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Hand in hand in oval

From Sheen (2016)

Hand in hand in oval is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 6.8682 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 172.1), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0162 of each other at a top speed of 8.01, line up 8 times a period, and the computed loop closes to 4.7×10⁻²⁵.

Measured over one period

Period: 6.868162020
Masses: 1 : 1 : 1
Energy: -1.73944
Angular momentum: 1.2638
Closest approach: 0.01615
Top speed: 8.014
Path length: 17.583
Alignments per period: 8
Topology: unresolved (close passages hide the crossings in the drawing)
Stability: unstable (|λ|max 172.1)
Loop closure: 4.7×10⁻²⁵

Neighbours on the map

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