A free-falling apparatus of length is released just above the Moon's surface

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

The Geometry of Gravity, Ch The tidal field: what free fall cannot remove

Problem

A free-falling apparatus of length

\ell = 2.0\ \mathrm{m}

is released just above the Moon's surface, radius

R_{\rm Moon} = 1.737\times10^{6}\ \mathrm{m}

and mass

M_{\rm Moon} = 7.342\times10^{22}\ \mathrm{kg}

. Its instruments can resolve a relative displacement of

d_{\rm res} = 10\ \mathrm{nm}

. Use

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

and the locality bound

\tfrac12|\mathcal{E}|\ell\,\Delta t^2 < d_{\rm res}

. ((a)) Estimate how long the apparatus stays inertial at this resolution when it is held with its long axis vertical (radial). ((b)) Estimate how long it stays inertial when it is held horizontal (transverse), and give the ratio of the two times.

Browse the problem library