Atlas2,922 of 3,942

Schubart region HS.829

From Hristov, Hristova & Tanikawa (2026)

Schubart region HS.829 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 330.42 time units, published by Hristov, Hristova & Tanikawa (2026). Stable orbits that pass extremely close to a binary collision, descended from Schubart’s rectilinear orbit. They needed 100-digit arithmetic to find. It is linearly stable (largest Floquet multiplier 1.000), so a small nudge only makes it wobble. The bodies pass within 0.000141 of each other at a top speed of 84.3, line up 502 times a period, and the computed loop closes to 3.4×10⁻²⁴.

Measured over one period

Period: 330.4154100
Masses: 1 : 1 : 1
Energy: -1.71348
Angular momentum: 0
Closest approach: 1.4×10⁻⁴
Top speed: 84.34
Path length: 881.99
Alignments per period: 502
Topology: ababABAbabABAbabABAbabABAbabABAbabABAbabABAbabABAbabaBABabaBABabaBABabaBABabaBABabaBABabaBABabaBABababABAbabABAbabABAbabABAbabABAbabABAbabABAbabABAbabABABabaBABabaBABabaBABabaBABabaBABabaBABabaBABabaBABAbabABAbabABAbabABAbabABAbabABAbabABAbabABAbabABABabaBABabaBABabaBABabaBABabaBABabaBABabaBABabaBAB (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 3.4×10⁻²⁴

Neighbours on the map

All Schubart region, the families of periodic three-body orbits, or the atlas map.