Atlas1,557 of 3,942

II.C.37

m₃ = 0.75

From Li & Liao (2017)

II.C.37 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 78.338 time units, published by Li & Liao (2017). The largest class in the atlas: hundreds of II.C orbits for seven mass ratios. It is linearly stable (largest Floquet multiplier 1.000), so a small nudge only makes it wobble. The bodies pass within 0.00224 of each other at a top speed of 22.6, line up 68 times a period, and the computed loop closes to 2.5×10⁻²⁵.

Measured over one period

Period: 78.33834539
Masses: 1 : 1 : 0.75
Energy: -0.995044
Angular momentum: 0
Closest approach: 0.002240
Top speed: 22.63
Path length: 173.77
Alignments per period: 68
Topology: abaBabaBAbabAbabABabABabaBAbaBAbaBAbabABabAB (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 2.5×10⁻²⁵

Neighbours on the map

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