Atlas2,153 of 3,942

II.C.64

m₃ = 0.5

From Li & Liao (2017)

II.C.64 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 64.573 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 4.407), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000825 of each other at a top speed of 40.2, line up 98 times a period, and the computed loop closes to 3.1×10⁻²⁵.

Measured over one period

Period: 64.57302782
Masses: 1 : 1 : 0.5
Energy: -1.10308
Angular momentum: 0
Closest approach: 8.3×10⁻⁴
Top speed: 40.19
Path length: 158.00
Alignments per period: 98
Topology: aaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBABabABabABabABabABabABabABabAB (free-group class)
Stability: weakly unstable (|λ|max 4.407)
Loop closure: 3.1×10⁻²⁵

Neighbours on the map

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