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Broucke region HS.634

From Hristov, Hristova & Tanikawa (2026)

Broucke region HS.634 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 411.74 time units, published by Hristov, Hristova & Tanikawa (2026). Stable orbits related to Broucke’s isosceles orbit, with one body swinging through the other two. It is linearly stable (largest Floquet multiplier 1.000), so a small nudge only makes it wobble. The bodies pass within 0.000279 of each other at a top speed of 59.9, line up 432 times a period, and the computed loop closes to 1.2×10⁻²⁴.

Measured over one period

Period: 411.7417245
Masses: 1 : 1 : 1
Energy: -1.37285
Angular momentum: 0
Closest approach: 2.8×10⁻⁴
Top speed: 59.91
Path length: 1048.0
Alignments per period: 432
Topology: aaBAbaBAbaBAbbABabABabAAbaBAbaBAbaBBabABabABaaBAbaBAbaBAbbABabABabAAbaBAbaBAbaBBabABabABaaBAbaBAbaBAbbABabABabAAbaBAbaBAbaBBabABabABaaBAbaBAbaBAbbABabABabABaaBAbaBAbaBBabABabABabAAbaBAbaBAbbABabABabABaaBAbaBAbaBBabABabABabAAbaBAbaBAbbABabABabABaaBAbaBAbaBBabABabABabAAbaBAbaBAbbABabABabAB (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 1.2×10⁻²⁴

Neighbours on the map

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