Atlas3,085 of 3,942

Broucke region HS.789

From Hristov, Hristova & Tanikawa (2026)

Broucke region HS.789 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 443.1 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 0.000171 of each other at a top speed of 76.5, line up 474 times a period, and the computed loop closes to 3.6×10⁻²⁴.

Measured over one period

Period: 443.1007344
Masses: 1 : 1 : 1
Energy: -1.39074
Angular momentum: 0
Closest approach: 1.7×10⁻⁴
Top speed: 76.46
Path length: 1136.5
Alignments per period: 474
Topology: aaBAbaBAbaBAbbABabABabAAbaBAbaBAbaBBabABabABaaBAbaBAbaBAbbABabABabABaaBAbaBAbaBBabABabABabAAbaBAbaBAbaBBabABabABaaBAbaBAbaBAbbABabABabABaaBAbaBAbaBBabABabABabAAbaBAbaBAbaBBabABabABaaBAbaBAbaBAbbABabABabAAbaBAbaBAbaBBabABabABabAAbaBAbaBAbbABabABabABaaBAbaBAbaBAbbABabABabAAbaBAbaBAbaBBabABabABabAAbaBAbaBAbbABabABabAB (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 3.6×10⁻²⁴

Neighbours on the map

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