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II.C.1

m₃ = 10

From Li & Liao (2017)

II.C.1 m₃ = 10 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 10 that return to their starting positions and velocities every 48.132 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 2135), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000107 of each other at a top speed of 412, line up 244 times a period, and the computed loop closes to 1.0×10⁻²³.

Measured over one period

Period: 48.13162036
Masses: 1 : 1 : 10
Energy: -18.2456
Angular momentum: 0
Closest approach: 1.1×10⁻⁴
Top speed: 412.0
Path length: 297.01
Alignments per period: 244
Topology: ababababababababababababababababABABABABABABABABABABABABABABABAbababababababababababababababaBABABABABABABABABABABABABABABAB (free-group class)
Stability: unstable (|λ|max 2135)
Loop closure: 1.0×10⁻²³

Neighbours on the map

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