Atlas1,524 of 3,942

II.C.7

m₃ = 5

From Li & Liao (2017)

II.C.7 m₃ = 5 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 5 that return to their starting positions and velocities every 144.08 time units, published by Li & Liao (2017). The largest class in the atlas: hundreds of II.C orbits for seven mass ratios. It is linearly stable (largest Floquet multiplier 1.000), so a small nudge only makes it wobble. The bodies pass within 0.0000128 of each other at a top speed of 807, line up 460 times a period, and the computed loop closes to 3.2×10⁻²².

Measured over one period

Period: 144.0759760
Masses: 1 : 1 : 5
Energy: -8.36132
Angular momentum: 0
Closest approach: 1.3×10⁻⁵
Top speed: 806.9
Path length: 639.77
Alignments per period: 460
Topology: ababababababababABABABABABABABababababababababABABABABABABABabababababababaBABABABABABABABabababababababaBABABABABABABABabababababababABABABABABABABABabababababababABABABABABABABAbabababababababABABABABABABABAbabababababababABABABABABABAB (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 3.2×10⁻²²

Neighbours on the map

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