Closed-form perturbation theory in the Sun-Jupiter restricted three body problem without relegation

TL;DR

This paper introduces a closed-form normalization method for analyzing the secular dynamics of small bodies in the Sun-Jupiter system, improving semi-analytical orbit representations without relegation.

Contribution

It presents a novel perturbation theory approach using a book-keeping parameter integrated into Lie series and Poisson brackets, enabling more accurate orbit modeling.

Findings

Effective semi-analytical orbit representation for main-belt asteroids

Enhanced normalization scheme with redefined remainders at each step

Applicable to secular dynamics analysis in the Sun-Jupiter system

Abstract

We present a closed-form normalization method suitable for the study of the secular dynamics of small bodies inside the trajectory of Jupiter. The method is based on a convenient use of a book-keeping parameter introduced not only in the Lie series organization but also in the Poisson bracket structure employed in all perturbative steps. In particular, we show how the above scheme leads to a redefinition of the remainder of the normal form at every step of the formal solution of the homological equation. An application is given for the semi-analytical representation of the orbits of main-belt asteroids.