A black hole of mass

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

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

Problem

M = 8.00\,M_\odot

, with

M_\odot = 1.989\times10^{30}\ \mathrm{kg}

, is treated throughout as a point mass, and

2GM/c^{2}

is used only as the school formula for its size. An instrument package falls freely towards it. Take

g = 9.81\ \mathrm{m\,s^{-2}}

and work to first order in the separations, which are small compared with the distance

r

from the hole. ((a)) Find the distance

r

at which the radial tidal stretch across a separation of

1.00\ \mathrm{m}

reaches

10g

. ((b)) At that distance, find the magnitude of the transverse tidal squeeze across a separation of

0.400\ \mathrm{m}

. ((c)) The same question as (a) is now asked for a hole of mass

64.0\,M_\odot

. Using the way

r

depends on

M

, state the factor by which the answer changes and give the new distance.

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