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
Read more about this topic: Gravitational Binding Energy
Famous quotes containing the word spheres:
“The world has already learned that woman has other virtues than meekness, patience, humility and endurance. She possesses courage above all fear, and a will that knows no obstacles; and when these are called forth by some great emergency, false modesty is trampled in the dust, and spheres are scattered to the winds.”
—A. Holley, U.S. women’s magazine contributor. The Lily, p. 38 (May 1852)