Atlas1,548 of 3,942

II.C.87

m₃ = 0.75

From Li & Liao (2017)

II.C.87 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 142.23 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 37.59), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00214 of each other at a top speed of 23, line up 120 times a period, and the computed loop closes to 3.0×10⁻²⁵.

Measured over one period

Period: 142.2301945
Masses: 1 : 1 : 0.75
Energy: -0.978263
Angular momentum: 0
Closest approach: 0.002142
Top speed: 23.04
Path length: 313.60
Alignments per period: 120
Topology: abaBabaBAbaBAbabAbabABabABabaBAbaBAbaBAbabABabABabaBabaBAbaBAbabAbabABabABabAB (free-group class)
Stability: unstable (|λ|max 37.59)
Loop closure: 3.0×10⁻²⁵

Neighbours on the map

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