Atlas2,174 of 3,942

II.C.37

m₃ = 0.5

From Li & Liao (2017)

II.C.37 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 50.27 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 10.63), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000295 of each other at a top speed of 67.2, line up 62 times a period, and the computed loop closes to 2.7×10⁻²⁵.

Measured over one period

Period: 50.26963845
Masses: 1 : 1 : 0.5
Energy: -0.964196
Angular momentum: 0
Closest approach: 3.0×10⁻⁴
Top speed: 67.20
Path length: 113.87
Alignments per period: 62
Topology: aabAbaBABabABabABabABabABabABaaBAbbAABaBB (free-group class)
Stability: unstable (|λ|max 10.63)
Loop closure: 2.7×10⁻²⁵

Neighbours on the map

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