Atlas2,987 of 3,942

Schubart region HS.785

From Hristov, Hristova & Tanikawa (2026)

Schubart region HS.785 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 270.43 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 0.000077 of each other at a top speed of 114, line up 490 times a period, and the computed loop closes to 2.6×10⁻²³.

Measured over one period

Period: 270.4334728
Masses: 1 : 1 : 1
Energy: -1.93021
Angular momentum: 0
Closest approach: 7.7×10⁻⁵
Top speed: 113.9
Path length: 770.45
Alignments per period: 490
Topology: ababABabaBABAbabABabaBABAbabABabaBABAbabABabaBABAbabABabaBABAbabABabaBABAbabABabaBABAbabABabaBABAbabABabaBABAbabABabaBABAbabABabaBABAbabABabaBABAbabABababABAbaBABababABAbaBABababABAbaBABababABAbaBABababABAbaBABababABAbaBABababABAbaBABababABAbaBABababABAbaBABababABAbaBABababABAbaBABababABAbaBAB (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.