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Broucke region HS.532

From Hristov, Hristova & Tanikawa (2026)

Broucke region HS.532 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 378.34 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 0.00685 of each other at a top speed of 12.1, line up 396 times a period, and the computed loop closes to 2.0×10⁻²⁵.

Measured over one period

Period: 378.3398361
Masses: 1 : 1 : 1
Energy: -1.37063
Angular momentum: 0
Closest approach: 0.006855
Top speed: 12.09
Path length: 961.31
Alignments per period: 396
Topology: (aaBAbaBAbaBAbbABabABabAAbaBAbaBAbaBBabABabAB)⁶ (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 2.0×10⁻²⁵

Neighbours on the map

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