Atlas1,819 of 3,942

II.C.73

m₃ = 0.5

From Li & Liao (2017)

II.C.73 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 95.184 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 135.6), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000663 of each other at a top speed of 44.9, line up 106 times a period, and the computed loop closes to 8.2×10⁻²⁵.

Measured over one period

Period: 95.18412127
Masses: 1 : 1 : 0.5
Energy: -0.916278
Angular momentum: 0
Closest approach: 6.6×10⁻⁴
Top speed: 44.85
Path length: 218.75
Alignments per period: 106
Topology: aaBAbaBAbabABabAAbaBAbabABabAAbaBAbabABabAAbaBAbaBABabABaaBAbaBABabAB (free-group class)
Stability: unstable (|λ|max 135.6)
Loop closure: 8.2×10⁻²⁵

Neighbours on the map

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