On the Moon (mass

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · The equivalence principle and gravity as geometry · The equivalence principle and gravity as geometry

Relativity and Gravitation, Ch Gravity as curved spacetime: redshift and local inertial frames

Problem

On the Moon (mass

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

, radius

R = 1.738\times10^{6}\ \mathrm{m}

, non-rotating, no atmosphere) a clock is thrown vertically upward from a marked point and caught at the same point

T = 6.00\ \mathrm{s}

later. A second, identical clock is held at rest at the marked point throughout. Treat the field as uniform over the flight, and work to first order in

\Phi/c^{2}

and

v^{2}/c^{2}

, with

\Phi

measured from the launch point. Take

G = 6.674\times10^{-11}\ \mathrm{N\,m^{2}\,kg^{-2}}

and

c = 2.998\times10^{8}\ \mathrm{m\,s^{-1}}

. ((a)) Find the surface gravitational field strength

g

of the Moon. ((b)) Find the greatest height above the launch point reached by the thrown clock. ((c)) By how much proper time is the thrown clock ahead of the held clock when they meet again?

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