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Schubart region HS.499

From Hristov, Hristova & Tanikawa (2026)

Schubart region HS.499 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 217.93 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 0.0000595 of each other at a top speed of 13, line up 414 times a period, and the computed loop closes to 6.6×10⁻²⁴.

Measured over one period

Period: 217.9270496
Masses: 1 : 1 : 1
Energy: -1.95828
Angular momentum: 0
Closest approach: 5.9×10⁻⁵
Top speed: 129.7
Path length: 581.75
Alignments per period: 414
Topology: ababABAbabaBABababABABababABAbabaBABababABABabaBABAbabaBABababABAbabaBABAbabABABababABAbabaBABAbabABABabaBABAbabaBABababABABabaBABAbabABABababABABabaBABAbabABABababABAbabaBABAbabABABabaBABAbabaBABababABABabaBABAbabaBABababABAbabaBABAbabABAB (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 6.6×10⁻²⁴

Neighbours on the map

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