Atlas2,218 of 3,942

II.C.35

m₃ = 0.5

From Li & Liao (2017)

II.C.35 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 48.227 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 2.057), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000339 of each other at a top speed of 62.7, line up 60 times a period, and the computed loop closes to 5.4×10⁻²⁵.

Measured over one period

Period: 48.22702263
Masses: 1 : 1 : 0.5
Energy: -0.960500
Angular momentum: 0
Closest approach: 3.4×10⁻⁴
Top speed: 62.70
Path length: 106.89
Alignments per period: 60
Topology: aabAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbbAABaBB (free-group class)
Stability: weakly unstable (|λ|max 2.057)
Loop closure: 5.4×10⁻²⁵

Neighbours on the map

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