Investigation of evolution of orbits similar to that of (4179) Toutatis

This project compared the orbital evolution of asteroid (4179) Toutatis to that of several fictitious asteroids in similar orbits. The nominal orbit of Toutatis along with orbits with varying initial values of inclination and eccentricity were numerically integrated for a period of 10,000 years. A limited run of 1,500 years using the nominal orbit for Toutatis but with a different timestep confirmed the effect of its highly chaotic behavior on attempts to numerically integrate this orbit. Runs with various inclinations showed a variety of chaotic behaviors resulting from the frequent close encounters with the inner planets. Dependence of the frequency of encounters on the orbital inclination relative to the inner planets was observed. Encounters usually but not always disrupted the 3:1 mean motion resonance with Jupiter. A test using the orbital elements of Toutatis but an eccentricity of 0.0 showed periodic behavior with the eccentricity increasing to 0.12 in a period of 10,000 years.