Atlas1,556 of 3,942

II.C.121

m₃ = 0.75

From Li & Liao (2017)

II.C.121 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 197.85 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 6061), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00667 of each other at a top speed of 13.1, line up 176 times a period, and the computed loop closes to 5.2×10⁻²⁵.

Measured over one period

Period: 197.8478046
Masses: 1 : 1 : 0.75
Energy: -1.01190
Angular momentum: 0
Closest approach: 0.006667
Top speed: 13.06
Path length: 442.43
Alignments per period: 176
Topology: abaBabaBAbaBAbabAbabABabABabaBAbaBAbabABabABabABabaBAbaBAbabABabABabaBabaBAbaBAbabAbabABabABabaBAbaBAbaBAbabABabAB (free-group class)
Stability: unstable (|λ|max 6061)
Loop closure: 5.2×10⁻²⁵

Neighbours on the map

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