Exercise 2.2: A three body problem

Let us consider astronomical units, and values for the masses $m_1/M=0.001$ and $m_2/M=0.01$. Consider initial positions $r_1=1$ and $r_2=4/3$ and velocities ${\mathbf v}_{1,2}=(0,\sqrt{GM/r_{1,2}})$.

1. Write a program to calculate the trajectories of the two planets, and plot them.

2. What would the shape and the periods of the orbits be if the don't interact? What is the qualitative effect of the interaction. Why is one planet affected more by the interaction that the other? Are the angular momentum and energy of planet 1 conserved? Is the total momentum an energy of the two planets conserved?