Atlas2,144 of 3,942

II.C.74

m₃ = 0.5

From Li & Liao (2017)

II.C.74 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 69.501 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 18.4), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000333 of each other at a top speed of 63.3, line up 110 times a period, and the computed loop closes to 8.5×10⁻²⁵.

Measured over one period

Period: 69.50109960
Masses: 1 : 1 : 0.5
Energy: -1.13372
Angular momentum: 0
Closest approach: 3.3×10⁻⁴
Top speed: 63.27
Path length: 170.38
Alignments per period: 110
Topology: aabAbaBABabAbabABabABabABabABabABabABabABabABabABabABabAAbbABaaBAbbAABaBB (free-group class)
Stability: unstable (|λ|max 18.40)
Loop closure: 8.5×10⁻²⁵

Neighbours on the map

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