Atlas829 of 3,942

I.B.107

m₃ = 0.75

From Li & Liao (2017)

I.B.107 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 135.45 time units, published by Li & Liao (2017). Class I.B orbits, for equal and unequal masses. It is weakly unstable (largest Floquet multiplier 1.017), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000786 of each other at a top speed of 121, line up 292 times a period, and the computed loop closes to 4.9×10⁻¹⁷.

Measured over one period

Period: 135.4481208
Masses: 1 : 1 : 0.75
Energy: -1.74700
Angular momentum: 0
Closest approach: 7.9×10⁻⁵
Top speed: 120.6
Path length: 341.65
Alignments per period: 292
Topology: ababABababABAbabABAbabaBAbabABABabaBAbabaBABabaBABababABababABAbaBABAbabABAbabABABabABAbabaBAbabaBABabaBABababABabaBABAbabABababABAbabABAbabaBAbabaBABabABABabaBABabaBABAbaBAB (free-group class)
Stability: weakly unstable (|λ|max 1.017)
Loop closure: 4.9×10⁻¹⁷

Neighbours on the map

All I.B orbits, the families of periodic three-body orbits, or the atlas map.