Three Body Orbits

Families / Belgrade classes

Sheen’s orbits

A dozen orbits Matthew Sheen found in 2016 with a root finder and hand-picked starting guesses while a teaching assistant on Cornell’s dynamics course, named for what they look like; six hang in the Belgrade gallery. Most of them carry angular momentum.

Sheen’s orbits are periodic solutions of the planar three-body problem. The atlas holds 12 of them, with periods from 1.251 to 8.095, all with equal masses; 2 of them are linearly stable. They come from Sheen (2016), Periodic three-body solutions found with a root finder, example code for Cornell’s Intermediate Dynamics course. Every orbit is precomputed to machine precision and plays one period at a time; open one to watch it, nudge it or rate it.

Sheen (2016). Periodic three-body solutions found with a root finder, example code for Cornell’s Intermediate Dynamics course. GitHub, mws262/MAE5730_examples; six of them in the Belgrade three-body gallery (link)

See them on the mapOpen Loop-ended triangles

All 12 orbits

Gear inside oval, a periodic three-body orbitGear inside ovalT 5.957Hand in hand in oval, a periodic three-body orbitHand in hand in ovalT 6.868Loop-ended triangles, a periodic three-body orbitLoop-ended trianglesT 3.821 stableNewton’s cradle, a periodic three-body orbitNewton’s cradleT 3.551Oval, catface and starship, a periodic three-body orbitOval, catface and starshipT 5.026Ovals with flourishes, a periodic three-body orbitOvals with flourishesT 8.095PT1, a periodic three-body orbitPT1T 5.403PT2, a periodic three-body orbitPT2T 5.428Skinny pineapple, a periodic three-body orbitSkinny pineappleT 5.095Three bouncing, a periodic three-body orbitThree bouncingT 1.251Three ovals, a periodic three-body orbitThree ovalsT 5.179 stableTwo ovals, a periodic three-body orbitTwo ovalsT 4.012