I think you may have misunderstood the GPS satellite system. The reason the USAF have to reset the GPS clock every day is because they are slightly further away from the gravity-well that is the earth so are fractionally less affected than we are. As they are in a geostationary orbit they would be travelling through space at the same speed as ourselves so I don't see their relative speed as a factor here. At least that's what Brian Cox said on the BBC recently and he's a nuclear physics professor at CERN so I'm going with him