Fast error-safe MOID computation involving hyperbolic orbits

TL;DR

This paper presents an extended, efficient algorithm for computing the minimum orbital intersection distance (MOID) that accurately handles hyperbolic and mixed orbit types, ensuring high numerical reliability and performance.

Contribution

The authors extend their previous MOID algorithm to include hyperbolic orbits and mixed ellipse-hyperbola cases, improving its applicability and robustness.

Findings

Algorithm accurately computes MOID for hyperbolic orbits.

Benchmarks confirm high numerical reliability and performance.

The method finds all stationary points via roots of a 16th degree polynomial.

Abstract

We extend our previous algorithm computing the minimum orbital intersection distance (MOID) to include hyperbolic orbits, and mixed combinations ellipse--hyperbola. The MOID is computed by finding all stationary points of the distance function, equivalent to finding all the roots of an algebraic polynomial equation of 16th degree. The updated algorithm carries about numerical errors as well, and benchmarks confirmed its numeric reliability together with high computing performance.