Atlas1,793 of 3,942

II.C.161

m₃ = 0.5

From Li & Liao (2017)

II.C.161 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 105.18 time units, published by Li & Liao (2017). The largest class in the atlas: hundreds of II.C orbits for seven mass ratios. It is linearly stable (largest Floquet multiplier 1.014), so a small nudge only makes it wobble. The bodies pass within 0.0000271 of each other at a top speed of 222, line up 198 times a period, and the computed loop closes to 7.9×10⁻¹⁷.

Measured over one period

Period: 105.1805255
Masses: 1 : 1 : 0.5
Energy: -1.26576
Angular momentum: 0
Closest approach: 2.7×10⁻⁵
Top speed: 221.9
Path length: 265.98
Alignments per period: 198
Topology: aaBAbaBAbaBAbaBabaBAbABAbaBabaBAbABAbaBabaBAbABAbaBabaBAbABAbaBabaBAbABAbaBAbbAAbaBBaaBAbbAAbaBBaaBAbbAAbaBBaaBAbbAAbaBBaaBAbbAAbaBB (free-group class)
Stability: stable (|λ|max 1.014)
Loop closure: 7.9×10⁻¹⁷

Neighbours on the map

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