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Broucke region HS.695

From Hristov, Hristova & Tanikawa (2026)

Broucke region HS.695 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 405.12 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 0.0000643 of each other at a top speed of 125, line up 450 times a period, and the computed loop closes to 8.2×10⁻²³.

Measured over one period

Period: 405.1219839
Masses: 1 : 1 : 1
Energy: -1.42568
Angular momentum: 0
Closest approach: 6.4×10⁻⁵
Top speed: 124.7
Path length: 1038.4
Alignments per period: 450
Topology: aaBAbaBAbaBBabABabAAbaBAbaBAbbABabABabAAbaBAbaBAbbABabABaaBAbaBAbaBBabABabABaaBAbaBAbbABabABabAAbaBAbaBAbbABabABaaBAbaBAbaBBabABabABaaBAbaBAbbABabABabAAbaBAbaBAbbABabABaaBAbaBAbaBBabABabABaaBAbaBAbaBBabABabAAbaBAbaBAbbABabABabAAbaBAbaBBabABabABaaBAbaBAbaBBabABabAAbaBAbaBAbbABabABabAAbaBAbaBBabABabAB (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 8.2×10⁻²³

Neighbours on the map

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