The Earth is classified as an oblate spheroid, characterized by a polar radius shorter than its equatorial radius, which ensures stability and prevents tumbling. If the polar radius were to exceed the equatorial radius, the Earth would adopt a spindle shape, leading to instability and potential tumbling. The discussion highlights that while oblate spheroids and oblate ellipsoids are effectively the same, larger celestial bodies tend to collapse into spherical shapes due to gravitational forces. Tidal forces can also deform celestial bodies into prolate ellipsoids, with consequences similar to excessive spin, including potential disintegration at the Roche limit.
PREREQUISITESAstronomers, astrophysicists, and students of planetary science will benefit from this discussion, particularly those interested in the stability and shape of celestial bodies.
Brilliant responses. My post should have been r^2/a^2 + z^2/b^2 = 1. Will study the references, and thanks!Bandersnatch said:Oblate spheroid and oblate ellipsoid are the same thing, no? One axis shorter than the remaining (and equal) two.
Anyhow. Other than spin doing the oblate thing, tidal forces try to deform bodies into prolate ellipsoids. The possible consequences of this process are similar to those of excessive spin, and may include disintegration when self-cohesion forces are exceeded (cf. 'Roche limit'). Use tidal forces responsibly. Keep away fromchildrendwarf planets.
It's not a planet, but Haumea is in hydrostatic equilibrium or very close to it with three different axes. The fast rotation makes this a stable configuration.Ibix said:And I don't think it's possible to have a planet with three different values for ##a##, ##b## and ##c##. An asteroid or small moon, sure, but anything larger will collapse under its own weight into pretty near a sphere. That may be made oblate due to spin, but the spin implies rotational symmetry about the spin axis.