Atlas1,573 of 3,942

II.C.22

m₃ = 2

From Li & Liao (2017)

II.C.22 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 78.645 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 3.177), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000659 of each other at a top speed of 63.5, line up 136 times a period, and the computed loop closes to 9.1×10⁻²⁵.

Measured over one period

Period: 78.64458049
Masses: 1 : 1 : 2
Energy: -2.96073
Angular momentum: 0
Closest approach: 6.6×10⁻⁴
Top speed: 63.52
Path length: 230.56
Alignments per period: 136
Topology: abababaBABABAbababaBABABAbabababABABABabababABABABabababABABABabababABABAB (free-group class)
Stability: weakly unstable (|λ|max 3.177)
Loop closure: 9.1×10⁻²⁵

Neighbours on the map

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