The stability of Uranus Trojans over the age of the Solar system

Abstract

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°, 5°, 15°, and 30° relative to the ecliptic plane. Initial eccentricities ranged from 0 to 0.1 for i0 = 0° and 5°, and 0 to 0.2 for i0 = 15° and 30°. 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° from the nominal L4 Lagrange point, and orbits in the L5 swarm had mean longitudes 18.2° from the nominal L5 point. I integrated 10 000 massless clones per nominal orbit in the six-body problem (Sun, test particle, and 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 per cent were associated with the nominal orbit with i0 = 0° 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, 286, 56, and 237 Myr for nominal orbits with i0 = 0°, 5°, 15°, and 30°, respectively. The half-lives associated with L5 orbits were 103, 281, 25, and 46 Myr, respectively. The overall results showed that the ecliptic plane is one good place to search for primordial Uranus Trojans.