A sealed laboratory falls freely near Mars (mass

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

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

Problem

A sealed laboratory falls freely near Mars (mass M=6.42×1023 kgM = 6.42\times10^{23}\ \mathrm{kg}, treated as a non-rotating sphere) at a distance r=4.00×106 mr = 4.00\times10^{6}\ \mathrm{m} from the planet's centre. Two small test masses are released at rest relative to the laboratory, one directly above the other along the line to the planet's centre, a distance L=2.00 mL = 2.00\ \mathrm{m} apart. Take G=6.674×10−11 N m2 kg−2G = 6.674\times10^{-11}\ \mathrm{N\,m^{2}\,kg^{-2}}. Treat rr as effectively constant over the times asked about. ((a)) Find the magnitude of the relevant component of the tidal field, ∣Err∣|\mathcal{E}_{rr}|, at this distance, and say whether the pair stretches or converges. ((b)) Find the change in their separation after 10.0 s10.0\ \mathrm{s}. ((c)) For how long does this laboratory count as an inertial frame if separations of this pair can be measured to a resolution δ=0.50 mm\delta = 0.50\ \mathrm{mm}?

Browse the problem library