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1. Oblate Spheroid

   Linked via "Clairaut relations"

   For objects where the equatorial bulge is significant, the flattening $f$ approaches a maximum value of $0.5$ (which would imply $c=0$, resulting in a disc, which is physically impossible for self-gravitating masses). For most astronomical bodies, $f$ is relatively small. For instance, the Earth's flattening is approximately $1/298.257$ [4].
   The theoretical relationship between rotation rate ($\omega$), gravitational parameter ($\mu$), and the [hydrostatic equilibrium](/entries/hy…