Atlas2,214 of 3,942

II.C.71

m₃ = 0.5

From Li & Liao (2017)

II.C.71 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 95.475 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 3.781), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000785 of each other at a top speed of 13, line up 108 times a period, and the computed loop closes to 8.3×10⁻²⁴.

Measured over one period

Period: 95.47529360
Masses: 1 : 1 : 0.5
Energy: -0.901780
Angular momentum: 0
Closest approach: 7.8×10⁻⁵
Top speed: 130.3
Path length: 201.52
Alignments per period: 108
Topology: aabAbaBAbaBAbaBBaaBAbbAABaBBaaBAbaBAbaBABaBBaabAbaBABaBAbaBAbaBAbbAABaBB (free-group class)
Stability: weakly unstable (|λ|max 3.781)
Loop closure: 8.3×10⁻²⁴

Neighbours on the map

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