= Main-sequence mass-radius relation
{title2=$R_*\propto M^q$}
An approximate relation between the mass and radius of <main-sequence stars> in a specified composition and mass range. It is not determined by <hydrostatic equilibrium> alone. For gas-pressure <stellar homology> with <Kramers' opacity law>, <radiative diffusion> gives $L\propto\mu^{15/2}M^{11/2}R_*^{-1/2}$. Substitution of $R_*\propto M^q$ gives $L\propto M^{(11-q)/2}$ at fixed composition, explaining precisely which extra radius assumption produces any claimed exponent.
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