Abstract:
This work presents an efficient analytical approach for estimating long-term satellite encounter rates using the Center for Space Standards and Innovation’s (CSSI) volumetric encounter method. The method addresses limitations of short-term conjunction analysis by assuming unknown along-track phasing and instead evaluating geometric incursions between orbital paths over extended time horizons. Encounter regions are modeled as swept volumes, including spherical and ellipsoidal shapes defined in relative orbital frames, and encounters are counted in mean anomaly space to derive encounter probability and frequency. Secular and short-period perturbations such as Earth oblateness, drag, solar radiation pressure, and low-thrust maneuvers are incorporated to capture realistic long-term orbital evolution. Extensive Monte Carlo simulations, including cases with tens of millions of samples, are used to validate the analytical results, demonstrating agreement typically better than 0.2 percent while achieving orders-of-magnitude improvements in computational efficiency. Application examples show how the method can estimate encounter rates for individual satellites, entire catalogs, and large constellations across LEO, GEO, and transfer orbits. The results illustrate the rapid growth of encounter rates in the New Space era and demonstrate that volumetric encounter analysis provides a practical, scalable tool for long-term collision risk assessment, space traffic management planning, and orbital sustainability studies.
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Oltrogge, D.L., and Alfano, S., “Efficient assessment of long-term encounter rates with CSSI’s volumetric encounter method,” 6th European Workshop on Space Debris Modeling and Remediation, Milan, Italy, 18-19 May 2022.
