Atlas1,609 of 3,942

II.C.45

m₃ = 0.75

From Li & Liao (2017)

II.C.45 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 87.199 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 68.89), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0123 of each other at a top speed of 9.57, line up 80 times a period, and the computed loop closes to 4.5×10⁻²⁷.

Measured over one period

Period: 87.19923952
Masses: 1 : 1 : 0.75
Energy: -1.03447
Angular momentum: 0
Closest approach: 0.01226
Top speed: 9.575
Path length: 197.70
Alignments per period: 80
Topology: abaBabaBAbabAbabABabABabABabaBAbaBAbaBAbabABabABabAB (free-group class)
Stability: unstable (|λ|max 68.89)
Loop closure: 4.5×10⁻²⁷

Neighbours on the map

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