[Atomic-S (OP)]

Consider a planet of  uniform density composed of a plastic substance, spinning so that it has a substantial equatorial bulge. Assuming Newtonian physics, is the shape of this planet a true ellipsoid, or some other shape?

[guest39538]

Consider a planet of  uniform density composed of a plastic substance, spinning so that it has a substantial equatorial bulge. Assuming Newtonian physics, is the shape of this planet a true ellipsoid, or some other shape?

The shape is an oblate so I believe.

[evan_au]

The "ideal" spinning shape would have two equatorial axes of the same length (a=b), with the axis of rotation being a smaller distance (c<a=b). This makes it an oblate spheroid. Isaac Newton proved this.

The shape of the Earth if it were made entirely of water is called the Reference Ellipsoid.

GPS uses a more complex shape called the Geoid, which takes into account the fact that the density of the Earth varies slightly from place to place, causing the ocean to "pile up" in some places. Part of these density variations are due to the continents and the ocean basins. GPS measures the height above sea level as the height above the Geoid.