Gravitational resonances for satellites

Question

I read on the website of European Space Agency that the altitude of Galileo satellites, which is 29600 Km from the center of the Earth, is chosen to avoid gravitational resonances so that station keeping manoeuvres are not needed during the lifetime of a satellite.

Note: I read before that GPS satellites' manoeuvres are controlled from the ground. GPS satellites are at an altitude of 26561 Km.

Note 2: Galieo and GPS satellites are orbiting on circular orbits.

1. What is gravitational resonance?
2. How it is calculated?

Answer 1

The Earth isn't a perfect sphere (or even a perfect oblate spheroid) so its gravitational field is not axially symmetric. You've probably seen the geoid measured by the GOCE and GRACE satellites. As the Earth rotates the asymmetries in its gravitational field rotate with it, and any satellite whose orbital period is a ratio of one day can build up a resonance with the daily variations in the Earth's gravity. This is essentially the same physics as the resonances seen in, for example, the moons of Jupiter.

I had a quick Google and found this paper that gives a fairly detailed analysis of the phenomenon. See in particular section 1.4.

The Galileo satellites orbit 17 times every 10 days. This is sufficiently far from a simple ratio that resonances don't build up.