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Broucke region HS.450

From Hristov, Hristova & Tanikawa (2026)

Broucke region HS.450 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 332.15 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 0.0000427 of each other at a top speed of 153, line up 366 times a period, and the computed loop closes to 5.5×10⁻²³.

Measured over one period

Period: 332.1486542
Masses: 1 : 1 : 1
Energy: -1.41825
Angular momentum: 0
Closest approach: 4.3×10⁻⁵
Top speed: 153.0
Path length: 854.17
Alignments per period: 366
Topology: aaBAbaBAbaBAbbABabABabAAbaBAbaBAbbABabABabAAbaBAbaBAbbABabABabAAbaBAbaBAbbABabABabAAbaBAbaBAbbABabABabAAbaBAbaBAbbABabABabAAbaBAbaBAbaBBabABabABaaBAbaBAbaBBabABabABaaBAbaBAbaBBabABabABaaBAbaBAbaBBabABabABaaBAbaBAbaBBabABabABaaBAbaBAbaBBabABabAB (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 5.5×10⁻²³

Neighbours on the map

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