Three Body Orbits

Families / Broucke

Broucke–Boggs orbits

Broucke and Boggs’s 1975 survey of periodic orbits at many mass ratios, most of them reported linearly stable.

Broucke–Boggs orbits are periodic solutions of the planar three-body problem. The atlas holds 23 of them, with periods from 4.269 to 12.57, for several mass ratios; 22 of them are linearly stable. They come from Broucke & Boggs (1975), Periodic orbits in 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 & Boggs (1975). Periodic orbits in the planar general three-body problem. Celestial Mechanics 11, 13–38 (doi)

See them on the mapOpen Broucke–Boggs S3

All 23 orbits

Broucke–Boggs S3, a periodic three-body orbitBroucke–Boggs S3 (0.03, 0.03, 2.94)T 6.102 stableBroucke–Boggs S4, a periodic three-body orbitBroucke–Boggs S4T 4.269 stableBroucke–Boggs S20, a periodic three-body orbitBroucke–Boggs S20 (0.03, 0.03, 2.94)T 12.57 stableBroucke–Boggs S21, a periodic three-body orbitBroucke–Boggs S21 (0.033, 0.03, 2.937)T 12.57 stableBroucke–Boggs S22, a periodic three-body orbitBroucke–Boggs S22 (0.045, 0.03, 2.925)T 12.57 stableBroucke–Boggs S23, a periodic three-body orbitBroucke–Boggs S23 (0.09, 0.03, 2.88)T 12.57 stableBroucke–Boggs S24, a periodic three-body orbitBroucke–Boggs S24 (0.15, 0.03, 2.82)T 12.57 stableBroucke–Boggs S25, a periodic three-body orbitBroucke–Boggs S25 (0.225, 0.03, 2.745)T 12.57 stableBroucke–Boggs S26, a periodic three-body orbitBroucke–Boggs S26 (0.3, 0.03, 2.67)T 12.57 stableBroucke–Boggs S27, a periodic three-body orbitBroucke–Boggs S27 (0.3, 0.075, 2.625)T 12.57 stableBroucke–Boggs S28, a periodic three-body orbitBroucke–Boggs S28 (0.3, 0.15, 2.55)T 12.57 stableBroucke–Boggs S29, a periodic three-body orbitBroucke–Boggs S29 (0.3, 0.225, 2.475)T 12.57 stableBroucke–Boggs S30, a periodic three-body orbitBroucke–Boggs S30 (0.3, 0.3, 2.4)T 12.57 stableBroucke–Boggs S31, a periodic three-body orbitBroucke–Boggs S31 (0.375, 0.3, 2.325)T 12.57 stableBroucke–Boggs S32, a periodic three-body orbitBroucke–Boggs S32 (0.495, 0.3, 2.205)T 12.57 stableBroucke–Boggs S33, a periodic three-body orbitBroucke–Boggs S33 (0.6, 0.3, 2.1)T 12.57 stableBroucke–Boggs S34, a periodic three-body orbitBroucke–Boggs S34 (0.705, 0.3, 1.995)T 12.57 stableBroucke–Boggs S35, a periodic three-body orbitBroucke–Boggs S35 (0.855, 0.3, 1.845)T 12.57 stableBroucke–Boggs S36, a periodic three-body orbitBroucke–Boggs S36 (0.999, 0.3, 1.701)T 12.57 stableBroucke–Boggs S37, a periodic three-body orbitBroucke–Boggs S37 (0.999, 0.45, 1.551)T 12.57 stableBroucke–Boggs S38, a periodic three-body orbitBroucke–Boggs S38 (0.999, 0.63, 1.371)T 12.57 stableBroucke–Boggs S39, a periodic three-body orbitBroucke–Boggs S39 (0.999, 0.81, 1.191)T 12.57 stableBroucke–Boggs S122, a periodic three-body orbitBroucke–Boggs S122T 8.750