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Schubart region HS.646

From Hristov, Hristova & Tanikawa (2026)

Schubart region HS.646 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 249.03 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 0.0000684 of each other at a top speed of 121, line up 450 times a period, and the computed loop closes to 2.6×10⁻²³.

Measured over one period

Period: 249.0288510
Masses: 1 : 1 : 1
Energy: -1.92673
Angular momentum: 0
Closest approach: 6.8×10⁻⁵
Top speed: 120.9
Path length: 708.79
Alignments per period: 450
Topology: ababABabaBABAbabABabaBABAbabABabaBABAbabABabaBABAbabABabaBABAbabABabaBABAbabABabaBABAbabABabaBABAbabABabaBABAbabABabaBABAbabABabaBABAbabABababABAbaBABababABAbaBABababABAbaBABababABAbaBABababABAbaBABababABAbaBABababABAbaBABababABAbaBABababABAbaBABababABAbaBABababABAbaBAB (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 2.6×10⁻²³

Neighbours on the map

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