Atlas1,632 of 3,942

II.C.31

m₃ = 0.5

From Li & Liao (2017)

II.C.31 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 25.812 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 855.4), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00272 of each other at a top speed of 22.2, line up 52 times a period, and the computed loop closes to 3.2×10⁻²⁶.

Measured over one period

Period: 25.81150286
Masses: 1 : 1 : 0.5
Energy: -1.40431
Angular momentum: 0
Closest approach: 0.002719
Top speed: 22.24
Path length: 74.848
Alignments per period: 52
Topology: aaabAbaBAABabABabABaaaBAbbAAABaBB (free-group class)
Stability: unstable (|λ|max 855.4)
Loop closure: 3.2×10⁻²⁶

Neighbours on the map

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