Atlas2,038 of 3,942

II.C.56

m₃ = 0.5

From Li & Liao (2017)

II.C.56 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 56.987 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 8028), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00427 of each other at a top speed of 17.6, line up 84 times a period, and the computed loop closes to 4.4×10⁻²⁵.

Measured over one period

Period: 56.98740781
Masses: 1 : 1 : 0.5
Energy: -1.09767
Angular momentum: 0
Closest approach: 0.004269
Top speed: 17.64
Path length: 142.16
Alignments per period: 84
Topology: aaBAbaBAbaBAbabABabAAbaBAbaBAbabABabAAbaBAbaBAbaBABabAB (free-group class)
Stability: unstable (|λ|max 8028)
Loop closure: 4.4×10⁻²⁵

Neighbours on the map

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