Three Body Orbits

Families / Broucke

Broucke R orbits

Retrograde relatives of the A family, with the third body circling the other way.

Broucke R orbits are periodic solutions of the planar three-body problem. The atlas holds 13 of them, with periods from 5.089 to 22.76, all with equal masses; 8 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 R3

All 13 orbits

Broucke R1, a periodic three-body orbitBroucke R1T 5.227Broucke R2, a periodic three-body orbitBroucke R2T 5.704Broucke R3, a periodic three-body orbitBroucke R3T 5.561 stableBroucke R4, a periodic three-body orbitBroucke R4T 5.396 stableBroucke R5, a periodic three-body orbitBroucke R5T 5.267 stableBroucke R6, a periodic three-body orbitBroucke R6T 5.167 stableBroucke R7, a periodic three-body orbitBroucke R7T 5.089 stableBroucke R8, a periodic three-body orbitBroucke R8T 11.22Broucke R9, a periodic three-body orbitBroucke R9T 11.30 stableBroucke R10, a periodic three-body orbitBroucke R10T 10.95 stableBroucke R11, a periodic three-body orbitBroucke R11T 17.02Broucke R12, a periodic three-body orbitBroucke R12T 17.02 stableBroucke R13, a periodic three-body orbitBroucke R13T 22.76