Atlas2,000 of 3,942

II.C.134

m₃ = 0.75

From Li & Liao (2017)

II.C.134 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 99.693 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 1.304), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00000887 of each other at a top speed of 359, line up 222 times a period, and the computed loop closes to 1.1×10⁻¹⁶.

Measured over one period

Period: 99.69341198
Masses: 1 : 1 : 0.75
Energy: -1.78270
Angular momentum: 0
Closest approach: 8.9×10⁻⁶
Top speed: 359.0
Path length: 250.14
Alignments per period: 222
Topology: ababABababABAbabABAbabaBAbabABABabaBABabaBABAbaBABAbabABababABABabABAbabaBABabABABababABabaBABAbaBABAbabABAbabABABabaBAbabaBABabaBAB (free-group class)
Stability: weakly unstable (|λ|max 1.304)
Loop closure: 1.1×10⁻¹⁶

Neighbours on the map

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