The orbit of Mercury around the Sun is an ellipse (a= 0.39 AU and e=0.206). 1. Simulate the orbit of Mercury and calculate the period by treating Mercury and the Sun as a two-body system. 2. Take the general relativity ( FG GMsME/r^2 (1+/r^2 ) ) into account and simulate the precession of the Mercurys orbit (rotation of the perihelion/aphelion). 2.1 Reproduce Fig. 4.8 in the textbook for =0.01. 2.2 Use simulation to get angular velocities of the precession for different values, do least-squares fitting, and extrapolate the real value for the procession of Mercurys orbit. Note: For the least-squares fitting, you CANNOT use the MATLAB built-in fitting functions, such as polyfit. You have to implement the equations in Appendix D.