Atlas3,905 of 3,942

SN.9

From Šuvakov (2026). Thirteen equal-mass orbits with angular momentum from Milovan Šuvakov’s own searches, shared with this atlas.

SN.9 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 3.4941 time units. Thirteen equal-mass orbits with angular momentum from Milovan Šuvakov’s own searches, shared with this atlas in September 2026. Seven are the figure-eight carried to nonzero angular momentum, its 1/5 to 2/3 resonances, all linearly stable; four lie on a branch that ends, at zero angular momentum, in Broucke’s isosceles collision orbit; two branch off Broucke’s A family. Numbered as in his file. It is weakly unstable (largest Floquet multiplier 9.860), so a small nudge makes it unravel over a few periods. The bodies pass within 0.157 of each other at a top speed of 2.91, line up 8 times a period, and the computed loop closes to 1.7×10⁻²⁹.

Measured over one period

Period: 3.494099869
Masses: 1 : 1 : 1
Energy: -2.25487
Angular momentum: -0.74357
Closest approach: 0.1568
Top speed: 2.910
Path length: 11.646
Alignments per period: 8
Topology: (a)⁴ (free-group class, read from the drawing)
Stability: weakly unstable (|λ|max 9.860)
Loop closure: 1.7×10⁻²⁹

Neighbours on the map

All Šuvakov’s other orbits, the families of periodic three-body orbits, or the atlas map.