model an incompressible liquid under the influence of its own gravity. the completely static solution is a sphere, and there is probably a rotating hydrostatic solution the shape of an oblate ellipsoid. exactly which ellipsoidoid (because might not exactly be an ellipsoid)?
what if general relativity?
if the fluid is allowed to move, then things likely become insane due to Navier-Stokes. turbulence might cause droplets to break off and be ejected faster than escape velocity.
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