Atlas2,087 of 3,942

II.C.50

m₃ = 0.75

From Li & Liao (2017)

II.C.50 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 46.366 time units, published by Li & Liao (2017). The largest class in the atlas: hundreds of II.C orbits for seven mass ratios. It is unstable (largest Floquet multiplier 10.17), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00014 of each other at a top speed of 90.1, line up 92 times a period, and the computed loop closes to 6.8×10⁻²⁵.

Measured over one period

Period: 46.36586029
Masses: 1 : 1 : 0.75
Energy: -1.67509
Angular momentum: 0
Closest approach: 1.4×10⁻⁴
Top speed: 90.09
Path length: 119.80
Alignments per period: 92
Topology: ababAbabaBababABAbaBABAbaBABabaBAbabaBAbabABAbaBABAbaBAB (free-group class)
Stability: unstable (|λ|max 10.17)
Loop closure: 6.8×10⁻²⁵

Neighbours on the map

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