Atlas1,919 of 3,942

II.C.58

m₃ = 0.5

From Li & Liao (2017)

II.C.58 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 41.187 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 6.122), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000506 of each other at a top speed of 51.3, line up 90 times a period, and the computed loop closes to 7.6×10⁻²⁵.

Measured over one period

Period: 41.18707392
Masses: 1 : 1 : 0.5
Energy: -1.39910
Angular momentum: 0
Closest approach: 5.1×10⁻⁴
Top speed: 51.27
Path length: 107.28
Alignments per period: 90
Topology: aabAbaBAbaBAbaBBaabAbbAABaBAbaBAbaBAbbAABaBBaabAbaBAbbAABaBB (free-group class)
Stability: weakly unstable (|λ|max 6.122)
Loop closure: 7.6×10⁻²⁵

Neighbours on the map

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