Jacobi Ellipsoid

Relevant to this is the J2 Perturbation [1], commonly used when accurately modeling the Earth as an oblate spheroid (like in the article image, but less drastic) rather than a perfect sphere. This has resultant effects on orbits, such as the "gravity wells" in the GEO belt at 105degW and 75degE. There are higher-order perturbations [2] as you closer approximate the Earth's actual shape, such as J3, J4, etc.

[1] https://ai-solutions.com/_freeflyeruniversityguide/j2_pertur...

[2] https://oer.pressbooks.pub/lynnanegeorge/chapter/chapter-10-...

That page didn't have a formula, in either cartesian or polar coordinates, for the shape of the object. Lots of formulas, but I didn't see anything I could use to create a 3d mesh and print one of these things out on my printer.

This is surprising, but less surprising when you realise it is rotating about one of the foci, not the centre.