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Schubart region HS.612

From Hristov, Hristova & Tanikawa (2026)

Schubart region HS.612 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 295.51 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 0.000146 of each other at a top speed of 82.7, line up 452 times a period, and the computed loop closes to 1.1×10⁻²³.

Measured over one period

Period: 295.5064384
Masses: 1 : 1 : 1
Energy: -1.69479
Angular momentum: 0
Closest approach: 1.5×10⁻⁴
Top speed: 82.71
Path length: 732.44
Alignments per period: 452
Topology: ababABAbabaBABababABAbabaBABAbabaBABababABABabaBABababABABababABAbabaBABAbabABABabaBABAbabaBABababABABababABAbabABABababABAbabaBABAbabaBABababABAbabaBABababABABababABAbabaBABAbabABAbabaBABAbabaBABababABABabaBABAbabABABababABAbabaBABAbabaBABabaBABAbabaBABababABAB (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 1.1×10⁻²³

Neighbours on the map

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