(b) Consider a planar three-body problem: There are three Suns with same mass Mo. Randomly choose...

 

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(b) Consider a planar three-body problem: There are three Suns with same mass Mo. Randomly choose a set of initial conditions and plot the orbit (in 2D figures, using matplotlib.animation) to show this orbit is not periodic. This is the initial conditions of an example with periodic orbit: [x1,y1, Vx1, Vy1, X2, V2, Vx2. Vy2, X3, ya, Vx3, Vya] = [R,0,0, VR-R,0,0,- VR,0,0,0,0] 5 GM R where R 1 x 101m and v = Plot the orbit and explain it. Try to find more (2) sets of initial conditions with periodic and stable orbits. (c) Add an Earth in the three-body system in example. It is required that all 4 celestial bodies have periodic orbits with the same angular velocity. Hint: There are 8 equilibrium positions for Earth in total. Are all of them stable? (b) Consider a planar three-body problem: There are three Suns with same mass Mo. Randomly choose a set of initial conditions and plot the orbit (in 2D figures, using matplotlib.animation) to show this orbit is not periodic. This is the initial conditions of an example with periodic orbit: [x1,y1, Vx1, Vy1, X2, V2, Vx2. Vy2, X3, ya, Vx3, Vya] = [R,0,0, VR-R,0,0,- VR,0,0,0,0] 5 GM R where R 1 x 101m and v = Plot the orbit and explain it. Try to find more (2) sets of initial conditions with periodic and stable orbits. (c) Add an Earth in the three-body system in example. It is required that all 4 celestial bodies have periodic orbits with the same angular velocity. Hint: There are 8 equilibrium positions for Earth in total. Are all of them stable?