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II.C.45

m₃ = 0.5

From Li & Liao (2017)

II.C.45 m₃ = 0.5 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 0.5 that return to their starting positions and velocities every 36.075 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 220.8), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000717 of each other at a top speed of 136, line up 68 times a period, and the computed loop closes to 1.1×10⁻²⁴.

Measured over one period

Period: 36.07514188
Masses: 1 : 1 : 0.5
Energy: -1.34894
Angular momentum: 0
Closest approach: 7.2×10⁻⁵
Top speed: 136.3
Path length: 103.55
Alignments per period: 68
Stability: unstable (|λ|max 220.8)
Loop closure: 1.1×10⁻²⁴

Neighbours on the map

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