Atlas3,076 of 3,942

Broucke region HS.875

From Hristov, Hristova & Tanikawa (2026)

Broucke region HS.875 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 466.37 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 0.000205 of each other at a top speed of 69.9, line up 498 times a period, and the computed loop closes to 1.8×10⁻²⁴.

Measured over one period

Period: 466.3674709
Masses: 1 : 1 : 1
Energy: -1.38848
Angular momentum: 0
Closest approach: 2.0×10⁻⁴
Top speed: 69.93
Path length: 1150.0
Alignments per period: 498
Topology: aaBAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBAbbABabABaaBAbaBAbbABabABaaBAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBAbbABabABaaBAbaBAbbABabABaaBAbaBAbaBBabABabAAbaBAbaBBabABabAAbaBAbaBAbbABabABaaBAbaBAbbABabABaaBAbaBAbbABabABaaBAbaBAbbABabABaaBAbaBAbbABabABaaBAbaBAbbABabAB (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 1.8×10⁻²⁴

Neighbours on the map

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