Long term evolution of the Galileo constellation due to gravitational forces

Abstract

Abstract The Galileo system will be based on a constellation of 30 satellites planned to fly on circular orbits at an altitude of 23,616 km and an inclination of 56° to the equator. At this altitude, satellites orbit in 14 h and 21 min: the Galileo satellites will orbit in a (5,3)-commensurability with the Earth’s rotation which causes resonance effects with the Earth’s gravity field on the orbital motion. Mixed with the effect of third bodies (Moon and Sun), this commensurability is on the basis of a strong instability of the Galileo constellation. This paper is devoted to a modelling of that 4-body system (satellite, Earth, Moon, Sun). Some interesting characteristics of the whole constellation can be deduced. We show that resonance effects considerably modify the initial configuration of the constellation, strongly depending on initial longitudes of satellites if the motion is free-of-manoeuvres. As a result, these resonance effects must be taken into account to perform the necessary Galileo constellation analysis, and to study its long-term evolution.