Two instrument packages drift freely at from the centre of the Moon

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

Relativity and Gravitation, Ch Tidal forces and the Newtonian tidal field

Problem

Two instrument packages drift freely at

r = 3.00\times10^{6}\ \mathrm{m}

from the centre of the Moon, of mass

M = 7.35\times10^{22}\ \mathrm{kg}

, treated as a point mass. Their separation is

\xi = 12.0\ \mathrm{m}

, perpendicular to the line joining them to the Moon's centre. Their mutual gravity is ignored and the separation is small compared with

r

, so first-order tidal results apply. Take

x

along the outward radius and

y

along the separation. ((a)) Find the magnitude of their relative acceleration. ((b)) Write the values of

\mathcal{E}_{xx}

and

\mathcal{E}_{yy}

for these axes.

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