Atlas1,888 of 3,942

II.C.76

m₃ = 0.5

From Li & Liao (2017)

II.C.76 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 92.829 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 17.51), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000442 of each other at a top speed of 54.9, line up 110 times a period, and the computed loop closes to 3.0×10⁻¹⁴.

Measured over one period

Period: 92.82945476
Masses: 1 : 1 : 0.5
Energy: -0.949419
Angular momentum: 0
Closest approach: 4.4×10⁻⁴
Top speed: 54.90
Path length: 215.63
Alignments per period: 110
Topology: aaBAbaBAbabABabABaaBAbaBAbaBABabABaaBAbaBAbaBABabABabAAbaBAbaBABabABabAB (free-group class)
Stability: unstable (|λ|max 17.51)
Loop closure: 3.0×10⁻¹⁴

Neighbours on the map

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