Atlas1,732 of 3,942

II.C.97

m₃ = 0.75

From Li & Liao (2017)

II.C.97 m₃ = 0.75 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 0.75 that return to their starting positions and velocities every 75.821 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 1769), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00046 of each other at a top speed of 49.7, line up 138 times a period, and the computed loop closes to 3.6×10⁻²⁴.

Measured over one period

Period: 75.82060372
Masses: 1 : 1 : 0.75
Energy: -1.61930
Angular momentum: 0
Closest approach: 4.6×10⁻⁴
Top speed: 49.73
Path length: 211.08
Alignments per period: 138
Topology: ababAbabAbabABabaBAbaBABabABabaBAbaBABabABabaBAbabABabABAbaBAbabABabABAbaBAbabABabaBabaB (free-group class)
Stability: unstable (|λ|max 1769)
Loop closure: 3.6×10⁻²⁴

Neighbours on the map

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