Abstract:
Presented here is a planning and characterization tool to estimate satellite encounter rates for a prospective orbit regime. The prescribed method can be used to estimate the satellite conjunction operational tempo (i.e., the pace of conjunction activity associated with the operation of a satellite) for a given orbit against a satellite catalog. The encounter volume is defined by an ellipsoid that is constant in size, shape, and orientation in the satellite’s Radial-InTrack-CrossTrack frame. For a given pair of satellites, we evaluate volumetric proximity by defining a traveling ellipsoid about the second satellite’s Keplerian orbit and assessing if/when the first satellite’s orbit traverses it; if inside the volume it is considered proximate. To ensure that no encounter is missed, the ellipsoid is moved along the second satellite’s circular or elliptical orbit in increments of true anomaly corresponding to in-track movement much smaller than the ellipsoid’s minor axis. An incremental determination of encounter probability is made if/when the first satellite’s orbit track contacts the ellipsoid. When this takes place, the orbit true anomalies at ellipsoid entry and exit are captured for both satellites and converted to their respective mean anomaly ranges. The likelihood that both satellites will simultaneously be inside that encounter region is then determined from these ranges. In addition to estimating probability, the number of expected encounters over a given time span can also be approximated. The method is valid for both coplanar and non-coplanar orbits. However, our assumption of uniformly distributed, relative in-track positions is not applicable in all satellite pairings. This trending tool is also useful in identifying such regions as graveyard orbits that are least likely to produce encounters. It can also be used to estimate how often neighboring satellites will trigger volumetric warnings when considering a candidate orbit.
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5. Alfano, S and Oltrogge, D.L., “Volumetric assessment of satellite encounter rates,” Acta Astronautica 2018, https://doi.org/10.1016/j.actaastro.2018.09.030, 1 October 2018, accessible at https://comspoc.com/Resources/Content/Private/C-20220424T140946/Paper/Volumetric%20assessment%20of%20satellite%20encounter%20rates_Golden_Open_Access_AA_FINAL.pdf
