A Rapid Method for Orbital Coverage Statistics with J2 Using Ergodic Theory

Abstract

Quantifying long-term statistical properties of satellite trajectories typically entails time-consuming trajectory propagation. We present a fast, ergodic1 method of an- alytically estimating these for J2− perturbed elliptical orbits, broadly agreeing with trajectory propagation-based values. We extend the approach in Graven and Lo (2019)2 to estimate: (1) Satellite-ground station coverage with limited satellite field of view and ground station elevation angle with numerically optimized for- mulae, and (2) long-term averages of general functions of satellite position. This method is fast enough to facilitate real-time, interactive tools for satellite constel- lation and network design, with an approximate 1000× GPU speedup.