Atlas3,938 of 3,942

Gear inside oval

From Sheen (2016)

Gear inside oval is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 5.957 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 2.698), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00017 of each other at a top speed of 45.6, line up 474 times a period, and the computed loop closes to 7.7×10⁻³.

Measured over one period

Period: 5.957022316
Masses: 1 : 1 : 1
Energy: -17.1095
Angular momentum: 0.90167
Closest approach: 1.7×10⁻⁴
Top speed: 45.64
Path length: 40.912
Alignments per period: 474
Topology: unresolved (close passages hide the crossings in the drawing)
Stability: weakly unstable (|λ|max 2.698)
Loop closure: 7.7×10⁻³

Neighbours on the map

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