The Stability of Uranus Trojans Over the Age of the Solar System

TL;DR

This study assesses the long-term stability of hypothetical Uranus Trojan orbits over 4.5 billion years, revealing that low-inclination L4 Trojans are most likely to survive, suggesting the ecliptic plane as a prime search area.

Contribution

It provides the first extensive numerical analysis of Uranus Trojan stability over the age of the Solar System, highlighting the importance of initial inclination and orbit location.

Findings

L4 Trojans with i0=0° have the longest half-life (~1258 Myr).

Most surviving Trojans are associated with low-inclination orbits.

Ecliptic plane is a promising region for primordial Uranus Trojans.

Abstract

The stability of eight nominal fictitious Uranus Trojan orbits over the age of the Solar system has been measured. The initial inclinations, i0, were 0 deg., 5 deg., 15 deg., and 30 deg. relative to the ecliptic plane. Initial eccentricities ranged from 0 to 0.1 for i0 = 0 deg., 5 deg., and 0 to 0.2 for i0 = 15 deg., 30 deg. Half of the orbits were in the L4 swarm, and half were in the L5 swarm. Orbits in the L4 swarm had mean longitudes 8.8 deg. from the nominal L4 Lagrange point, and orbits in the L5 swarm had mean longitudes 18.2 deg. from the nominal L5 point. I integrated 10,000 massless clones per nominal orbit in the six-body problem (Sun, test particle, four giant planets) for 4.5 Gyr and calculated the half-life for each orbit. A total of 1291 test particles survived for the entire integration time. Of these survivors, 99% were associated with the nominal orbit with i0 = 0 deg. in the L4 swarm. These surviving test particles had initial eccentricities in the range e0 < 0.07. The half-lives associated with L4 orbits were 1258 Myr, 286 Myr, 56 Myr, and 237 Myr for nominal orbits with i0 = 0 deg., 5 deg., 15 deg., and 30 deg., respectively. The half-lives associated with L5 orbits were 103 Myr, 281 Myr, 25 Myr, and 46 Myr, respectively. The overall results showed that the ecliptic plane is one good place to search for primordial Uranus Trojans.