Gravitational Binding Energy - Non-uniform Spheres

Non-uniform Spheres

Planets and stars have radial density gradients from their lower density surfaces to their much larger density compressed cores. Degenerate matter objects (white dwarfs; neutron star pulsars) have radial density gradients plus relativistic corrections. Dave Typinski demonstrates iron-cored Earth's homogeneous average density gravitational binding energy value is 31% larger than its more accurate integrated-over-density vs. radius value. The moon's homogeneous average density gravitational binding energy value is 1.8% higher than its more accurate mantle plus core radial density value.

Neutron star relativistic equations of state provided by Jim Lattimer include a graph of radius vs. mass for various models. The most likely radii for a given neutron star mass are bracketed by models AP4 (smallest radius) and MS2 (largest radius). BE is the ratio of gravitational binding energy mass equivalent to observed neutron star gravitational mass of "M" kilograms with radius "R" meters,

Given current values

and star masses "M" commonly reported as multiples of one solar mass,

then the relativistic fractional binding energy of a neutron star is