Atlas2,120 of 3,942

II.C.161

m₃ = 0.75

From Li & Liao (2017)

II.C.161 m₃ = 0.75 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 0.75 that return to their starting positions and velocities every 161.62 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 1.008), so a small nudge only makes it wobble. The bodies pass within 0.0000261 of each other at a top speed of 209, line up 316 times a period, and the computed loop closes to 1.3×10⁻¹⁵.

Measured over one period

Period: 161.6167189
Masses: 1 : 1 : 0.75
Energy: -1.64614
Angular momentum: 0
Closest approach: 2.6×10⁻⁵
Top speed: 209.4
Path length: 410.78
Alignments per period: 316
Topology: ababABababABAbaBABAbabABababABabaBABabaBABabaBABabaBABabaBABabaBABabaBABabaBABabABABabaBAbabaBABabABABabABAbabaBAbabABABabABAbabABAbabABAbabABAbabABAbabABAbabABAbabABAbabABababABabaBABAbaBAB (free-group class)
Stability: stable (|λ|max 1.008)
Loop closure: 1.3×10⁻¹⁵

Neighbours on the map

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