Atlas3,058 of 3,942

Broucke region HS.140

From Hristov, Hristova & Tanikawa (2026)

Broucke region HS.140 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 195.83 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 0.00105 of each other at a top speed of 30.9, line up 210 times a period, and the computed loop closes to 1.4×10⁻²⁵.

Measured over one period

Period: 195.8266959
Masses: 1 : 1 : 1
Energy: -1.39311
Angular momentum: 0
Closest approach: 0.001046
Top speed: 30.93
Path length: 503.69
Alignments per period: 210
Topology: aaBAbaBAbaBAbbABabABabAAbaBAbaBAbaBBabABabABabAAbaBAbaBAbaBBabABabABabAAbaBAbaBAbaBBabABabABaaBAbaBAbaBAbbABabABabABaaBAbaBAbaBAbbABabABabAB (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 1.4×10⁻²⁵

Neighbours on the map

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