Model Mars as a 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 Mars as a sphere of uniform density with mass

M = 6.417 \times 10^{23}\ \mathrm{kg}

and radius

R = 3.390 \times 10^{6}\ \mathrm{m}

. It is not rotating, and no other body contributes to the field. Take

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

and the gravitational potential to be zero at infinity. ((a)) Find the magnitude of the gravitational field strength at the surface. ((b)) Find the gravitational potential at the surface. ((c)) Find the magnitude of the field strength at a point halfway from the centre to the surface, at

r = R/2

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