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##Data Analysis  To study the evolution of the proto-solar system model, I analyzed how the orbital parameters of the particles and Neptune changed over the course of the simulation. I particularly focused on the orbit parameters of Neptune, which could be studied quantitatively given the data output by the FORTRAN code. The FORTRAN code output calculated raw data, which was plotted and further analyzed using two IDL codes. The first IDL code, orbit_parameters.pro (see attached code), took Neptune orbital radius and energy  data as its input. In addition to simply plotting the orbital radius as a function of time, this This  program used identified  the apoapsis and periapsis of every orbit by finding local minima/maxima in the radius data, and used these  to calculate the  semi-major axis $a$, orbital period $p$, and eccentricity $e$ as a function of time, via the following formulae: \begin {equation}  a=\frac{r_apo+r_peri} a=\frac{r_{apo}+r_{peri}}  {2}  \end {equation}  \begin {equation}  p=2(t_apo-t_peri) p=2(t_{apo}-t_{peri})  \end {equation}  \begin {equation}  e=\frac{r_apo-r_peri}  {r_apo+r_peri} e=\frac{r_{apo}-r_{peri}}  {r_{apo}+r_{peri}}  \end {equation}  This program also plotted the kinetic, potential, and orbital energy of the system as a function of time, using data directly from the FORTRAN code.   The second IDL code, plot_position.pro (see attached code), took position data for every particle, which was output by the Fortran code every 1000 time steps, and plotted these to create 'snapshots' of the actual system. This provides both an overhead view (xy-plane) and an edge-on view (xz-plane) of the system, at roughly 10 orbit intervals over the course of the 1000 orbit simulation (about 100 frames). Migration of disk particles other than Neptune, though not analyzed quantitatively, can be seen in the evolution of these 'snapshots' overtime, as well as a change in the overall shape of the disk.