular orbit at height 400 km above the surface, inclined at

45^\circ

to Mars's equator. Using

R_{\rm Mars}=3.390\times10^6\ \mathrm{m}

G_{\rm N}M_{\rm Mars}=4.283\times10^{13}\ \mathrm{m^3\,s^{-2}}

and

J_2=1.96\times10^{-3}

for Mars, calculate the rate at which the orbit's line of nodes drifts, in degrees per day.

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