Up&Down: Not quite spherical Earth

In the recent mailbag column on how up and down are defined with relation to the Earth’s surface http://www.straightdope.com/mailbag/mdownup.html , it was said in part:

However, there is one case in which the oblateness of the Earth does make a crucial difference- in the orbit of satellites.

If the Earth were an exact perfect sphere, the orbit of a satellite would remain fixed with respect to the stars indefinitely. (Not counting orbital decay due to atmospheric drag, or very tiny perturbations due to the sun’s gravity, etc.) Because the Earth does have that equatoral bulge however, the plane of a satellite’s orbit will gradually shift, and if the orbit is elliptical, the apogee or high point of the orbit will shift as well. In fact, in order to rendevous with a satellite or space station, it’s necessary to even take into account smaller second-order deviations from a perfect sphere, such as the fact that the northern and southern hemisphers aren’t symmetrical.