Atlas2,097 of 3,942

II.C.221

m₃ = 0.5

From Li & Liao (2017)

II.C.221 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 190.44 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 2.406), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000111 of each other at a top speed of 11, line up 256 times a period, and the computed loop closes to 3.3×10⁻²⁴.

Measured over one period

Period: 190.4434521
Masses: 1 : 1 : 0.5
Energy: -1.01591
Angular momentum: 0
Closest approach: 1.1×10⁻⁴
Top speed: 109.8
Path length: 446.27
Alignments per period: 256
Topology: aaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbabABabABabABabABabABabABabABabABabABabABabAAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBABabABabABabABabABabABabABabABabABabABabABabAB (free-group class)
Stability: weakly unstable (|λ|max 2.406)
Loop closure: 3.3×10⁻²⁴

Neighbours on the map

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