Atlas1,703 of 3,942

II.C.91

m₃ = 0.5

From Li & Liao (2017)

II.C.91 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 66.051 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 31.51), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000388 of each other at a top speed of 185, line up 132 times a period, and the computed loop closes to 9.6×10⁻²⁴.

Measured over one period

Period: 66.05058967
Masses: 1 : 1 : 0.5
Energy: -1.31721
Angular momentum: 0
Closest approach: 3.9×10⁻⁵
Top speed: 185.4
Path length: 173.27
Alignments per period: 132
Topology: aabAbaBABaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBBaaBAbbAABaBB (free-group class)
Stability: unstable (|λ|max 31.51)
Loop closure: 9.6×10⁻²⁴

Neighbours on the map

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