Atlas1,974 of 3,942

II.C.138

m₃ = 0.75

From Li & Liao (2017)

II.C.138 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 158.62 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 1.020), so a small nudge only makes it wobble. The bodies pass within 0.00002 of each other at a top speed of 239, line up 226 times a period, and the computed loop closes to 3.2×10⁻²².

Measured over one period

Period: 158.6249795
Masses: 1 : 1 : 0.75
Energy: -1.35589
Angular momentum: 0
Closest approach: 2.0×10⁻⁵
Top speed: 238.9
Path length: 390.10
Alignments per period: 226
Topology: abaBAbabABabaBAbabABAbaBABabaBAbabABabaBAbabABAbaBABabABAbaBABabaBAbabABAbaBABabABAbabABabaBAbabABabaBABabABAbaBABabaBAbabABAbaBABabABAbaBAB (free-group class)
Stability: stable (|λ|max 1.020)
Loop closure: 3.2×10⁻²²

Neighbours on the map

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