Two boulders of a shattered moonlet fall freely side by side at from the centre of Jupiter

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 boulders of a shattered moonlet fall freely side by side at

r = 4.22\times10^{8}\ \mathrm{m}

from the centre of Jupiter, of mass

M = 1.898\times10^{27}\ \mathrm{kg}

, treated as a point mass. Their separation is

\xi = 50.0\ \mathrm{m}

, perpendicular to the radius. Their mutual gravity is ignored and the separation is far smaller than

r

, so first-order tidal results apply. Use axes with

x

along the outward radius and

y

along the separation. ((a)) Write the values of

\mathcal{E}_{xx}

\mathcal{E}_{yy}

and

\mathcal{E}_{zz}

. ((b)) Find the magnitude of the relative acceleration of the two boulders.

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