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II.C.123

From Li & Liao (2017)

II.C.123 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 128.75 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 6.130), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000951 of each other at a top speed of 32.4, line up 180 times a period, and the computed loop closes to 4.7×10⁻²⁵.

Measured over one period

Period: 128.7472867
Masses: 1 : 1 : 1
Energy: -1.62386
Angular momentum: 0
Closest approach: 9.5×10⁻⁴
Top speed: 32.43
Path length: 336.41
Alignments per period: 180
Topology: ababABAbabABAbabABAbabABAbabABAbabABAbabABAbabABAbabABAbaBABabaBABabaBABabaBABabaBABabaBABabaBABabaBABabaBAB (free-group class)
Stability: weakly unstable (|λ|max 6.130)
Loop closure: 4.7×10⁻²⁵

Neighbours on the map

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