Three Body Orbits

Families / Li–Liao classes

II.A orbits

Class II.A orbits with an unequal third mass.

II.A orbits are periodic solutions of the planar three-body problem. The atlas holds 20 of them, with periods from 24.26 to 180.7, for several mass ratios; 5 of them are linearly stable. They come from Li, Jing & Liao (2018), Over a thousand new periodic orbits of a planar three-body system with unequal masses. Every orbit is precomputed to machine precision and plays one period at a time; open one to watch it, nudge it or rate it.

Li, Jing & Liao (2018). Over a thousand new periodic orbits of a planar three-body system with unequal masses. Publications of the Astronomical Society of Japan 70, 64 (doi)

See them on the mapOpen II.A.2

All 20 orbits

II.A.1, a periodic three-body orbitII.A.1 m₃ = 0.5T 30.39II.A.1, a periodic three-body orbitII.A.1 m₃ = 0.75T 35.78II.A.1, a periodic three-body orbitII.A.1T 121.7II.A.1, a periodic three-body orbitII.A.1 m₃ = 2T 35.72II.A.1, a periodic three-body orbitII.A.1 m₃ = 4T 80.56II.A.1, a periodic three-body orbitII.A.1 m₃ = 10T 24.26II.A.2, a periodic three-body orbitII.A.2 m₃ = 0.5T 41.00II.A.2, a periodic three-body orbitII.A.2 m₃ = 0.75T 177.4 stableII.A.2, a periodic three-body orbitII.A.2T 135.9II.A.2, a periodic three-body orbitII.A.2 m₃ = 2T 85.74 stableII.A.2, a periodic three-body orbitII.A.2 m₃ = 4T 118.0 stableII.A.3, a periodic three-body orbitII.A.3 m₃ = 0.5T 71.82II.A.3, a periodic three-body orbitII.A.3T 145.3II.A.3, a periodic three-body orbitII.A.3 m₃ = 2T 101.0II.A.4, a periodic three-body orbitII.A.4 m₃ = 0.5T 57.61 stableII.A.4, a periodic three-body orbitII.A.4T 46.58II.A.4, a periodic three-body orbitII.A.4 m₃ = 2T 179.4II.A.5, a periodic three-body orbitII.A.5 m₃ = 0.5T 37.31II.A.6, a periodic three-body orbitII.A.6 m₃ = 0.5T 115.6 stableII.A.7, a periodic three-body orbitII.A.7 m₃ = 0.5T 180.7