The Lifetimes of Earth Trojan Asteroids and Tadpole Orbits

Trojan asteroids orbit the Sun but remain bound to the Lagrange points, L4 (60° leading) or L5 (60° trailing) of a planets orbit. In the circular three-body approximation the stability of a massless Trojan asteroid depends on the ratio of the host planet mass and the central mass, in our case the Sun. For the inner planets, the range for theoretical stability does become increasingly small, making primordial Trojans rare or unlikely. The detection of one Earth Trojan 2010 TK₇ and several Mars Trojans and 2013 ND₁₅ a possible Venus Trojan shows that inner Trojan populations do exist today, though the estimated lifetimes of known inner system Trojans are less than a million years. We use simulation to place constraints on possible Earth Trojan populations and to determine likelihoods of the existence of primordial Earth Trojans. We injected Earth Trojans through a random sampling of Keplerian orbital elements and use the n-body particle code REBOUND to simulate our solar system. We model the injected Earth Trojan asteroids, Sun, and eight planets. The initial planetary positions are gathered from the JPL HORIZONS system at an epoch of JD2458475.30035. For our first model we find that roughly 0.47% of our Earth Trojans remain after 20 Myr of simulation. ETAs that remain have initial orbits with semi-major axes in the range of 0.996–1.005 au, eccentricities of 0–0.3 and inclinations of 0°–40° with a strong instability for orbits near 20° inclinations. These ranges of orbital stabilities are consistent with previous simulations of Earth Trojan Asteroids. The rate of loss of Earth Trojans in our model decays logarithmically and indicates zero Earth Trojans will remain by 250 Myr. This result is influenced by our initial asteroid distributions so further work is being done to better constrain this result.