Since the Earth is flattened at the poles and bulges at the equator, geodesy represents the shape of the Earth with an oblate spheroid. The oblate spheroid, or oblate ellipsoid, is an ellipsoid of revolution obtained by rotating an ellipse about its shorter axis.
We know also that it is not a perfect sphere: the diameter from pole to pole is shorter than the diameter at the equator. The difference is small: the equatorial diameter is about 12,700 kilometers, and the pole to pole diameter is only about 40 km shorter.
This is the shape after the first bifurcation on the Jacobi path. For lack of a better name, and in honour of Poincaré, the name piriform has persisted. The movie shows the full transition, starting from the current shape of the Earth. As the angular momentum increases, the shape becomes an ellipsoid with two equal axes: the MacLaurin ellipsoid. It then reaches a bifurcation point and turns into a Jacobi ellipsoid. At the first bifurcation point on the Jacobi path, we get Poincaré's 'pear'.
Poincaré also came up with the idea that this shape could explain the formation of planets. Imagine that part of the pointed end of the 'pear' (where centrifugal forces are the highest) gets pinched off, and is sent into orbit. However, this is a mechanism that was never confirmed by other studies.
because we are revolving with a ceartain velocilty.