Atlas1,669 of 3,942

II.C.69

m₃ = 0.75

From Li & Liao (2017)

II.C.69 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 98.561 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 622), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00159 of each other at a top speed of 26.8, line up 92 times a period, and the computed loop closes to 7.8×10⁻²⁵.

Measured over one period

Period: 98.56060693
Masses: 1 : 1 : 0.75
Energy: -1.08696
Angular momentum: 0
Closest approach: 0.001594
Top speed: 26.75
Path length: 234.16
Alignments per period: 92
Topology: aaBAbabAAbaBAbabABaaBABabAAbaBAbabAAbaBABaaBAbabABabAAbaBAB (free-group class)
Stability: unstable (|λ|max 6220)
Loop closure: 7.8×10⁻²⁵

Neighbours on the map

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