Proper elements for resonant planet-crossing asteroids

TL;DR

This paper develops a new method to compute proper elements for resonant, planet-crossing asteroids, accounting for their mean-motion resonance effects, which improves the accuracy of long-term orbital evolution descriptions.

Contribution

It introduces a novel technique for calculating proper elements of resonant NEOs, addressing limitations of previous methods designed for non-resonant asteroids.

Findings

Proper elements of known resonant NEOs are provided.

Resonance effects significantly influence proper element calculations.

The new method improves accuracy over non-resonant models.

Abstract

Proper elements are quasi-integrals of motion, meaning that they can be considered constant over a certain timespan, and they permit to describe the long-term evolution with a few parameters. Near-Earth objects (NEOs) generally have a large eccentricity and therefore they can cross the orbits of the planets. Moreover, some of them are known to be currently in a mean-motion resonance with a planet. Thus, the methods previously used for the computation of main-belt asteroid proper elements are not appropriate for such objects. In this paper, we introduce a technique for the computation of proper elements of planet-crossing asteroids that are in a mean-motion resonance with a planet. First, we numerically average the Hamiltonian over the fast angles while keeping all the resonant terms, and we describe how to continue a solution beyond orbit crossing singularities. Proper elements are then extracted from a frequency analysis of the averaged orbit-crossing solutions. We give proper elements of some known resonant NEOs, and provide comparisons with non-resonant models. These examples show that it is necessary to take into account the effect of the resonance for the computation of accurate proper elements.