A white dwarf of radius has a surface gravitational field strength of ; it is spherical

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 white dwarf of radius

7.00\times10^{6}\ \mathrm{m}

has a surface gravitational field strength of

2.00\times10^{6}\ \mathrm{m\,s^{-2}}

; it is spherical, so outside it the field is that of a point mass. An interstellar probe coasts in free fall past the star and, at a distance

r = 1.00\times10^{8}\ \mathrm{m}

from its centre, releases two beads at rest relative to itself,

1.00\ \mathrm{m}

apart. The beads are in free fall and their own gravity is negligible. Work to first order in (separation)/

r

, treating the relative acceleration as constant over the interval below. The probe's speed relative to the star is small, so the flyby is Newtonian and the star's frame and the probe's agree for parts ((a)) to (c). A distant station, far from any mass, moves at

0.800c

relative to the probe. Any effect of gravity on clock rates is to be ignored here: include only the time dilation due to the relative speed. (a) Find the relative acceleration of the beads when their separation is perpendicular to the radius. ((b)) Find it when the separation lies along the radius instead. ((c)) For the perpendicular pair, find how much their separation has closed after

10.0\ \mathrm{s}

measured by the probe's own clock. ((d)) What interval does the station's clock record for that same

10.0\ \mathrm{s}

of probe time?

Browse the problem library