mass-radius relation

A mass-radius relation is an equation relating a star's mass with its radius. A very rough version for main sequence stars (in units of Rsun and Msun) relates the radius to an exponent of the mass:

R = M0.8

One adjusted version based upon observation:

log R = 0.003 + 0.724 log M

This latter is based on a least-squares fit to find the best exponent and constant of proportionality to fit data covering main sequence stars over a variety of masses and radii, the data derived from eclipsing binaries and radial velocities. Better fits are found by limiting the interval of mass values, such as varying the constants based upon the mass. The mass-limit regarding whether a star has significant convection is one of the criteria for choosing which of such more specific relations. Along with the mass-luminosity relation and color index, this relation can be used for rough stellar parameter determinations.

Such mass-radius relations have been developed for other types of astronomical objects, such as planets (e.g., gas planets) and white dwarfs.