In this project, we will calculate the trajectories of a mini solar system consisting of the Sun, Mercury, Earth, and the Moon. The motion of celestial bodies is governed by Newton's second law of motion and gravity. The program SunEarthMoon.m on the class website simulates the orbits of the Sun, Earth, and the Moon.
Modify this program to include the motion of Mercury as well. You need to research and code in the right mass/distance/velocity parameters for Mercury in order for this simulation to work.
For Programming Assignment #2:
- Reformulate the system of second order ODEs into a system of first order ODEs, and solve the system with the matlab function ode45.
- Your program should take the same input arguments years and framerate.
- Your output should be
- a plot depicting the orbits of the Moon and the Earth.
- a plot depicting the orbits of the Earth, Mercury, and the Sun.