A white dwarf has mass with

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

Relativity and Gravitation, Ch Gravitational field, potential and Gauss's law for gravity

Problem

A white dwarf has mass

M = 1.00\,M_\odot

with

M_\odot = 1.989 \times 10^{30}\ \mathrm{kg}

, and radius

R = 7.0 \times 10^{6}\ \mathrm{m}

, about the radius of the Earth. Estimate its gravitational self-energy by treating it as a cold uniform sphere assembled at rest, for which

E_{\rm grav} = -3GM^{2}/5R

. Take

G = 6.674 \times 10^{-11}\ \mathrm{N\,m^{2}\,kg^{-2}}

and

c = 2.998 \times 10^{8}\ \mathrm{m\,s^{-1}}

. ((a)) Estimate

|E_{\rm grav}|/Mc^{2}

, the uniform-sphere estimate of the star's gravitational mass defect as a fraction of its rest energy. ((b)) Estimate

|E_{\rm grav}|

in joules. ((c)) Estimate the mass equivalent of this energy in kilograms. Say why the mass actually missing from the star is smaller than this, and why the number itself is only an estimate of the scale.

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