Atlas1,490 of 3,942

II.C.18

m₃ = 0.75

From Li & Liao (2017)

II.C.18 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 56.738 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 26.89), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0175 of each other at a top speed of 8.03, line up 46 times a period, and the computed loop closes to 7.8×10⁻²⁶.

Measured over one period

Period: 56.73795127
Masses: 1 : 1 : 0.75
Energy: -0.953957
Angular momentum: 0
Closest approach: 0.01745
Top speed: 8.026
Path length: 123.85
Alignments per period: 46
Topology: abaBabaBAbaBAbabAbabABabABabAB (free-group class)
Stability: unstable (|λ|max 26.89)
Loop closure: 7.8×10⁻²⁶

Neighbours on the map

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