Three Body Orbits

Families / Belgrade classes

Moth IVc orbits

Moth-like shapes from a third topological class.

Moth IVc orbits are periodic solutions of the planar three-body problem. The atlas holds 22 of them, with periods from 25.84 to 95.08, all with equal masses; 9 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 Moth IVc.12.B

All 22 orbits

Moth IVc.5.A, a periodic three-body orbitMoth IVc.5.AT 25.84Moth IVc.8.A, a periodic three-body orbitMoth IVc.8.AT 57.99Moth IVc.8.B, a periodic three-body orbitMoth IVc.8.BT 57.99Moth IVc.8.C, a periodic three-body orbitMoth IVc.8.CT 37.18Moth IVc.12.Aα, a periodic three-body orbitMoth IVc.12.AαT 68.65Moth IVc.12.Aβ, a periodic three-body orbitMoth IVc.12.AβT 64.87Moth IVc.12.B, a periodic three-body orbitMoth IVc.12.BT 54.85 stableMoth IVc.13.A, a periodic three-body orbitMoth IVc.13.AT 55.38 stableMoth IVc.15.A, a periodic three-body orbitMoth IVc.15.AT 68.07 stableMoth IVc.15.B, a periodic three-body orbitMoth IVc.15.BT 61.18Moth IVc.15.C, a periodic three-body orbitMoth IVc.15.CT 61.28Moth IVc.16.A, a periodic three-body orbitMoth IVc.16.AT 77.84Moth IVc.16.B, a periodic three-body orbitMoth IVc.16.BT 69.04 stableMoth IVc.16.C, a periodic three-body orbitMoth IVc.16.CT 69.18 stableMoth IVc.17.A, a periodic three-body orbitMoth IVc.17.AT 82.86 stableMoth IVc.17.B, a periodic three-body orbitMoth IVc.17.BT 85.38Moth IVc.18.A, a periodic three-body orbitMoth IVc.18.AT 81.15Moth IVc.19.A, a periodic three-body orbitMoth IVc.19.AT 93.79 stableMoth IVc.19.Bα, a periodic three-body orbitMoth IVc.19.BαT 94.77Moth IVc.19.Bβ, a periodic three-body orbitMoth IVc.19.BβT 90.90Moth IVc.21.A, a periodic three-body orbitMoth IVc.21.AT 94.65 stableMoth IVc.22.A, a periodic three-body orbitMoth IVc.22.AT 95.08 stable