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PT1

From Sheen (2016)

PT1 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 5.403 time units, published by Sheen (2016). 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. His loop-ended triangles turned out to be Broucke and Boggs’s S4 of 1975, mirrored, and is listed under that name. It is unstable (largest Floquet multiplier 1031), so a small nudge makes it unravel over a few periods. The bodies pass within 0.001 of each other at a top speed of 32, line up 16 times a period, and the computed loop closes to 2.8×10⁻²⁵.

Measured over one period

Period: 5.403020912
Masses: 1 : 1 : 1
Energy: -2.56806
Angular momentum: -0.10226
Closest approach: 0.001001
Top speed: 32.00
Path length: 14.699
Alignments per period: 16
Topology: unresolved (close passages hide the crossings in the drawing)
Stability: unstable (|λ|max 1031)
Loop closure: 2.8×10⁻²⁵

Neighbours on the map

All Sheen’s orbits, the families of periodic three-body orbits, or the atlas map.