A survey rod is carried past a station at with its length along the direction of motion

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Newtonian gravitation as a field theory · Special relativity: spacetime and kinematics

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

Problem

A survey rod is carried past a station at

v = 0.600c

with its length along the direction of motion, and the station measures its length as

1.60\ \mathrm{m}

. The same rod is later delivered to a probe in free fall near a neutron star of radius

1.20\times10^{4}\ \mathrm{m}

whose escape speed at its surface is

1.60\times10^{8}\ \mathrm{m\,s^{-1}}

. At a distance

r = 1.00\times10^{5}\ \mathrm{m}

from the star's centre, two small test masses are released from rest relative to the probe, separated by the rod's proper length. The star is spherical, so outside it the field is that of a point mass; the test masses are in free fall, and their own gravity is negligible. Work to first order in (separation)/

r

. ((a)) Find the proper length of the rod. ((b)) Find the relative acceleration of the two test masses when their separation lies along the radius, and say whether it is a stretch or a squeeze. ((c)) Find the relative acceleration for the same separation placed perpendicular to the radius, and say whether it is a stretch or a squeeze.

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