007 · a three-day experiment · day one
The Third Body Is the Question
Before three bodies betray prediction, let them keep a promise. Equal masses can chase one another around one curve and return. The instruments are here because tomorrow, resemblance will no longer be evidence.
equal massequal massequal mass
simulation time0.0000 periods
centre of mass0.00e+0
total momentum0.00e+0
relative energy error0.00e+0
angular momentum0.00e+0
measured initial state · G = m = 1
A special answer
The three-body problem has islands of exact order. This figure-eight is periodic: the bodies share one path, one third of a period apart. A special solution is not a general solution—but it proves that “three” does not simply mean “random.”
aᵢ = Σⱼ≠ᵢ (rⱼ − rᵢ) / |rⱼ − rᵢ|³
Four witnesses
A beautiful orbit can be a numerical lie. Centre of mass, momentum, energy and angular momentum are independent witnesses. The leapfrog step lets energy breathe within a narrow bound instead of steadily leaking away.
origin, failed path & handles →