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BH-1252

From Three Body Orbits (2026)

BH-1252 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 783.8 time units, published by Three Body Orbits (2026). Three linearly stable orbits found here in September 2026 by pushing the Broucke region past the published catalogue’s limit of T* = 800: two continue known lap sequences, one is a seventeen-fold resonant satellite of the Broucke-region orbit B1. Verified independently to 160 bits and again by this atlas’s own tool; not published elsewhere. It is linearly stable (largest Floquet multiplier 1.000), so a small nudge only makes it wobble. The bodies pass within 0.0256 of each other at a top speed of 6.25, line up 816 times a period, and the computed loop closes to 4.1×10⁻²⁶. How they were found, verified and compared with the catalogues is set out in the research note.

Measured over one period

Period: 783.7954589
Masses: 1 : 1 : 1
Energy: -1.36666
Angular momentum: 0
Closest approach: 0.02565
Top speed: 6.253
Path length: 2028.5
Alignments per period: 816
Topology: (aaBAbaBAbaBAbaBAbbABabABabABabAB)¹⁷ (free-group class)
Stability: stable (|λ|max 1.000)
Loop closure: 4.1×10⁻²⁶

Neighbours on the map

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