Information routing in satellite constellations via stereographic projection and static digraph

Satellite constellations are receiving growing attention as they become fundamental to modern space applications. Because intersatellite communication is being included in these networks, optimizing data routing is crucial to ensure efficient, timely, and reliable information transfer. This study introduces a novel method to optimize information routing in satellite constellations and provides numerical evaluation of its performance. The stereographic projection onto the equatorial plane is used to derive analytical equations that allow the rapid identification of the mutual connectivity opportunities between any pair of satellites within a desired time horizon. These connectivity events are used as states to build a Markov decision process, in which actions consist of either forwarding data or withholding it. The resulting directed graph (digraph) models the information routing process, applying both (a) value iteration and (b) Dijkstra’s algorithms. Value iteration (a) allows defining the optimal policy for each satellite — whether forward or withhold data — so as to minimize the time required to transfer information to the target satellite. Dijkstra’s algorithm (b) is employed to identify minimum-latency and minimum-hop paths for data transfer between satellites within the constellation. Numerical simulations are performed on Walker constellations of 32 through 128 satellites, with a maximum intersatellite distance ranging from 500 to 2500 km. The results show that the minimum latency is limited (typically, tens of minutes), while the minimum-hop count is in the interval [1,32], depending on the constellation size and maximum intersat distance. Simulations demonstrate the effectiveness of this approach in optimizing information flow across medium-size constellations dedicated to Earth observation, monitoring, and remote sensing.