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II.C.59

From Li & Liao (2017)

II.C.59 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 88.017 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 1.653), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000037 of each other at a top speed of 164, line up 190 times a period, and the computed loop closes to 4.2×10⁻²³.

Measured over one period

Period: 88.01680463
Masses: 1 : 1 : 1
Energy: -2.13092
Angular momentum: 0
Closest approach: 3.7×10⁻⁵
Top speed: 164.4
Path length: 243.40
Alignments per period: 190
Topology: ababABAbabaBABababABABababABAbabaBABAbabABABabaBABAbabaBABababABABababABAbabaBABababABABabaBABAbabaBABAbabABAB (free-group class)
Stability: weakly unstable (|λ|max 1.653)
Loop closure: 4.2×10⁻²³

Neighbours on the map

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