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II.C.2

m₃ = 10

From Li & Liao (2017)

II.C.2 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 49.869 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 6.197), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000152 of each other at a top speed of 1092, line up 256 times a period, and the computed loop closes to 1.3×10⁻²¹.

Measured over one period

Period: 49.86852070
Masses: 1 : 1 : 10
Energy: -18.3852
Angular momentum: 0
Closest approach: 1.5×10⁻⁵
Top speed: 1092
Path length: 306.35
Alignments per period: 256
Stability: weakly unstable (|λ|max 6.197)
Loop closure: 1.3×10⁻²¹

Neighbours on the map

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