Atlas1,937 of 3,942

II.C.166

m₃ = 0.5

From Li & Liao (2017)

II.C.166 m₃ = 0.5 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 0.5 that return to their starting positions and velocities every 104.23 time units, published by Li & Liao (2017). The largest class in the atlas: hundreds of II.C orbits for seven mass ratios. It is linearly stable (largest Floquet multiplier 1.000), so a small nudge only makes it wobble. The bodies pass within 0.0000774 of each other at a top speed of 131, line up 208 times a period, and the computed loop closes to 9.7×10⁻²⁴.

Measured over one period

Period: 104.2330202
Masses: 1 : 1 : 0.5
Energy: -1.30004
Angular momentum: 0
Closest approach: 7.7×10⁻⁵
Top speed: 131.2
Path length: 262.60
Alignments per period: 208
Topology: ababAbaBABaBABabAbabABabABAbABAbaBAbaBAbaBABaBABabABabABabABAbABAbaBAbaBAbaBABaBABabABabABabABAbABAbaBAbaBAbaBABaBABabABabaBabABAbABAbaB (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 9.7×10⁻²⁴

Neighbours on the map

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