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Quantifying long-term statistical properties of satellite trajectoriestypically 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 trajectorypropagation-derived results. We extend the approach in Graven and Lo (2019) toestimate: (1) Satellite-ground station coverage with limited satellite field ofview and ground station elevation angle with numerically optimized formulae,and (2) long-term averages of general functions of satellite position. Thismethod is fast enough to facilitate real-time, interactive tools for satelliteconstellation and network design, with an approximate $1000\times$ GPU speedup.

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