Problem $2\mathrm{.}2$: Astronomical Problem

Set up the equations of motion for the Sun and the four largest planets in the solar system taking

into account the gravitational effects of these objects but ignoring the effects of the rest of the solar

system and of the wider universe. It will be very important to your prospect for success that you

employ accurate initial conditions. These should be available from a number of online sources such

as the Jet Propulsion Laboratory. Produce a simulation for the motion of these objects for a period

of at least two cycles of Neptune. By implementing numerical quadrature determine whether your

simulated data accords with Kepler$$s second law. Also determine whether your simulated data

accords with Kepler$$s first and third laws. Visualise by creating an animation $($using MATLAB$$s

VideoWriter or suitable Python code$)$ which shows the movement of these objects over a period of

at least two orbits of the Neptune about the Sun. As in lecture notes, if using MATLAB, you will

find the sphere and surf commands to be useful in creating a $3$D graphics object which looks

approximately like a ball