A visitor of height m

PHYSICS · Subjective · 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

A visitor of height

1.7

m, falling freely head-first towards a black hole, will tolerate a head-to-foot tidal stretch of at most about

15\ \mathrm{m\,s^{-2}}

. Estimate the smallest mass of black hole for which the visitor can reach the distance

r = 2GM/c^{2}

(the school size of the hole) with the stretch still below that limit. Treat the hole as a Newtonian point mass, use the first-order radial stretch with the visitor's height along the radius, and treat head and feet as free particles. Take

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

c = 2.998\times10^{8}\ \mathrm{m\,s^{-1}}

and

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

. Give the answer to one significant figure in kg and in solar masses.

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