Atlas1,822 of 3,942

II.C.73

m₃ = 0.75

From Li & Liao (2017)

II.C.73 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 132.56 time units, published by Li & Liao (2017). The largest class in the atlas: hundreds of II.C orbits for seven mass ratios. It is weakly unstable (largest Floquet multiplier 5.705), so a small nudge makes it unravel over a few periods. The bodies pass within 0.00427 of each other at a top speed of 16.4, line up 98 times a period, and the computed loop closes to 3.0×10⁻²⁵.

Measured over one period

Period: 132.5567714
Masses: 1 : 1 : 0.75
Energy: -0.931015
Angular momentum: 0
Closest approach: 0.004274
Top speed: 16.36
Path length: 286.56
Alignments per period: 98
Topology: aaBAbabAAbaBAbabABaaBABabAAbaBAbabAAbaBABabABaaBAbabAAbaBABabAB (free-group class)
Stability: weakly unstable (|λ|max 5.705)
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.