A Rapid Method For Orbital Coverage Statistics With $\mathbf{J_2}$ Using Ergodic Theory

TL;DR

This paper introduces a rapid, ergodic theory-based method to analytically estimate long-term orbital coverage statistics for J2-perturbed satellites, enabling real-time satellite network design with significant computational speedup.

Contribution

It extends previous ergodic methods to include coverage and ground station elevation angle estimates, providing a fast, analytical alternative to trajectory propagation.

Findings

Achieves approximately 1000x GPU speedup.

Broadly agrees with traditional trajectory propagation results.

Enables real-time satellite constellation analysis.

Abstract

Quantifying long-term statistical properties of satellite trajectories typically entails time-consuming trajectory propagation. We present a fast, ergodic\cite{Arnold} method of analytically estimating these for $J_2-$perturbed elliptical orbits, broadly agreeing with trajectory propagation-derived results. We extend the approach in Graven and Lo (2019) to estimate: (1) Satellite-ground station coverage with limited satellite field of view and ground station elevation angle with numerically optimized formulae, and (2) long-term averages of general functions of satellite position. This method is fast enough to facilitate real-time, interactive tools for satellite constellation and network design, with an approximate $1000\times$ GPU speedup.