Atlas2,172 of 3,942

II.C.132

m₃ = 0.5

From Li & Liao (2017)

II.C.132 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 124.26 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 154.7), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000833 of each other at a top speed of 127, line up 168 times a period, and the computed loop closes to 1.7×10⁻²³.

Measured over one period

Period: 124.2563024
Masses: 1 : 1 : 0.5
Energy: -1.01510
Angular momentum: 0
Closest approach: 8.3×10⁻⁵
Top speed: 126.5
Path length: 286.72
Alignments per period: 168
Topology: aabAbaBABaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBBaaBAbbAABaBB (free-group class)
Stability: unstable (|λ|max 154.7)
Loop closure: 1.7×10⁻²³

Neighbours on the map

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