Atlas3,057 of 3,942

Broucke region HS.616

From Hristov, Hristova & Tanikawa (2026)

Broucke region HS.616 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 397.81 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 0.000547 of each other at a top speed of 42.8, line up 426 times a period, and the computed loop closes to 5.5×10⁻²⁵.

Measured over one period

Period: 397.8134393
Masses: 1 : 1 : 1
Energy: -1.39183
Angular momentum: 0
Closest approach: 5.5×10⁻⁴
Top speed: 42.78
Path length: 1023.6
Alignments per period: 426
Topology: aaBAbaBAbaBAbbABabABabAAbaBAbaBAbaBBabABabABabAAbaBAbaBAbaBBabABabABabAAbaBAbaBAbaBBabABabABabAAbaBAbaBAbaBBabABabABabAAbaBAbaBAbaBBabABabABabAAbaBAbaBAbaBBabABabABaaBAbaBAbaBAbbABabABabABaaBAbaBAbaBAbbABabABabABaaBAbaBAbaBAbbABabABabABaaBAbaBAbaBAbbABabABabABaaBAbaBAbaBAbbABabABabAB (free-group class)
Stability: stable (|λ|max 1.000, published)
Loop closure: 5.5×10⁻²⁵

Neighbours on the map

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