Atlas2,163 of 3,942

II.C.137

m₃ = 0.5

From Li & Liao (2017)

II.C.137 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 106.99 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 0.00025 of each other at a top speed of 73, line up 176 times a period, and the computed loop closes to 9.3×10⁻¹⁸.

Measured over one period

Period: 106.9936961
Masses: 1 : 1 : 0.5
Energy: -1.14871
Angular momentum: 0
Closest approach: 2.5×10⁻⁴
Top speed: 73.01
Path length: 257.14
Alignments per period: 176
Topology: ababAbaBABaBAbabAbabABaBABabABabABabABabABabaBabaBAbaBAbaBAbaBAbaBAbaBAbabAbabABabABabABabABabABAbABabaBabaBAbABAbaB (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 9.3×10⁻¹⁸

Neighbours on the map

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