Numerical Integration of the Solar System

This is a demonstration of the Stormer-Verlet method applied to the outer solar system consisting of Jupiter through Pluto. The computation was carried out in Matlab with a time step of 200 days, a final time of 200,000 days, distances in astronomical units (AU), and masses normalized by the Sun's mass. The masses of Mercury through Mars were lumped together with the Sun. The initial conditions for position and velocity along with the scaled masses were obtained from pg. 13-14 of the 2nd Ed. of "Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations" by Hairer, Lubich, and Wanner.

To reproduce this plot, download the main script and functions linked below and run the main script with the functions either in the same folder as the main script or somewhere else in Matlab's search path (for Windows users C:\Users\YourUserName\Documents\MATLAB). The only variable that needs editing in the script is "method = methods{index}", where "index" should be the number corresponding to the numerical method you want to use from the list given below.

The numerical methods provided include:
1) Forward Euler
2) Runge-Kutta 23
3) Runge-Kutta 45
4) Symplectic Forward Euler
5) Stormer-Verlet

Main script:
Solar_System_Example.m
https://drive.google.com/file/d/15hzHrNtRuSudn8t2B_yyBobFYzexAWY4/view?usp=sharing

Functions:
solarSysDiffEQ.m
https://drive.google.com/file/d/1ycdie6XUNQdq1otkDvRYH0ctPX6yfQ3y/view
solarSysHam.m
https://drive.google.com/file/d/1Mo_6XRmO_CO34-HmkNZjtC99dbqhd3Zk/view