# A lower bound of the distance between two elliptic orbits

## TL;DR

This paper derives an explicit positive lower bound for the minimum orbit intersection distance (MOID) between two noncoplanar elliptic orbits, enhancing computational efficiency in asteroid catalog analysis.

## Contribution

It introduces a new explicit lower bound for the MOID between two elliptic orbits, improving speed and accuracy in orbit analysis.

## Key findings

- Lower bound is positive unless orbits intersect
- Bound is expressed with elementary functions
- Significant speed improvements in asteroid catalog processing

## Abstract

We obtain a lower bound of the distance function (MOID) between two noncoplanar bounded Keplerian orbits (either circular or elliptic) with a common focus. This lower bound is positive and vanishes if and only if the orbits intersect. It is expressed explicitly, using only elementary functions of orbital elements, and allows us to significantly increase the speed of processing for large asteroid catalogs. Benchmarks confirm high practical benefits of the lower bound constructed.