> It will not greatly affect the orbit of any satellite, because the Earth's center of gravity can't be shifted ...
Even if the center of gravity is not moved, there is an impact on trajectories. We are used to use a simplification that consider only the gravity center (using this theorem http://en.wikipedia.org/wiki/Shell_theorem) but this theorem doesn't apply if we want to be really precise.
Is it the case that you might explain such a thing with words that look something like "Some small effect from a different mass distribution will be caused and it will have to be taken into effect, but when you care about these effects as far as I know you have to measure them empirically anyhow, because if you care at that level of detail it turns out there's a lot of noise as the Earth warms and cools and has various flows within it and as water moves hither and yon and so on. So while it will have some effect it is merely one of very many such things."? If only I had thought to add such words to my original post. Alas.
Even if the center of gravity is not moved, there is an impact on trajectories. We are used to use a simplification that consider only the gravity center (using this theorem http://en.wikipedia.org/wiki/Shell_theorem) but this theorem doesn't apply if we want to be really precise.