One Mass-Radius relation for Planets, White Dwarfs and Neutron Stars

Abstract

We produce the simple formula for the radius R of a cold body of mass M, (4 pi rho/3)^{1/3} R = I.M^{1/3} / [1+ (M/Mp)^{2/3}], where I is one for white dwarfs with non-relativistic electrons, but depends on the ratio of the total mass to Mch, the Chandrasekhar mass. Mp is the mass of the planet of maximum radius and rho is the density of the material at low pressure. Mp and rho are derived in terms of fundamental constants and Mp/Mch is basically given by the three halves power of the fine structure constant. The aim of the discussion is to emphasise physical principles and to connect the masses derived to the fundamental constants, so mathematical niceties are sacrificed and replaced by interpolations between simple exact limits.