= Roche model of a uniformly rotating star
{c}
{title2=$\phi=-GM/r-\Omega^2\varpi^2/2$}
This approximation represents the <gravitational potential> by a central point mass while retaining the <centrifugal potential>. A surface through polar radius $R_p$ satisfies $R_p/r+q(r/R_p)^2\sin^2\theta/2=1$, where $q=\Omega^2R_p^3/(GM)$. The inner closed surface is regular below $q=8/27$; at the limiting value its equatorial radius is $3R_p/2$ and equatorial effective gravity vanishes. The approximation is useful for illustrating oblateness and <gravity darkening>, rather than modeling the density distribution of every rotating star.
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