Atlas1,902 of 3,942

II.C.39

m₃ = 0.75

From Li & Liao (2017)

II.C.39 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 48.09 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 1.310), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000221 of each other at a top speed of 71.9, line up 74 times a period, and the computed loop closes to 1.2×10⁻²⁴.

Measured over one period

Period: 48.09032669
Masses: 1 : 1 : 0.75
Energy: -1.42989
Angular momentum: 0
Closest approach: 2.2×10⁻⁴
Top speed: 71.92
Path length: 121.89
Alignments per period: 74
Topology: abaBAbabABabaBAbabABabaBAbabABAbaBABabABAbaBAB (free-group class)
Stability: weakly unstable (|λ|max 1.310)
Loop closure: 1.2×10⁻²⁴

Neighbours on the map

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