Three Body Orbits

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Broucke region

Stable orbits related to Broucke’s isosceles orbit, with one body swinging through the other two.

Broucke region are periodic solutions of the planar three-body problem. The atlas holds 74 of them, with periods from 102.8 to 481.9, all with equal masses; all of them are linearly stable. They come from Hristov, Hristova & Tanikawa (2026), An extensive search for stable periodic orbits of the equal-mass zero angular momentum three-body problem. Every orbit is precomputed to machine precision and plays one period at a time; open one to watch it, nudge it or rate it.

Hristov, Hristova & Tanikawa (2026). An extensive search for stable periodic orbits of the equal-mass zero angular momentum three-body problem. New Astronomy 125 (link)

See them on the mapOpen Broucke region HS.47

All 74 orbits

Broucke region HS.47, a periodic three-body orbitBroucke region HS.47T 102.8 stableBroucke region HS.60, a periodic three-body orbitBroucke region HS.60T 128.9 stableBroucke region HS.103, a periodic three-body orbitBroucke region HS.103T 163.9 stableBroucke region HS.104, a periodic three-body orbitBroucke region HS.104T 164.9 stableBroucke region HS.110, a periodic three-body orbitBroucke region HS.110T 184.9 stableBroucke region HS.140, a periodic three-body orbitBroucke region HS.140T 195.8 stableBroucke region HS.145, a periodic three-body orbitBroucke region HS.145T 202.6 stableBroucke region HS.150, a periodic three-body orbitBroucke region HS.150T 207.9 stableBroucke region HS.169, a periodic three-body orbitBroucke region HS.169T 192.8 stableBroucke region HS.171, a periodic three-body orbitBroucke region HS.171T 206.5 stableBroucke region HS.178, a periodic three-body orbitBroucke region HS.178T 209.7 stableBroucke region HS.186, a periodic three-body orbitBroucke region HS.186T 219.1 stableBroucke region HS.188, a periodic three-body orbitBroucke region HS.188T 223.6 stableBroucke region HS.223, a periodic three-body orbitBroucke region HS.223T 239.0 stableBroucke region HS.224, a periodic three-body orbitBroucke region HS.224T 249.7 stableBroucke region HS.238, a periodic three-body orbitBroucke region HS.238T 252.6 stableBroucke region HS.239, a periodic three-body orbitBroucke region HS.239T 263.8 stableBroucke region HS.255, a periodic three-body orbitBroucke region HS.255T 254.0 stableBroucke region HS.256, a periodic three-body orbitBroucke region HS.256T 263.4 stableBroucke region HS.267, a periodic three-body orbitBroucke region HS.267T 249.4 stableBroucke region HS.268, a periodic three-body orbitBroucke region HS.268T 266.3 stableBroucke region HS.269, a periodic three-body orbitBroucke region HS.269T 275.0 stableBroucke region HS.279, a periodic three-body orbitBroucke region HS.279T 263.9 stableBroucke region HS.280, a periodic three-body orbitBroucke region HS.280T 268.5 stableBroucke region HS.290, a periodic three-body orbitBroucke region HS.290T 274.6 stableBroucke region HS.328, a periodic three-body orbitBroucke region HS.328T 309.4 stableBroucke region HS.370, a periodic three-body orbitBroucke region HS.370T 276.7 stableBroucke region HS.372, a periodic three-body orbitBroucke region HS.372T 266.7 stableBroucke region HS.374, a periodic three-body orbitBroucke region HS.374T 315.0 stableBroucke region HS.377, a periodic three-body orbitBroucke region HS.377T 328.1 stableBroucke region HS.387, a periodic three-body orbitBroucke region HS.387T 319.4 stableBroucke region HS.397, a periodic three-body orbitBroucke region HS.397T 288.5 stableBroucke region HS.420, a periodic three-body orbitBroucke region HS.420T 318.2 stableBroucke region HS.434, a periodic three-body orbitBroucke region HS.434T 300.6 stableBroucke region HS.436, a periodic three-body orbitBroucke region HS.436T 324.9 stableBroucke region HS.450, a periodic three-body orbitBroucke region HS.450T 332.1 stableBroucke region HS.451, a periodic three-body orbitBroucke region HS.451T 348.7 stableBroucke region HS.485, a periodic three-body orbitBroucke region HS.485T 334.2 stableBroucke region HS.489, a periodic three-body orbitBroucke region HS.489T 342.7 stableBroucke region HS.492, a periodic three-body orbitBroucke region HS.492T 348.0 stableBroucke region HS.500, a periodic three-body orbitBroucke region HS.500T 346.5 stableBroucke region HS.501, a periodic three-body orbitBroucke region HS.501T 319.7 stableBroucke region HS.532, a periodic three-body orbitBroucke region HS.532T 378.3 stableBroucke region HS.540, a periodic three-body orbitBroucke region HS.540T 360.2 stableBroucke region HS.541, a periodic three-body orbitBroucke region HS.541T 377.1 stableBroucke region HS.557, a periodic three-body orbitBroucke region HS.557T 389.6 stableBroucke region HS.581, a periodic three-body orbitBroucke region HS.581T 345.1 stableBroucke region HS.583, a periodic three-body orbitBroucke region HS.583T 375.3 stableBroucke region HS.615, a periodic three-body orbitBroucke region HS.615T 376.8 stableBroucke region HS.616, a periodic three-body orbitBroucke region HS.616T 397.8 stableBroucke region HS.633, a periodic three-body orbitBroucke region HS.633T 351.5 stableBroucke region HS.634, a periodic three-body orbitBroucke region HS.634T 411.7 stableBroucke region HS.635, a periodic three-body orbitBroucke region HS.635T 406.1 stableBroucke region HS.658, a periodic three-body orbitBroucke region HS.658T 389.0 stableBroucke region HS.659, a periodic three-body orbitBroucke region HS.659T 397.7 stableBroucke region HS.660, a periodic three-body orbitBroucke region HS.660T 409.6 stableBroucke region HS.677, a periodic three-body orbitBroucke region HS.677T 402.5 stableBroucke region HS.695, a periodic three-body orbitBroucke region HS.695T 405.1 stableBroucke region HS.721, a periodic three-body orbitBroucke region HS.721T 374.3 stableBroucke region HS.722, a periodic three-body orbitBroucke region HS.722T 407.1 stableBroucke region HS.742, a periodic three-body orbitBroucke region HS.742T 438.2 stableBroucke region HS.743, a periodic three-body orbitBroucke region HS.743T 445.8 stableBroucke region HS.745, a periodic three-body orbitBroucke region HS.745T 441.3 stableBroucke region HS.787, a periodic three-body orbitBroucke region HS.787T 397.2 stableBroucke region HS.789, a periodic three-body orbitBroucke region HS.789T 443.1 stableBroucke region HS.830, a periodic three-body orbitBroucke region HS.830T 441.2 stableBroucke region HS.831, a periodic three-body orbitBroucke region HS.831T 446.4 stableBroucke region HS.875, a periodic three-body orbitBroucke region HS.875T 466.4 stableBroucke region HS.901, a periodic three-body orbitBroucke region HS.901T 448.4 stableBroucke region HS.902, a periodic three-body orbitBroucke region HS.902T 457.0 stableBroucke region HS.903, a periodic three-body orbitBroucke region HS.903T 473.3 stableBroucke region HS.921, a periodic three-body orbitBroucke region HS.921T 476.7 stableBroucke region HS.949, a periodic three-body orbitBroucke region HS.949T 481.9 stableBroucke region HS.970, a periodic three-body orbitBroucke region HS.970T 442.9 stable