A Ptolemaic Approach Improving the Conjunction Analysis Pipeline for Leo

Abstract

Low-Earth-Orbit (LEO) region congestion is becoming one of the big issues of the modern space era. To avoid the Kessler syndrome, now more than ever it is needed to improve awareness about space traffic, and upgrade the entire monitoring process. Extensive literature is available covering the topics of orbital conjunction filtering techniques and computation of the Minimum Orbital Intersection Distance (MOID). The present paper investigates Funding and/or Conflicts of interests/Conflict of interest. An alternative filtering method exploits the near-circularity of certain orbits (a condition often verified in LEO), to improve conjunction analysis performance. Elliptical orbits are reshaped through an auxiliary deferent model, inspired by C. Ptolemy’s orbital theory, replacing the real motion along conjunction analysis. To recover satellites’ averaged mean orbital elements, CelesTrack LEO catalogue was considered and propagated. Based on averaged parameters, off-centric circular orbits are considered instead of elliptical ones. The resulting deferents (off-centric circles) are not far from osculating orbits due to LEOs low eccentricities, becoming the basis for the conjunction analysis algorithm. The algorithm is conceived as a sequence of pre-filters and a final MOID computation. Performances are inspected through an all-vs-all analysis, taking as reference a combination of Hoots’ and Gronchi’s algorithms. This method achieves good performance as compared with these traditional benchmarks. Adopting this approach could reduce the time needed for a preliminary conjunction inspection during the first phases of the Collision Avoidance (CA) process, especially in LEO, where pre-filtering aims to reduce the number of orbit couples where precise MOID computation is needed.