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II.C.89

From Li & Liao (2017)

II.C.89 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 113.78 time units, published by Li & Liao (2017). The largest class in the atlas: hundreds of II.C orbits for seven mass ratios. It is unstable (largest Floquet multiplier 124), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0166 of each other at a top speed of 7.77, line up 114 times a period, and the computed loop closes to 9.4×10⁻²⁷.

Measured over one period

Period: 113.7789662
Masses: 1 : 1 : 1
Energy: -1.33258
Angular momentum: 0
Closest approach: 0.01660
Top speed: 7.766
Path length: 292.61
Alignments per period: 114
Topology: aaBAbaBAbaBAbaBAbaBAbbABabABabABabABaaBAbaBAbaBAbaBAbaBAbbABabABabABabABabAB (free-group class)
Stability: unstable (|λ|max 124.0)
Loop closure: 9.4×10⁻²⁷

Neighbours on the map

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