deletions | additions       diff --git a/Conclusions.md b/Conclusions.md  index 5fdcd3a..bdb71b7 100644  --- a/Conclusions.md  +++ b/Conclusions.md 
...
#Conclusions  The general shape of the proto-solar system evolved significantly over time, undergoing the most drastic changes near the beginning of the simulation. Early-on, many disk particles were dispersed into orbits higher than the edge of the initial 0.1 radius disk, and a dense ring-like structure formed in the vicinity of the orbit of Neptune. As particles began to deviate from their randomly assigned trajectories, and assume a more natural distribution, the number density of the disk evolved from being uniform to one which has a clear radial dependence - decreasing with larger radii. At all stages of evolution, a 0.1 radius region around the Sun remained almost completely void of particles - an unstable a  region where particles are unable to enter and maintain stable orbits. As the disk evolved, a few major trends were observed. The disk grew radially due to disk particles being dispersed into higher orbits, and and the disk slightly expanded in the z-direction (becoming thicker, particularly near the edges.) This expansion in the z direction suggests an increase in the orbital inclination of particles, as it requires that particles follow more tilted trajectories relative to the plane of the disk. Neptune gradually migrated outward, apparently stabilizing near the end of the simulation at a radius slightly smaller than the initial edge of the disk. This result mirrors that of Gomes (2004), in which a similar migration and stabilization was observed. A notable difference, however, is that Gomes included a Jupiter-like planet, which cleared out particles with an angular momentum less than that of Neptune, and thus assisted Neptune's outward migration. Though the mechanism responsible for the migration of Neptune in this simulation is unclear, it seems to have been sensitive to the local density of particles. It appears that the formation and dissapearance of a dense ring of material in which Neptune was embedded may have been responsible for an early reversal of the direction in which it migrated. Neptune continued to migrate outwards, so it must have been continuously accelerated in the direction of its motion by nearby particles, As it approached the edge of the disk, this driving mechanism must have dwindled, since the semi-major axis and orbital period began to stabilize. The semi-major axis and orbital period of Neptune, on average ,increased over time. The eccentricity, though highly variable, seemed to oscillate about the same average value over the entire course of the simulation. Neptune remained bound to the system, but diverged considerably from it's initial circular orbit, midway between the Sun and the edge of the disk.