Atlas3,914 of 3,942

SN.20

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

SN.20 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 18.317 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 linearly stable (largest Floquet multiplier 1.000), so a small nudge only makes it wobble. The bodies pass within 0.215 of each other at a top speed of 2.11, line up 30 times a period, and the computed loop closes to 3.2×10⁻²⁹.

Measured over one period

Period: 18.31667215
Masses: 1 : 1 : 1
Energy: -1.83747
Angular momentum: -0.13761
Closest approach: 0.2154
Top speed: 2.114
Path length: 55.504
Alignments per period: 30
Topology: abAB (free-group class, read from the drawing, shape period T/5)
Stability: stable (|λ|max 1.000)
Loop closure: 3.2×10⁻²⁹

Neighbours on the map

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