Model the Moon as a static sphere of uniform density with mass and radius

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Newtonian gravitation as a field theory · Newtonian gravitation as a field theory

Relativity and Gravitation, Ch Gravitational field, potential and Gauss's law for gravity

Problem

Model the Moon as a static sphere of uniform density with mass

M = 7.346 \times 10^{22}\ \mathrm{kg}

and radius

R = 1.737 \times 10^{6}\ \mathrm{m}

, with no other body contributing to the field. Take

G = 6.674 \times 10^{-11}\ \mathrm{N\,m^{2}\,kg^{-2}}

and

\Phi = 0

at infinity. ((a)) Find the magnitude of the gravitational field strength at the surface. ((b)) Find the gravitational potential at the surface. ((c)) In this uniform model, find the depth below the surface at which the magnitude of the field strength is

0.40

of its surface value.

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