Atlas1,846 of 3,942

II.C.69

m₃ = 0.5

From Li & Liao (2017)

II.C.69 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 50.301 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 3.608), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000219 of each other at a top speed of 78, line up 108 times a period, and the computed loop closes to 8.7×10⁻²⁵.

Measured over one period

Period: 50.30060722
Masses: 1 : 1 : 0.5
Energy: -1.38244
Angular momentum: 0
Closest approach: 2.2×10⁻⁴
Top speed: 78.04
Path length: 131.64
Alignments per period: 108
Topology: aabAbaBAbaBAbaBAbaBAbbAABaBBaabAbaBAbaBAbaBBaabAbbAABaBAbaBAbaBAbbAABaBB (free-group class)
Stability: weakly unstable (|λ|max 3.608)
Loop closure: 8.7×10⁻²⁵

Neighbours on the map

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