Three Body Orbits

Families / Belgrade classes

Rose’s Bestiary

Orbits from Rose’s survey of the symmetry-reduced problem, which reaches parts of phase space the other searches do not.

Rose’s Bestiary are periodic solutions of the planar three-body problem. The atlas holds 13 of them, with periods from 15.05 to 193.6, all with equal masses; 4 of them are linearly stable. They come from Rose (2016), Geometric phase and periodic orbits of the equal-mass, planar three-body problem with vanishing angular momentum. Every orbit is precomputed to machine precision and plays one period at a time; open one to watch it, nudge it or rate it.

Rose (2016). Geometric phase and periodic orbits of the equal-mass, planar three-body problem with vanishing angular momentum. PhD thesis, University of Sydney (link)

See them on the mapOpen Bestiary t0(2,4)

All 13 orbits

Bestiary t0(2,4), a periodic three-body orbitBestiary t0(2,4)T 193.6 stableBestiary t0(2,11), a periodic three-body orbitBestiary t0(2,11)T 39.64Bestiary t0(2,63), a periodic three-body orbitBestiary t0(2,63)T 15.05Bestiary t0(2,66), a periodic three-body orbitBestiary t0(2,66)T 36.94Bestiary t0(2,72), a periodic three-body orbitBestiary t0(2,72)T 73.85Bestiary t0(2,85), a periodic three-body orbitBestiary t0(2,85)T 129.3Bestiary t0(2,86), a periodic three-body orbitBestiary t0(2,86)T 134.0Bestiary t0(2,94), a periodic three-body orbitBestiary t0(2,94)T 156.3Bestiary t0(4,2), a periodic three-body orbitBestiary t0(4,2)T 174.8 stableBestiary t0(4,52), a periodic three-body orbitBestiary t0(4,52)T 79.27Bestiary t0(8,3), a periodic three-body orbitBestiary t0(8,3)T 69.60 stableBestiary t0(8,4), a periodic three-body orbitBestiary t0(8,4)T 85.56 stableBestiary t0(8,6), a periodic three-body orbitBestiary t0(8,6)T 107.7