Atlas2,094 of 3,942

II.C.61

m₃ = 0.5

From Li & Liao (2017)

II.C.61 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 57.867 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 13.67), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00132 of each other at a top speed of 31.8, line up 92 times a period, and the computed loop closes to 1.3×10⁻²⁵.

Measured over one period

Period: 57.86692412
Masses: 1 : 1 : 0.5
Energy: -1.13836
Angular momentum: 0
Closest approach: 0.001321
Top speed: 31.77
Path length: 142.14
Alignments per period: 92
Topology: aabAbaBABabAbabABabABabABabABabABabABabABabAAbbABaaBAbbAABaBB (free-group class)
Stability: unstable (|λ|max 13.67)
Loop closure: 1.3×10⁻²⁵

Neighbours on the map

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