Estimate how close a m long piece of a human body could be taken to a black hole of…

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

Estimate how close a

1.0

m long piece of a human body could be taken to a black hole of mass

M = 15\,M_\odot

before the tidal stretch across that metre becomes seriously dangerous. Take the danger threshold to be a relative acceleration of about

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

across

1.0

m, roughly three times the acceleration of free fall at Earth's surface (

g \approx 9.8\ \mathrm{m\,s^{-2}}

). Treat the hole as a Newtonian point mass, take the metre to lie along the radius, treat its ends as free particles, and use the first-order tidal expression. Take

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

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

and

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

. ((a)) Estimate this distance to one significant figure. ((b)) Estimate, to one significant figure, how many times the hole's school size

2GM/c^{2}

this distance is.

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