New Hamiltonian expansions adapted to the Trojan problem

TL;DR

This paper develops new Hamiltonian expansions tailored for the Trojan problem, enabling analytical prediction of secondary resonance locations crucial for understanding the long-term stability of Trojan asteroids.

Contribution

It introduces adapted Hamiltonian expansions that improve the analytical prediction of secondary resonances in Trojan dynamics.

Findings

Analytical method successfully predicts secondary resonance locations.

Enhances understanding of phase space structure in Trojan systems.

Applicable to both Solar System and extrasolar Trojan bodies.

Abstract

A number of studies, referring to the observed Trojan asteroids of various planets in our Solar System, or to hypothetical Trojan bodies in extrasolar planetary systems, have emphasized the importance of so-called secondary resonances in the problem of the long term stability of Trojan motions. Such resonances describe commensurabilities between the fast, synodic, and secular frequency of the Trojan body, and, possibly, additional slow frequencies produced by more than one perturbing bodies. The presence of secondary resonances sculpts the dynamical structure of the phase space. Hence, identifying their location is a relevant task for theoretical studies. In the present paper we combine the methods introduced in two recent papers (Paez & Efthymiopoulos, 2015, Paez & Locatelli, 2015) in order to analytically predict the location of secondary resonances in the Trojan problem (SEE FILE FOR COMPLETE ABSTRACT)