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Three ovals

From Sheen (2016)

Three ovals is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 5.1795 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 linearly stable (largest Floquet multiplier 1.000), so a small nudge only makes it wobble. The bodies pass within 0.0561 of each other at a top speed of 4.28, line up 8 times a period, and the computed loop closes to 3.9×10⁻³⁰.

Measured over one period

Period: 5.179484544
Masses: 1 : 1 : 1
Energy: -2.44814
Angular momentum: 0.63047
Closest approach: 0.05615
Top speed: 4.277
Path length: 16.488
Alignments per period: 8
Topology: unresolved (close passages hide the crossings in the drawing)
Stability: stable (|λ|max 1.000)
Loop closure: 3.9×10⁻³⁰

Neighbours on the map

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