Atlas3,915 of 3,915

Loop-ended triangles

From Sheen (2016)

Loop-ended triangles is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 3.8208 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. It is linearly stable (largest Floquet multiplier 1.000), so a small nudge only makes it wobble. The bodies pass within 0.298 of each other at a top speed of 2.15, line up 6 times a period, and the computed loop closes to 7.8×10⁻²⁶.

Measured over one period

Period: 3.820761962
Masses: 1 : 1 : 1
Energy: -1.85568
Angular momentum: -0.76478
Closest approach: 0.2980
Top speed: 2.145
Path length: 11.831
Alignments per period: 6
Stability: stable (|λ|max 1.000)
Loop closure: 7.8×10⁻²⁶

Neighbours on the map

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