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BHH satellites

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.

BHH satellites are periodic solutions of the planar three-body problem. The atlas holds 15 of them, with periods from 3.581 to 190.6, for several mass ratios; all of them are linearly stable. They come from Three Body Orbits (2026), Stable satellites of the Broucke–Hadjidemetriou–Hénon family. Every orbit is precomputed to machine precision and plays one period at a time; open one to watch it, nudge it or rate it.

Three Body Orbits (2026). Stable satellites of the Broucke–Hadjidemetriou–Hénon family. Research note, threebodyorbits.com, 27 September 2026