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,

d²r/dt² = - 100 r/r³ - 0.1(r-r')/|r-r'|³

d²r'/dt² = - 100 r'/r'3 + (r-r')/|r-r'|3

where r = |r| = sqrt{x²+y²} 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: dr(0)/dt = (0,1), dr'(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.