A novel conjunction filter based on the minimum distance between perturbed trajectories

TL;DR

This paper introduces an analytical conjunction filter that accurately estimates the minimum distance between perturbed Earth orbits by incorporating zonal harmonics, significantly improving conjunction analysis efficiency and reliability.

Contribution

It extends Cook's secular theory to include higher-order eccentricity effects and develops an efficient algorithm for conjunction filtering considering perturbations.

Findings

Achieves sub-kilometer accuracy in 99% of cases

Enables high-efficiency conjunction filtering

Validated with high-fidelity propagator and extensive dataset

Abstract

The increasing congestion in the near-Earth space environment has amplified the need for robust and efficient conjunction analysis techniques including the computation of the minimum distance between orbital paths in the presence of perturbations. After showing that classical Minimum Orbit Intersection Distance (MOID) computation schemes are unsuitable to treat Earth orbiting objects, the article presents an analytical approach to provide a more accurate estimate of the true distance between perturbed trajectories by incorporating the effect of zonal harmonics of arbitrary order. Cook's linear secular theory for the motion of the eccentricity vector is extended to include higher order eccentricity effects and applied to the computation of the minimum and maximum radii attained by two orbits at their mutual nodes, which can be employed to estimate the true distance between the two orbital paths and to establish an efficient algorithm for determining or excluding potential conjunctions. Extensive testing and validation are conducted using a high-fidelity propagator and a comprehensive dataset of resident space objects. The results demonstrate an accuracy below the km level for the orbit distance computation in 99\% of cases, which enables high-efficiency conjunction filtering.