The Three-Body Problem

The mathematics of the three-body problem in plain words, with the equations printed and read out loud, the pictures computed from the equations, and the orbits found rather than copied.

Live: https://nanobotco.github.io/three-body/

What is on it

• Math — 13 chapters: the inverse-square law, two bodies solved in closed form, the equations for three, the ten conserved quantities and the two theorems that say there are no more of the usable kind, chaos and the Lyapunov time, the restricted problem and the five Lagrange points, Euler's line and Lagrange's triangle, the figure eight and the shape sphere, Sundman's convergent and useless series, singularities, how it is stepped on a computer, and what usually happens. 34 equations, each with a plain reading underneath.
• Orbits — 9 periodic orbits, found here by scanning 40,000 starting speeds and then solving each near-miss until it closed. Each one carries its initial conditions, its period and the distance it returns to.
• History — 27 events, Newton 1687 to Webb at L2.
• Code — the whole thing in thirty lines of Python with no libraries, which prints the figure eight as characters and checks its own energy.
• Words — 38 terms. Sources — 45.
• 10 demos in the browser, all running the same leapfrog as the Python.

Figures computed at build time, not typed

figure	value
Lyapunov time for the reference start	3.5144 time units
Sun–Earth L1, from the quintic	1,491,539 km
random triples that ejected a body in 60 time units	435 of 643 (67.7%)
the same starts at a third of the step	same share, 69% of individual triples end the same way

The last row is the point of the site in one line: the statistics are reproducible and the trajectories are not.

Build

python3 tools/find_orbits.py scan      # the return map over starting speeds (~3.5 min)
python3 -c "import sys;sys.path.insert(0,'tools');import find_orbits as F;F.harvest(0.12)"
python3 tools/draw.py                  # the pictures
python3 tests/check_data.py            # the gate: every orbit re-integrated here
./publish.sh                           # build/ → docs/, which GitHub Pages serves
python3 tools/serve.py 8846            # http://127.0.0.1:8846/three-body/

Needs Python 3, numpy and pillow. three_body.py needs nothing.

Licence

Code MIT. Text, data and pictures CC BY 4.0 — use them, credit NaNoBotCo, link back.

Elsewhere from the same publisher

• Mot Dang — city directory for Chiang Mai and Chiang Rai
• The Mae Hong Son Loop — motorcycling the 600 km loop out of Chiang Mai — curves counted, air measured
• Muay Thai — the eight limbs, the thirty named techniques, the ceremony, and every gym on the map
• Roads of Chiang Mai — the square of 1296, four rings, and what each one did to the city — counted from the map
• wichaa — Lanna manuscripts, the amulet market, and the traditions around them
• Hand Poke — 28 traditions of marking skin by hand — the leg-tattoo zone of Burma, the Shan States and Lanna, counted
• Black Holes, Drawn — black holes modelled and drawn from the equations — generators, the past, present and future, the legends
• Quantum Computing, plainly — the history and theory of quantum computing in plain words, with demos; refreshed weekly
• Goin' Fast — a dirt-simple explainer about speed — twenty measured speeds from the ground under the house to light, and what each one costs
• Exceptional Magic — the octonions, triality, the magic square and E8, computed and drawn — a plain-spoken reading of one paper
• Amulet Atlas — amulets, charms and talismans worldwide
• Carolina Barbecue — barbecue in North and South Carolina
• Wing Country — the American chicken wing
• Pink Box — the American mom-and-pop donut shop
• Basque Tables — Basque dining rooms of California, Nevada and Idaho
• Pinot Country — pinot noir: the vine, the regions, the cellars
• Care Abroad — treatment across borders, with published prices and their dates
• Thai Roots — a root dictionary of Thai, with a word decomposer
• The index — every corpus, site and repository, counted
• Uptake — a field manual on publishing for machines that copy
• NaNoBotCo — the portal
• ฮักฝรั่ง — เรื่องเงิน วีซ่า และชีวิตกับแฟนฝรั่ง
• Offrampt — turning crypto into spendable local money, Thailand first

All of it, counted: https://nanobotco.github.io/index/ · roster as JSON: https://nanobotco.github.io/index/fleet.json