Atlas1,689 of 3,942

II.C.80

m₃ = 0.75

From Li & Liao (2017)

II.C.80 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 109.73 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 2433), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00162 of each other at a top speed of 26.6, line up 104 times a period, and the computed loop closes to 3.3×10⁻²⁵.

Measured over one period

Period: 109.7290498
Masses: 1 : 1 : 0.75
Energy: -1.09973
Angular momentum: 0
Closest approach: 0.001622
Top speed: 26.56
Path length: 260.80
Alignments per period: 104
Topology: aaBAbabAAbaBAbabABaaBAbaBABabAAbaBAbabAAbaBABabAAbaBAbabAAbaBAbabAB (free-group class)
Stability: unstable (|λ|max 2433)
Loop closure: 3.3×10⁻²⁵

Neighbours on the map

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