Risk of collision for the navigation constellations: the case of the forthcoming Galileo

The satellite global positioning systems presently in space are the American NAVSTAR--GPS and the Russian GLONASS. Within this decade the European system, Galileo, should be operational in the same altitude range, dubbed MEO, Medium Earth Orbit. In this paper the fragmentation of a spacecraft related to one of these three constellations has been simulated and the collision risk faced by the operational satellites has been analyzed. Both the intra-constellation and the inter-constellation risk have been studied. An improvement in the collision risk calculation method developed in (Valsecchi et al., Space Debris, 2000) is described in the paper. The new method overcomes the limitation in the application of 'Opik's theory of planetary encounters, dictated by the assumption of random orientation of the argument of perigee and the longitude of node of the projectiles, and allows its application to the Medium Earth orbital regime. In general terms it has been observed the the flux following a generic fragmentation is by far larger than the low background flux in MEO. The strong interrelation of the three constellations has been shown by analyzing the inter-constellation effects of the fragmentations. In particular the GPS and the GLONASS are strongly interacting, while the Galileo constellation, orbiting at somewhat higher altitude, is less affected by any unfortunate event happening in the two lower constellations.