# Pulsar gravitational binding energy?

A Newtonian homogeneous density sphere has gravitational binding energy in Joules $U = -(3/5)(GM^2)/r$, G=Newton's constant, M=gravitational mass, r=radius, mks. The fraction of binding energy to gravitational mass equivalent, $U/Mc^2$, is then (-885.975 meters)(Ms/r), Ms = solar masses of body, c=lightspeed.

This gives ratios that are less than half that quoted for pulsars (neutron stars), presumably for density gradient surface to core and General Relativity effects (e.g., billion surface gees). Please post a more accurate (brief?) formula acounting for the real world effects.

Examples: 1.74 solar-mass 465.1 Hz pulsar PSR J1903+0327, nominal radius 11,340 meters (AP4 model), calculates as 13.6% and is reported as 27%. A 2 sol neutron star calculates as 16.1% and is reported as 50%. There is an obvious nonlinearity.

Thank you.

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Please edit your post to make your question clearer. Your example is a string of numbers and jargon (e.g. AP4). Also, what is the nonlinearity you are talking about? –  pho Jan 14 '11 at 16:53
One nonrelatvistic effect that accounts for much of this is the density gradient within the NS. The density is a function of pressure (this would be the equation of state), which peaks at the center, so that the average binding energy will be greater than a uniform density model would suggest. –  Omega Centauri Jan 14 '11 at 17:34

Dear Uncle Al, your formula with the coefficient $3/5$ only holds in the Newtonian physics. But obviously, the Newtonian physics is not appropriate for the description of hugely heavy objects such as black holes or neutron stars that are not far from them. You need to use a more complete theory developed by the physicist named Albert Einstein.
It's called the special theory of relativity. Special relativity implies the $E=mc^2$ law - among other things you didn't mention in your question - while general relativity is needed to study very heavy objects that strongly curve the space such as the neutron stars.