Is the diameter of earth's north pole similar to the south? (Think axis of rotation+ axis of precession)

Question

Earth is an oblate spheroid, not a sphere, since it's rotation around the axis causes it to bulge along the equator.

Is it teally a symetric oblate spheroid though, or also not even that?

To explain: If we combine the effect due to the rotation around the axis, with the precession of the axis itself, is it correct to assume that there should also be some asymmetry between the geographic north and south poles?

Namely that there is at least a small difference between the diameter of the two? If so, how large is it?

Part two: If there is such asymetry, does it change in the duration of a milankovitch cycle?

Answer 1

Yes. By definition of "axis", that is a straight line through the center. Therefore, the angle between the axes of rotation and precession make the same one angle with each other, whether you measure North or south.

Of course, Earth is an oblate spheroid only to some approximation. In reality there are hills and mountains. So if you walked and swam along the imaginary circle spanned by those two axes, you would get more wet I the north, cold in the south, and overall walk a different distance, simply because your distance from the center of Earth was different.