*Assignment for Lab 4: Molecular
dynamics (three-body problem).*

- Consider the Sun-Earth-Moon three-body system, with a set of artificial parameters, G=1, M=100, m=1, m'=0.1,

d^{2}**r**/dt^{2} = - 100 **r**/r^{3}
- 0.1(**r**-**r**')/|**r**-**r**'|^{3}

d^{2}**r**'/dt^{2} = - 100 **r**'/**r**'3
+ (**r**-**r**')/|**r**-**r**'|3

where r = |**r**| = sqrt{x^{2}+y^{2}}
and r' = |**r**'| = sqrt{x'^{2}+y'^{2}}.

(a) Find the orbits **r**(t) and **r**'(t) for 0
< t < 628 using symplectic algorithm C with the following initial
conditions: **r**(0) = (100,0), **r**'(0) = (95, 0); and initial
velocities: d**r**(0)/dt = (0,1), d**r**'(0)/dt = (0,0.6).

(b) Present a trajectory plot (x vs. y). Discuss features
of the orbits. (c) What should be a proper choice for step size h?

You may modify this molecular dynamics code (written by Dr. Wang Jian Shen) for your work.