Atlas1,821 of 3,942

II.C.126

m₃ = 0.75

From Li & Liao (2017)

II.C.126 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 199.31 time units, published by Li & Liao (2017). The largest class in the atlas: hundreds of II.C orbits for seven mass ratios. It is weakly unstable (largest Floquet multiplier 3.033), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000356 of each other at a top speed of 56.7, line up 168 times a period, and the computed loop closes to 1.0×10⁻²⁵.

Measured over one period

Period: 199.3101783
Masses: 1 : 1 : 0.75
Energy: -1.01608
Angular momentum: 0
Closest approach: 3.6×10⁻⁴
Top speed: 56.69
Path length: 448.78
Alignments per period: 168
Topology: aaBAbabAAbaBAbabABaaBABabAAbaBAbabAAbaBABabABaaBAbabAAbaBABabABaaBABabAAbaBAbabABaaBABabABaaBAbabAAbaBABabAB (free-group class)
Stability: weakly unstable (|λ|max 3.033)
Loop closure: 1.0×10⁻²⁵

Neighbours on the map

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