Most of the information you need for this week is in the assignment. You are using the same code you wrote for last week's assignment, only now you may have to add adaptive step sizes. This is quite doable, and was an optional extra in the fall term's Ph20 course. Procedural hint: think before you type.

Other applications of a 3D 3 body integrator include finding stable orbits around lagrange points, including those occupied by solar observatory spacecraft, and the Kozai effect, in which a small body in an off-axis orbit about a planet will gradually exchange eccentricity for inclination, and vice versa. To show this you need an exceptionally stable integrator, and probably a great deal of patience. One final example includes the dancing orbits of Saturnian moons, which exchange orbital parameters every now and then.