The Three-Body Problem: Introduction and Simulation
An introduction to the three-body problem with an explanation of the math and physics using a simulation written in python. Includes examples of stable solutions.
Music from #Uppbeat (free for Creators!):
https://uppbeat.io/t/revo/universal
License code: H8LISAQDTUVM057L
Thanks to Dr. Rhett Allain for the introduction to VPython and Trinket.io and his video on the 3-body problem here: • What is the Three Body Problem and How Do ...
I should also acknowledge Alain Chenciner and Richard Montgomery for their work in the discovery and analysis of the figure 8 solution (links below)
The figure-8 trinket: https://trinket.io/glowscript/b541844f22
Initial conditions for figure 8 in python: (with G=1)
Ax=.97000436, Ay=-.24308753
Bx=-97000436, By=0.24308753
Cx=0, Cy=0
A velocity = (.93240737/2,.86473/2)
B velocity = (.93240737/2,.86473/2)
C velocity = (-.93240737,-.86473146)
Initial conditions for the "rose petal window" in python: (with G=1)
mass values: A(mass)=.44, B(mass)=.87, C(mass)=1
Ax=-1.2, Ay=0
Bx=1, By=0
Cx=0, Cy=0
A velocity = (0,-.992852)
B velocity = (0,-.513024)
C velocity = (0,.882922)
Initial conditions for figure 8 in Universe Sandbox:..
m1=m2=m3=1.00 sun
pos1=(5e10 m,0,0)
pos2=(-5e10 m,0,0)
pos3=(0,0,0)
v1=v2=(p1,p2,0)
v3=(-2*p1,-2*p2,0)
p1=17884.34 m/s
p2=27447.95 m/s
These videos I've done recently cover more on the 3-body problem:
• Solving the 3-body Problem with Runge-Kutt...
• The 3-Body Problem: An Introduction by Ale...
More on the mathematics of the 3 body problem here:
https://www.scientificamerican.com/ar...
https://observablehq.com/@rreusser/pe...
https://arxiv.org/abs/math/0011268
https://adsabs.harvard.edu/full/1974C...