A satellite is placed in a circular orbit around the Earth at height 500 km above the…

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

A satellite is placed in a circular orbit around the Earth at height 500 km above the surface, inclined at

63.4^\circ

to the equator. Using

R_\oplus = 6.378\times10^6\ \mathrm{m}

G_{\rm N}M_\oplus = 3.986\times10^{14}\ \mathrm{m^3\,s^{-2}}

and

J_2 = 1.082\times10^{-3}

for the Earth, calculate the rate at which the orbit's line of nodes drifts, in degrees per day, and state whether the node regresses or advances.

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