Two rocks pulling on each other: solved, on a napkin, in 1687. Add a third rock and there is no napkin. This is why, in plain English, with the equations printed and read out loud.

13 chapters, 34 equations with a plain reading under each, 10 things to press, 9 closed orbits found on the machine that built this page, 29 events since Newton, 38 words defined, 47 sources.

The whole thing in five sentences

Every body pulls every other body, with a force that falls off as the square of the distance. For two bodies that rule can be solved once and for all: an ellipse, repeating forever, written on one line.

For three, the same rule gives you eighteen numbers to track and ten quantities that never change — and two theorems that say no further quantity of the usable kind exists, so the bookkeeping stops there. Worse, two starts a millionth apart drift apart at a rate that doubles, so knowing the start better buys you only a little more warning.

What is left is exact special cases, a catalogue of orbits that repeat, a method of stepping the equations forward with an audit attached, and a set of odds for what usually happens. That is the whole of this site.

Start here

1. Everything pulls on everything — the one law.
2. Two is easy — the case with an answer.
3. Add one rock — where the answer goes, with the sandbox: three weights dropped from rest in 1913, sixty time units of near misses, and one of them thrown out at the end.
4. A hair's difference, and a different sky — the reason it stays gone. Forty-eight copies of that same start, a billionth apart, ending differently.
5. What it is not — before the next headline.

Things on this site that were worked out here

• 9 closed orbits, 9 of them turned up by scanning 40,000 starting speeds and then solving; the worst of them returns to its own start within 4e-07. Orbits.
• The Lyapunov time for the start on the chaos page: 3.51 time units, fitted to the measured gap between two runs. Chaos.
• L1 for the Sun and the Earth: 1,491,539 km, from solving the fifth-degree equation while the page was being built. Shapes.
• 68% of 643 random triples threw a body out within 60 time units — and at a third of the step size, the same share, with only 69% of the individual triples ending the same way. Odds.