Atlas1,722 of 3,942

II.C.72

m₃ = 0.5

From Li & Liao (2017)

II.C.72 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 54.428 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 6.937), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00011 of each other at a top speed of 11, line up 108 times a period, and the computed loop closes to 3.1×10⁻²⁴.

Measured over one period

Period: 54.42763794
Masses: 1 : 1 : 0.5
Energy: -1.31096
Angular momentum: 0
Closest approach: 1.1×10⁻⁴
Top speed: 109.9
Path length: 141.87
Alignments per period: 108
Topology: aabAbaBABaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBBaaBAbbAABaBB (free-group class)
Stability: weakly unstable (|λ|max 6.937)
Loop closure: 3.1×10⁻²⁴

Neighbours on the map

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