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#Evolution of Neptune's Orbital Parameters  ##Semi-Major Axis and Orbital Radius  (Figure 1,2)  During the first 10 orbits of the simulation, the semi-major axis of Neptune's orbit radidly decreased from its initial value of 0.5 to about 0.475, in agreement with the analytical prediction that Neptune would initially undergo an inward migration. However, this trend soon reverses. For the next ~150 initial orbital periods, Neptune's semi-major axis gradually rises to a peak value of 0.74, a nearly 50%\ increase from its initial value. The semi-major axis then rapidly decreases down to a value of about 0.475 over the next ~100 initial orbit periods. This trend seems to coincide with the dissapearance of the particle 'ring' which had formed shortly after the beginning of the simulation, and the mixing of particle orbits into a more symmetrical and stable configuration. At about 250 initial orbit periods, Neptune's semi-major axis begins a long, gradual increase until around the 850th orbit. The curve then appears to flatten at a radius of about 0.95, reaching what appears to be atleast a temporary equilibrium. Since the simulation only spans 1000 initial orbit periods, whether or not Neptune's orbit truly stabilized at this time cannot be determined. However, this is one of the most stable periods in the evolution of Neptune's semi-major axis over the course of the simulation.