Atlas2,169 of 3,942

II.C.151

m₃ = 0.75

From Li & Liao (2017)

II.C.151 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 176.01 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 0.0000161 of each other at a top speed of 267, line up 272 times a period, and the computed loop closes to 4.3×10⁻¹⁷.

Measured over one period

Period: 176.0142373
Masses: 1 : 1 : 0.75
Energy: -1.40953
Angular momentum: 0
Closest approach: 1.6×10⁻⁵
Top speed: 266.8
Path length: 419.01
Alignments per period: 272
Topology: ababABabaBABabaBABabaBABabaBABabaBABabABABabaBAbabABAbabABAbabABAbabABAbabABAbabABAbaBABabaBABabaBABabaBABabaBABabaBABabaBAbabABABabABAbabABAbabABAbabABAbabABAbabAB (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 4.3×10⁻¹⁷

Neighbours on the map

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