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An atlas of periodic solutions to the three-body problem
The three-body problem remains unsolved—we can't generally predict the motion of three bodies for all starting conditions using regular maths—but there are many solutions showing periodic orbits given _specific_ conditions. Three Body Orbits is a beautiful "atlas" animating 3,942 of them.
> Three point masses attracting each other under Newtonian gravity have no general closed-form solution. Almost every starting arrangement ends in a chaotic dance and, eventually, an escape. Hidden in that chaos are periodic solutions: arrangements where all three bodies return, after one period, to exactly the positions and velocities they started with. This site collects the ones that have been found and published, and lets you watch each of them run.
The atlas divides solutions into 41 families which share a shape and a topology, "each traced back to the paper that found it," and has a 'battle' mode for comparing them. There's a leaderboard; currently Moth region HS.417 and Rosette 5:9 are neck-and-neck up top, with the minimalist Brouke-Boggs S34 and the ribbonlike Yin-Yang III.12.Aα among the front-runners. Least liked is II.C.44, which soon ends up a flat scribble in the visualizer. Be sure to check out Free-fall F1 and Gear inside oval.
You can "kick" the orbits to mess up the pattern, but some are resistant to light gravitational nudges. You can even make your own one.
Henri Poincaré showed that the three-body problem cannot be solved with standard mathematical operations more than a century ago, proving that small variations in deterministic systems lead to wildly divergent results and standing among the mathematicians who inspired chaos theory. Where each of them would stand now is impossible to predict.
**Previously:**
• Watch the trailer for the upcoming animated adaptation of The Three-Body Problem
• China's own live-action adaptation of The Three Body Problem is live now, with English subs
• N-body simulation of the gravitational collapse of Spongebob Squarepants
![Songs in the Key of Life came out September 28, 1976, exactly 50 years ago. I’m holding up the gatefold sleeve, with its warm orange-and-amber sunburst of concentric, ragged-edged rings around a small pen-and-ink portrait at the center. The title curves along the inner ring and Stevie Wonder's name in flowing script below it. A round sticker in the upper left reads "Collector's Album, Includes Two Records, A Something's Extra Bonus Record, 24-Page Lyric Booklet." That's the original double LP plus the bonus 7-inch EP, which was the whole point of the "collector's album" pitch. [I have lost the booklet and EP #alas]
Behind it, the turntable is in the middle of playing one of the discs, with a yellow-and-red Tamla label visible and the tonearm resting on the record. The player looks like a Marantz full-automatic. To the left, a shelf is stuffed with records and 45s, and up top there's a City of Ann Arbor, Michigan medallion among some challenge coins on the ledge.
ALT by Claude](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:pbsomovygkguz7sxqkktcecj/bafkreia23vwbuh7bvz3wgv2cttyndnpvt22nihzzoqykw5onm3y2hp2une)
