Atlas1,827 of 3,942

II.C.82

m₃ = 0.75

From Li & Liao (2017)

II.C.82 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 80.153 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 5.060), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000819 of each other at a top speed of 118, line up 118 times a period, and the computed loop closes to 7.4×10⁻¹⁷.

Measured over one period

Period: 80.15278496
Masses: 1 : 1 : 0.75
Energy: -1.41222
Angular momentum: 0
Closest approach: 8.2×10⁻⁵
Top speed: 118.1
Path length: 210.85
Alignments per period: 118
Topology: abaBabaBAbabAbabABabABabaBabaBAbabAbabABabABabaBAbaBAbabABabaBAbaBAbabABabAB (free-group class)
Stability: weakly unstable (|λ|max 5.060)
Loop closure: 7.4×10⁻¹⁷

Neighbours on the map

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