Atlas2,048 of 3,942

II.C.109

m₃ = 0.5

From Li & Liao (2017)

II.C.109 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 84.964 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 25.21), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0000934 of each other at a top speed of 119, line up 148 times a period, and the computed loop closes to 1.1×10⁻²³.

Measured over one period

Period: 84.96412546
Masses: 1 : 1 : 0.5
Energy: -1.21183
Angular momentum: 0
Closest approach: 9.3×10⁻⁵
Top speed: 119.4
Path length: 213.24
Alignments per period: 148
Topology: aabAbaBABabAbabABaBABabAbaaBBabAAbaBBaaBAbbAAbaBAbabAbaBABaBAbabABaBAAbbABaaBBabAAbbABaaBAbbAABaBB (free-group class)
Stability: unstable (|λ|max 25.21)
Loop closure: 1.1×10⁻²³

Neighbours on the map

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