Three Body Orbits

Families / Broucke

Broucke A orbits

Broucke’s 1975 family of orbits with a distant third body circling a close binary; several are linearly stable.

Broucke A orbits are periodic solutions of the planar three-body problem. The atlas holds 16 of them, with periods from 6.283 to 92.06, all with equal masses; 12 of them are linearly stable. They come from Broucke (1975), On relative periodic solutions of the planar general 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.

Broucke (1975). On relative periodic solutions of the planar general three-body problem. Celestial Mechanics 12, 439–462 (doi)

See them on the mapOpen Broucke A1

All 16 orbits

Broucke A1, a periodic three-body orbitBroucke A1T 6.283 stableBroucke A2, a periodic three-body orbitBroucke A2T 7.702 stableBroucke A3, a periodic three-body orbitBroucke A3T 7.910 stableBroucke A4, a periodic three-body orbitBroucke A4T 8.212 stableBroucke A5, a periodic three-body orbitBroucke A5T 8.689 stableBroucke A6, a periodic three-body orbitBroucke A6T 9.593 stableBroucke A7, a periodic three-body orbitBroucke A7T 12.06 stableBroucke A8, a periodic three-body orbitBroucke A8T 18.12 stableBroucke A9, a periodic three-body orbitBroucke A9T 20.90 stableBroucke A10, a periodic three-body orbitBroucke A10T 32.61Broucke A11, a periodic three-body orbitBroucke A11T 32.58 stableBroucke A12, a periodic three-body orbitBroucke A12T 42.82 stableBroucke A13, a periodic three-body orbitBroucke A13T 59.72Broucke A14, a periodic three-body orbitBroucke A14T 54.23 stableBroucke A15, a periodic three-body orbitBroucke A15T 92.06Broucke A16, a periodic three-body orbitBroucke A16T 90.87