Newton solved two bodies completely: two suns waltz on perfect ellipses, forever, and a formula tells you where they will be in a million years. Then he tried three, and the mathematics broke. It has stayed broken for three centuries: there is no formula, and there never will be. Below is the real thing: three suns, real gravity, computed honestly. Watch the miracle orbit. Then grab a sun and throw it.
For the curious kid.
Why is three so much harder than two? Because with two suns, each one feels a single, steady pull, and the dance repeats. Add a third and every sun is pulled two ways at once, the pulls keep changing as everyone moves, and the dance never repeats: tiny differences snowball until the future is unknowable. This is the same wildness you met in the double pendulum, written across the sky. And most games of three end the same way: two suns fall into a tight pair, and the third is hurled into the dark, alone, forever. Load three strangers and wait. Someone always leaves.
And yet: press the figure-eight. Three identical suns chase each other along a single looping track, each exactly a third of a lap behind the next, balanced like a coin standing on edge. A computer stumbled onto this orbit in 1993; two mathematicians proved in 2000 that it truly exists. Nothing in the universe is known to dance this dance, but gravity permits it, and that is enough for it to hang in this museum.
Deeper.
"No formula" has a precise meaning. In 1887 Bruns and Poincaré showed the three-body problem has too few conserved quantities to be solved by algebra, and Poincaré's work on it (for a prize offered by King Oscar II of Sweden) uncovered the tangled geometry we now call chaos. He wrote that "small differences in the initial conditions produce very great ones in the final phenomena." There is a fine print worth knowing: in 1912 Sundman did find an exact infinite series for the three-body problem. It converges so slowly that summing an astronomically absurd number of terms buys you one useful instant: a solution in name, useless in fact. The universe's answer is the one you can watch here: computation, one careful step at a time.
The presets are the field guide. Lagrange's triangle is a genuine equilibrium, an equilateral triangle rotating forever, but for equal masses it is unstable: this page seeds it with an error of one part in a billion, and you can watch that error bloom into anarchy within a few turns. A family shows the only arrangement gravity actually tolerates for long: a hierarchy, two bodies close, the third far away, pretending the pair is one. Real triple-star systems all live this way; democratic triples eject someone. The figure-eight is a choreography (Moore 1993, proven by Chenciner and Montgomery 2000) with exactly zero angular momentum, one of a growing zoo of such orbits, beautiful, and so fragile that none has ever been observed in nature.
An honesty note, since this museum keeps its arithmetic in the open: the integrator is fourth-order Runge-Kutta with steps that shrink as suns approach, its energy drift is displayed live beneath the pool of stars, and when two suns pass very close, the simulation refuses to skip ahead, so time itself appears to slow. It is not a bug. It is the price of telling the truth near a near-collision.
Two bodies write a poem that scans. Three write an argument that never ends, and the argument is where the universe keeps its surprises.