 Mass-radius relation

A mass-radius relation connects the sizes of a class of self-gravitating objects with their masses. It encodes both material properties and the mechanism supporting the object against gravity. For an illustrative sequence of uniform, fixed mass density $\rho$, the identity $M=4\pi \rho R^3/3$ gives $R\propto M^{1/3}$. Real self-compression changes that scaling.

A planetary mass-radius relation depends strongly on composition and any gas envelope. In compact objects, electron degeneracy pressure can make a larger mass correspond to a smaller radius. A relation therefore applies to a stated family under stated assumptions, rather than every object obeying one universal size law. Deviations can test an equation of state, but can also reflect differences in composition or age.