the latitude to be the angle between a tangent to the meridian and axis of rotation, the total gravity felt at latitude (including the effect of centrifugal force) is
:

This spheroid solution is stable up to a certain (critical) angular momentum (normalized by ), but in 1834, Carl Jacobi showed that it becomes unstable once the eccentricity reaches 0.81267 (or reaches 0.3302).Above the critical value, the solution becomes a Jacobi, or scalene, ellipsoid