An analysis of the Sun-Earth-Asteroid systems based on the two-centre problem

TL;DR

This paper introduces a novel analytical approach to the Sun-Earth-Asteroid system using the two-centre problem, enabling collision risk assessment and the study of complex dynamical structures like transition tori.

Contribution

It presents a new coordinate-based method tailored for analyzing Sun-Earth-Asteroid dynamics, facilitating collision risk evaluation and the existence of transition tori.

Findings

Method effectively assesses collision risk.

Supports existence of chains of transition tori.

Applicable to planar Sun-Earth-Asteroid systems.

Abstract

We propose a new analysis of the two--centre problem particularly suited to be used as a basis to study the dynamics of Sun--Earth--Asteroid systems. Our method, based on a tricky choice of initial coordinates, allows us to evaluate the risk of collisions between the Asteroid and Earth. Moreover, it seems to be fitted to prove the existence of chains of transition tori in the planar Sun--Earth--Asteroid systems.