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Two ovals

From Sheen (2016)

Two ovals is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 4.0122 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 weakly unstable (largest Floquet multiplier 1.409), so a small nudge makes it unravel over a few periods. The bodies pass within 0.238 of each other at a top speed of 2.31, line up 2 times a period, and the computed loop closes to 3.6×10⁻²⁵.

Measured over one period

Period: 4.012156416
Masses: 1 : 1 : 1
Energy: -1.47916
Angular momentum: 1.4527
Closest approach: 0.2378
Top speed: 2.315
Path length: 11.036
Alignments per period: 2
Topology: 0 (free-group class, read from the drawing)
Stability: weakly unstable (|λ|max 1.409)
Loop closure: 3.6×10⁻²⁵

Neighbours on the map

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