I read on Wikipedia that if the Angular Velocity of a star is above its Critical Angular Velocity, it reaches hydrostatic equilibrium in the shape of a Jacobi Ellipsoid.

But how exactly would I find the Critical Angular Velocity of the body to begin with? And if it is okay to ask this further question, "and at still faster rotation it is no longer ellipsoidal but piriform or oviform, with yet other shapes beyond that, though shapes beyond scalene are not stable", how can I find the upper bound in which it becomes piriform or oviform? As I am trying to avoid that, I want to be able to find out upper and lower bounds of a Jacobi Ellipsoid star.



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