Atlas2,041 of 3,942

II.C.79

m₃ = 0.5

From Li & Liao (2017)

II.C.79 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 80.1 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 3.417), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000365 of each other at a top speed of 60.5, line up 114 times a period, and the computed loop closes to 2.2×10⁻²⁵.

Measured over one period

Period: 80.10015033
Masses: 1 : 1 : 0.5
Energy: -1.06674
Angular momentum: 0
Closest approach: 3.6×10⁻⁴
Top speed: 60.47
Path length: 195.61
Alignments per period: 114
Topology: aaBAbaBAbaBAbabABabABabAAbaBAbaBAbaBABabABabABabAAbaBAbaBAbaBAbabABabABabAB (free-group class)
Stability: weakly unstable (|λ|max 3.417)
Loop closure: 2.2×10⁻²⁵

Neighbours on the map

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