New normal form approaches adapted to the Trojan problem

TL;DR

This paper introduces a novel Hamiltonian formulation to analyze Trojan orbits, effectively separating slow and fast dynamics, and demonstrates its success in modeling Trojan motion in Solar System and extrasolar systems.

Contribution

A new Hamiltonian approach tailored to Trojan orbits that isolates secular and librating motions, improving understanding of their dynamics.

Findings

The Basic Hamiltonian model captures key Trojan orbit features.

Model applicability extends to Solar System and extrasolar planetary systems.

Effective separation of temporal scales enhances dynamical analysis.

Abstract

The main subject of this work is the study of the problem of the Trojan orbits from a perturbative Hamiltonian perspective. We face this problem by introducing first a novel Hamiltonian formulation, exploiting the well-differentiated temporal scales of the Trojan motion. The resulting Hamiltonian allows to separate the secular (very slow) component of the motion from the librating and fast degrees of freedom. This decompositon provides the foundation of a so-called Basic Hamiltonian model (Hb), i.e. the part of the Hamiltonian for Trojan orbits independent of all secular angles. Our study shows that, up to some extent, the model Hb successfully represents the features of the motion under more complete models, in a range of physical parameters relevant for dynamics in the Solar System or in extrasolar planetary systems. (continues...)