Large constellations for fast acquisition and delivery of information: Design and analysis by stereographic projection onto the equatorial plane

Recent space projects are designed by satellite constellations with a large number of spacecraft, a global character (i.e., from equatorial to high inclination orbits), and the possibility to transfer information to different satellites of the constellation (inter satellite link) in order to deliver the information to the ground as soon as possible. To cope with a large number of parameters, a fast tool for constellation design, performance evaluation and networking strategies is needed. The aim of this paper is to obtain the performance of any constellation in less than 1 s, even when the number of satellites in the constellation and the duration of the analysis is large (e.g., more than 200 satellites in a period of some days). The proposed algorithm is based on analytical formulae obtained by using the stereographic projection on the equatorial plane of the satellite orbits and the projection of the target and ground station orbits. It is believed that the two-dimensional projection proposed here can offer some advantages with respect to the spatial analysis of satellite orbits and their ground tracks, such as the reduction in time required to calculate station/satellite and satellite/satellite encounter conditions, and the clear and simple representation of the motion of the satellite of the constellation and of the ground stations of interest. The planar stereographic projection of the orbits of large constellations allows the evaluation of the performance of a constellation of satellites (coverage, revisit time, and intersatellite link) in few seconds even when the number of satellite is high and the period of the ground track is long. Some examples of the efficiency of the proposed approach are given.image