Atlas1,697 of 3,942

II.C.49

m₃ = 0.5

From Li & Liao (2017)

II.C.49 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 40.984 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 623.9), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000816 of each other at a top speed of 40.3, line up 72 times a period, and the computed loop closes to 1.9×10⁻²⁴.

Measured over one period

Period: 40.98419424
Masses: 1 : 1 : 0.5
Energy: -1.29985
Angular momentum: 0
Closest approach: 8.2×10⁻⁴
Top speed: 40.32
Path length: 115.41
Alignments per period: 72
Topology: aaaaBAbbAAABabAbaaaBBaBAAAbbABaaabAbaBAAABaBB (free-group class)
Stability: unstable (|λ|max 623.9)
Loop closure: 1.9×10⁻²⁴

Neighbours on the map

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