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BHH A-family closure 2/3 (0.3:0.6:1)

From Three Body Orbits (2026)

BHH A-family closure 2/3 (0.3:0.6:1) is a periodic orbit of the planar three-body problem: three masses in the ratio 0.3 : 0.6 : 1 that return to their starting positions and velocities every 3.5809 time units, published by Three Body Orbits (2026). Satellites of the Broucke–Hadjidemetriou–Hénon family at equal masses, closed by a rational rotation. A satellite loop is k laps around the binary, of the retrograde (A) or the prograde (R) branch, and the pattern turns r/s of a turn per loop, so the orbit closes after s loops. Fourteen linearly stable ones from the site’s own September 2026 bifurcation search, none in the catalogues checked. Their words are powers of the family’s one-letter word: new orbits, not new topologies. Coded by branch, k and r/s. One further orbit, A 2/3 (0.3:0.6:1), is no satellite: a stable member of the A family itself at masses 0.3, 0.6 and 1, closed at two thirds of a turn per loop, a known family at a closure the catalogues do not list, included for its shape. It is linearly stable (largest Floquet multiplier 1.000), so a small nudge only makes it wobble. The bodies pass within 0.257 of each other at a top speed of 2.33, line up 6 times a period, and the computed loop closes to 8.3×10⁻²⁸. How they were found, checked against the catalogues and what is and is not new about them is set out in the research note.

Measured over one period

Period: 3.580933325
Masses: 0.3 : 0.6 : 1
Energy: -1.00000
Angular momentum: 0.38958
Closest approach: 0.2572
Top speed: 2.327
Path length: 10.722
Alignments per period: 6
Topology: a (free-group class, read from the drawing, shape period T/3)
Stability: stable (|λ|max 1.000)
Loop closure: 8.3×10⁻²⁸

Neighbours on the map

All BHH satellites, the families of periodic three-body orbits, or the atlas map.