{
 "title": "Stable satellites of the Broucke–Hadjidemetriou–Hénon family",
 "date": "2026-09-27",
 "units": "G = 1, unit masses, centre-of-mass frame, E = -1; state = x1, y1, x2, y2, x3, y3, vx1, vy1, vx2, vy2, vx3, vy3 (60 digits); T* = T|E|^(3/2)/M^(5/2), L* = L|E|^(1/2)/M^(5/2)",
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   "atlas_closure": 8.5e-14,
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  },
  {
   "key": "bhhsat_a7_17_9",
   "code": "A7 17/9",
   "branch": "A",
   "k": 7,
   "rotation_per_satellite_loop": "17/9",
   "masses": [
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    1
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   "atlas_closure": 9.1e-29,
   "atlas_stab": 1.0
  },
  {
   "key": "bhhsat_r4_13_11",
   "code": "R4 13/11",
   "branch": "R",
   "k": 4,
   "rotation_per_satellite_loop": "13/11",
   "masses": [
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    1
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   "energy": -1,
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   "closure_192bit": 2.8938897516458016e-33,
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 ],
 "exception": {
  "key": "bhhsat_a_2_3_m0p3_0p6_1",
  "code": "A 2/3 (0.3:0.6:1)",
  "note": "Not a satellite: a member of Broucke’s A family at unequal masses, closed at a rotation of 2/3 turn per loop (3 loops); a known family at a closure absent from the catalogues checked, included for its shape.",
  "masses": [
   "0.3",
   "0.6",
   "1"
  ],
  "energy": -1,
  "state": [
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  "word": "121212",
  "closure_192bit": 4.959845837214982e-37,
  "max_abs_multiplier_128bit": 1.0000000000022982,
  "atlas_closure": 8.300000000000001e-28,
  "atlas_stab": 1.0
 }
}