Atlas1,868 of 3,942

II.C.162

m₃ = 0.5

From Li & Liao (2017)

II.C.162 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 102.99 time units, published by Li & Liao (2017). The largest class in the atlas: hundreds of II.C orbits for seven mass ratios. It is weakly unstable (largest Floquet multiplier 2.696), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000405 of each other at a top speed of 181, line up 198 times a period, and the computed loop closes to 2.3×10⁻²³.

Measured over one period

Period: 102.9916395
Masses: 1 : 1 : 0.5
Energy: -1.28363
Angular momentum: 0
Closest approach: 4.1×10⁻⁵
Top speed: 181.3
Path length: 262.64
Alignments per period: 198
Topology: aaBabaBAbABAbaBabaBAbABAbaBabaBAbABAbaBabaBAbABAbaBabaBAbABAbaBAbaBAbaBAbaBAbbAAbaBBaaBAbbAAbaBBaaBAbbAAbaBBaaBAbbAAbaBBaaBAbbAAbaBB (free-group class)
Stability: weakly unstable (|λ|max 2.696)
Loop closure: 2.3×10⁻²³

Neighbours on the map

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