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Ovals with flourishes

From Sheen (2016)

Ovals with flourishes is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 8.0947 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 326.5), so a small nudge makes it unravel over a few periods. The bodies pass within 0.201 of each other at a top speed of 2.75, line up 4 times a period, and the computed loop closes to 2.8×10⁻²⁹.

Measured over one period

Period: 8.094721472
Masses: 1 : 1 : 1
Energy: -1.13234
Angular momentum: 1.5720
Closest approach: 0.2012
Top speed: 2.745
Path length: 18.856
Alignments per period: 4
Topology: a (free-group class, read from the drawing)
Stability: unstable (|λ|max 326.5)
Loop closure: 2.8×10⁻²⁹

Neighbours on the map

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