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Oval, catface and starship

From Sheen (2016)

Oval, catface and starship is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 5.0261 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 19.55), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0113 of each other at a top speed of 9.46, line up 6 times a period, and the computed loop closes to 1.8×10⁻²⁷.

Measured over one period

Period: 5.026081588
Masses: 1 : 1 : 1
Energy: -1.56905
Angular momentum: 1.1486
Closest approach: 0.01132
Top speed: 9.455
Path length: 12.276
Alignments per period: 6
Topology: unresolved (close passages hide the crossings in the drawing)
Stability: unstable (|λ|max 19.55)
Loop closure: 1.8×10⁻²⁷

Neighbours on the map

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