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II.C.39

From Li & Liao (2017)

II.C.39 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 80.038 time units, published by Li & Liao (2017). The largest class in the atlas: hundreds of II.C orbits for seven mass ratios. It is weakly unstable (largest Floquet multiplier 1.229), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000366 of each other at a top speed of 52.3, line up 110 times a period, and the computed loop closes to 5.4×10⁻²⁵.

Measured over one period

Period: 80.03822054
Masses: 1 : 1 : 1
Energy: -1.60535
Angular momentum: 0
Closest approach: 3.7×10⁻⁴
Top speed: 52.29
Path length: 207.77
Alignments per period: 110
Topology: ababABAbabABAbabABAbabABAbabABAbabABabaBABabaBABabaBABabaBABabaBAB (free-group class)
Stability: weakly unstable (|λ|max 1.229)
Loop closure: 5.4×10⁻²⁵

Neighbours on the map

All II.C orbits, the families of periodic three-body orbits, or the atlas map.