Atlas1,777 of 3,942

II.C.90

m₃ = 2

From Li & Liao (2017)

II.C.90 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 175.65 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 1.113), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000464 of each other at a top speed of 24, line up 460 times a period, and the computed loop closes to 4.1×10⁻¹⁶.

Measured over one period

Period: 175.6526253
Masses: 1 : 1 : 2
Energy: -3.88493
Angular momentum: 0
Closest approach: 4.6×10⁻⁵
Top speed: 239.9
Path length: 555.63
Alignments per period: 460
Topology: ababababABABABabababaBABABABabababaBABABAbabababABABABABabababaBABABAbabababABABABAbabababABABABababababABABABAbabababABABABabababaBABABABabababaBABABABabababaBABABABabababaBABABAbabababABABABAbabababABABABAbabababABABABAbabababABABABabababaBABABAB (free-group class)
Stability: weakly unstable (|λ|max 1.113)
Loop closure: 4.1×10⁻¹⁶

Neighbours on the map

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