A numerical exploration of the evolution of Trojan-type asteroidal orbits

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Asteroids, Orbital Mechanics, Solar Orbits, Solar System, Trojan Orbits, Liapunov Functions, Many Body Problem, Numerical Integration, Orbital Elements

Scientific paper

The evidence for stability of Trojanlike orbits for all the major planets in the solar system is discussed. For Saturn, Uranus, and Neptune the results are derived from 20 million year numerical orbit integrations, which demonstrate the stability of tadpole-type Trojan orbits for at least that time. The evolution of many unstable orbits is also followed. Several of these show an interesting tendency to spend long periods of time in orbits resembling that of Pluto. It is evident that there are many other resonances, mainly with Neptune, which can trap the asteroid for prolonged periods of time. For the inner planets, the stability is examined in terms of the results from a 2.25 million year numerical integration. The results indicate the existence of long-terms stability for both tadpole and horseshoe type orbits of asteroids coorbital with Venus, earth, and Mars.

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