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II.C.21

m₃ = 2

From Li & Liao (2017)

II.C.21 m₃ = 2 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 2 that return to their starting positions and velocities every 49.469 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 5.303), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00000257 of each other at a top speed of 1019, line up 126 times a period, and the computed loop closes to 2.1×10⁻²¹.

Measured over one period

Period: 49.46894635
Masses: 1 : 1 : 2
Energy: -3.81589
Angular momentum: 0
Closest approach: 2.6×10⁻⁶
Top speed: 1019
Path length: 156.51
Alignments per period: 126
Topology: 0 (free-group class)
Stability: weakly unstable (|λ|max 5.303)
Loop closure: 2.1×10⁻²¹

Neighbours on the map

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