Atlas1,851 of 3,942

II.C.92

m₃ = 2

From Li & Liao (2017)

II.C.92 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 174.4 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 1.158), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00000832 of each other at a top speed of 566, line up 472 times a period, and the computed loop closes to 7.4×10⁻¹⁷.

Measured over one period

Period: 174.4018735
Masses: 1 : 1 : 2
Energy: -3.96661
Angular momentum: 0
Closest approach: 8.3×10⁻⁶
Top speed: 566.3
Path length: 546.99
Alignments per period: 472
Topology: ababababABABABabababaBABABABabababaBABABABAbabababABABABAbabababABABABababababABABABAbabababABABABAbabababABABABAbabababABABABAbabababABABABAbabababaBABABABabababaBABABAbabababABABABAbabababaBABABABabababaBABABABabababaBABABABabababaBABABABabababaBABABAB (free-group class)
Stability: weakly unstable (|λ|max 1.158)
Loop closure: 7.4×10⁻¹⁷

Neighbours on the map

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