Atlas3,091 of 3,942

Broucke region HS.328

From Hristov, Hristova & Tanikawa (2026)

Broucke region HS.328 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 309.39 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 0.00043 of each other at a top speed of 48.2, line up 324 times a period, and the computed loop closes to 1.2×10⁻²⁴.

Measured over one period

Period: 309.3888876
Masses: 1 : 1 : 1
Energy: -1.37194
Angular momentum: 0
Closest approach: 4.3×10⁻⁴
Top speed: 48.23
Path length: 800.80
Alignments per period: 324
Topology: aaBAbaBAbaBAbaBAbbABabABabABabAAbaBAbaBAbaBAbaBBabABabABabABabAAbaBAbaBAbaBAbaBBabABabABabABaaBAbaBAbaBAbaBAbbABabABabABabABaaBAbaBAbaBAbaBBabABabABabABabAAbaBAbaBAbaBAbaBBabABabABabABabAAbaBAbaBAbaBAbbABabABabABabAB (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.