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##Evolution of the Proto-Solar Disk  Attached are 11 snapshots of the system in intervals of 10,000 time steps or 90 initial Neptune orbit periods, ranging from shortly after the first initial orbital period to the 900th initial orbit period.   ###Initial Orbit # 0  About one initial orbit period has elapsed since the beginning of the simulation. Neptune (the blue dot) remains at about its initial orbital radius of 0.5. It also lies almost exactly level with the plane of the disk, suggesting that it's orbital inclination has not significantly changed from its initial value of 0. Several particles have already been dispersed to large radii. It was expected that early in the simulation, some particles would take on elliptical orbits, since the initial velocity calculation for every particle relied on the assumption that the Sun was the only enclosed mass. Additionally, a clear ring-like structure of higher particle density has developed around the orbital radius of Neptune. Again, this may be due to a miscalculation in the initial circular velocities of the particles and a particle migration early-on because of elliptical trajectories. However, the fact that the radius of this ring seems to coincide with that of Neptune suggests that gravitational interactions may have played a role. Additionally, it's interesting to note that a small region of space around the Sun, with a radius of about 0.1, has already been completely cleared of particles, and the size of this empty region seems to remain constant over the entire course of the simulation. Excluding the ring-like structure, the group of particles which were quickly dispersed to higher radii, and the empty region around the Sun, the majority of the disk still looks circular with a uniform number density of particles implying that most particles still follow their initial (or similar) trajectories. From a side-view, the disk appears to be equally thick at all radii, suggesting that there isn't much variation in the inclination of particles.   ###Initial Orbit # 180  About 180 initial orbit periods have elapsed since the beginning of the simulation. Neptune appears to have moved slightly further away from the Sun and lies slightly above the plane of the disk, suggesting that it's semi-major axis and inclination have increased from their initial values. The radial extent of the disk appears to have increased as well, which suggests that the semi-major axis of disk particles has increased as well. In fact, we see a more dispersion to higher radii, but more symmetrical than 90 initial orbit periods ago. Any trace of the ring-like structure near the beginning of the simulation has dissapeared. With the exception of the empty region around the Sun, the number density of particles in the disk appears to be higher towards the center and lower towards the edge, as if decreasing with distance from the Sun. Overall, the system appears to be becoming more symmetrical, as the orbits of disk particles more naturally disperse.   ###Initial Orbit # 360  About 360 initial orbit periods have elapsed since the beginning of the simulation. Neptune's orbital radius has grown larger. The system still shows a similar symmetry as it did 90 initial orbit periods ago, with a higher number density of particles near the center and lower number density of particles near the edge, but looks like a smoother exponential trend than before. The radial extent of the disk seems to have increased very slightly.  ###Initial Orbit # 540  About 540 initial orbit periods have elapsed since the beginning of the simulation. Neptune 's orbital radius has grown larger. The disk has retained its shape, for the most part. However, the number density of particles near the Sun seems to be increasing slightly, suggesting disk particles have been migrating inward.   ###Initial Orbit # 720  About 720 initial orbit periods have elapsed since the beginning of the simulation. Viewed along the edge, the disk appears to have becoming slightly 'puffier' in the z-dimension near the edge of the disk than near the center of the system, suggesting that many particles now lie on more highly inclined orbits.   ###Initial Orbit # 900  About 900 initial orbit periods have elapsed since the beginning of the simulation. The shape of the disk has not evolved significantly. The number density of disk particles still appears to fall off with distance from the Sun and the disk appears to have more dispersion in the z-dimension near the edge of the disk than near the center. Neptune's orbital radius appears to be about the same.