Atlas1,975 of 3,942

II.C.127

m₃ = 0.75

From Li & Liao (2017)

II.C.127 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 127.46 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 1.005), so a small nudge only makes it wobble. The bodies pass within 0.000149 of each other at a top speed of 87.5, line up 194 times a period, and the computed loop closes to 2.7×10⁻¹⁷.

Measured over one period

Period: 127.4592957
Masses: 1 : 1 : 0.75
Energy: -1.41583
Angular momentum: 0
Closest approach: 1.5×10⁻⁴
Top speed: 87.54
Path length: 319.67
Alignments per period: 194
Topology: abaBAbabABabaBAbabABAbaBABabaBAbabABabaBABabABAbaBABabaBAbabABabaBABabABAbabABabaBAbabABAbaBABabABAbabABabaBAbabABAbaBAB (free-group class)
Stability: stable (|λ|max 1.005)
Loop closure: 2.7×10⁻¹⁷

Neighbours on the map

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