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BHH satellite R4 13/11

From Three Body Orbits (2026)

BHH satellite R4 13/11 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 190.57 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 0.534 of each other at a top speed of 1.49, line up 88 times a period, and the computed loop closes to 1.8×10⁻²⁸. 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: 190.5712239
Masses: 1 : 1 : 1
Energy: -1.00000
Angular momentum: 2.4834
Closest approach: 0.5340
Top speed: 1.489
Path length: 446.51
Alignments per period: 88
Topology: (a)⁴ (free-group class, read from the drawing, shape period T/11)
Stability: stable (|λ|max 1.000)
Loop closure: 1.8×10⁻²⁸

Neighbours on the map

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