Three Body Orbits

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Butterfly I orbits

Two wings of tight loops, with the bodies crossing through the centre at high speed.

Butterfly I orbits are periodic solutions of the planar three-body problem. The atlas holds 19 of them, with periods from 6.235 to 90.56, all with equal masses; 18 of them are linearly stable. They come from Šuvakov & Dmitrašinović (2013), Three classes of Newtonian three-body planar periodic orbits. Every orbit is precomputed to machine precision and plays one period at a time; open one to watch it, nudge it or rate it.

Šuvakov & Dmitrašinović (2013). Three classes of Newtonian three-body planar periodic orbits. Physical Review Letters 110, 114301 (doi)

See them on the mapOpen Butterfly I.2.B

All 19 orbits

Butterfly I.2.A, a periodic three-body orbitButterfly I.2.AT 6.235Butterfly I.2.B, a periodic three-body orbitButterfly I.2.BT 7.004 stableButterfly I.5.A, a periodic three-body orbitButterfly I.5.AT 20.75 stableButterfly I.8.A, a periodic three-body orbitButterfly I.8.AT 34.25 stableButterfly I.9.A, a periodic three-body orbitButterfly I.9.AT 34.71 stableButterfly I.11.A, a periodic three-body orbitButterfly I.11.AT 47.93 stableButterfly I.12.A, a periodic three-body orbitButterfly I.12.AT 48.49 stableButterfly I.13.A, a periodic three-body orbitButterfly I.13.AT 48.67 stableButterfly I.14.A, a periodic three-body orbitButterfly I.14.AT 61.32 stableButterfly I.16.A, a periodic three-body orbitButterfly I.16.AT 62.45 stableButterfly I.17.A, a periodic three-body orbitButterfly I.17.AT 62.63 stableButterfly I.18.A, a periodic three-body orbitButterfly I.18.AT 76.03 stableButterfly I.19.A, a periodic three-body orbitButterfly I.19.AT 76.22 stableButterfly I.20.A, a periodic three-body orbitButterfly I.20.AT 76.40 stableButterfly I.21.A, a periodic three-body orbitButterfly I.21.AT 76.59 stableButterfly I.22.A, a periodic three-body orbitButterfly I.22.AT 89.99 stableButterfly I.23.A, a periodic three-body orbitButterfly I.23.AT 90.18 stableButterfly I.24.A, a periodic three-body orbitButterfly I.24.AT 90.36 stableButterfly I.25.A, a periodic three-body orbitButterfly I.25.AT 90.56 stable