Atlas2,107 of 3,942

II.C.200

m₃ = 0.5

From Li & Liao (2017)

II.C.200 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 159.73 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 1.757), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00000559 of each other at a top speed of 488, line up 236 times a period, and the computed loop closes to 5.0×10⁻¹⁷.

Measured over one period

Period: 159.7348584
Masses: 1 : 1 : 0.5
Energy: -1.07965
Angular momentum: 0
Closest approach: 5.6×10⁻⁶
Top speed: 488.3
Path length: 384.85
Alignments per period: 236
Topology: aaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBAbaBABaBABabABabABabABabABabABabABabABabABabABabABabABabABabABabABabABabABabABaaBB (free-group class)
Stability: weakly unstable (|λ|max 1.757)
Loop closure: 5.0×10⁻¹⁷

Neighbours on the map

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