The orbit of 2010 TK7. Possible regions of stability for other Earth Trojan asteroids

TL;DR

This study investigates the stability and potential for additional Earth Trojan asteroids near Lagrange point L4, combining analytical and numerical methods to understand the dynamics and stability regions of such objects.

Contribution

It provides a comprehensive analysis of the stability of 2010 TK7 and explores the likelihood of discovering other Earth Trojans through phase space and numerical simulations.

Findings

2010 TK7 is in an unstable orbit near a stable zone edge

Potential for additional Earth Trojans exists in certain stable regions

Numerical simulations estimate capture and escape probabilities

Abstract

Recently the first Earth Trojan has been observed (Mainzer et al., ApJ 731) and found to be on an interesting orbit close to the Lagrange point L4 (Connors et al., Nature 475). In the present study we therefore perform a detailed investigation on the stability of its orbit and moreover extend the study to give an idea of the probability to find additional Earth-Trojans. Our results are derived using different approaches: a) we derive an analytical mapping in the spatial elliptic restricted three-body problem to find the phase space structure of the dynamical problem. We explore the stability of the asteroid in the context of the phase space geometry, including the indirect influence of the additional planets of our Solar system. b) We use precise numerical methods to integrate the orbit forward and backward in time in different dynamical models. Based on a set of 400 clone orbits we derive the probability of capture and escape of the Earth Trojan asteroids 2010 TK7. c) To this end we perform an extensive numerical investigation of the stability region of the Earth's Lagrangian points. We present a detailed parameter study in the regime of possible stable tadpole and horseshoe orbits of additional Earth-Trojans, i.e. with respect to the semi-major axes and inclinations of thousands of fictitious Trojans. All three approaches underline that the Earth Trojan asteroid 2010 TK7 finds himself in an unstable region on the edge of a stable zone; additional Earth-Trojan asteroids may be found in this regime of stability.