Three Body Orbits

Families / Belgrade classes

Yin-Yang III orbits

Two interlocking halves whose lobes wrap around each other.

Yin-Yang III orbits are periodic solutions of the planar three-body problem. The atlas holds 20 of them, with periods from 10.96 to 92.98, all with equal masses; 6 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 Yin-Yang III.12.Aα

All 20 orbits

Yin-Yang III.3.Aα, a periodic three-body orbitYin-Yang III.3.AαT 17.33Yin-Yang III.3.Aβ, a periodic three-body orbitYin-Yang III.3.AβT 10.96Yin-Yang III.9.Aα, a periodic three-body orbitYin-Yang III.9.AαT 50.41Yin-Yang III.9.Aβ, a periodic three-body orbitYin-Yang III.9.AβT 32.84Yin-Yang III.12.Aα, a periodic three-body orbitYin-Yang III.12.AαT 55.79 stableYin-Yang III.12.Aβ, a periodic three-body orbitYin-Yang III.12.AβT 55.79 stableYin-Yang III.13.Aα, a periodic three-body orbitYin-Yang III.13.AαT 60.15 stableYin-Yang III.13.Aβ, a periodic three-body orbitYin-Yang III.13.AβT 60.15 stableYin-Yang III.15.Aα, a periodic three-body orbitYin-Yang III.15.AαT 70.49 stableYin-Yang III.15.Aβ, a periodic three-body orbitYin-Yang III.15.AβT 66.75 stableYin-Yang III.15.Bα, a periodic three-body orbitYin-Yang III.15.BαT 85.13Yin-Yang III.15.Bβ, a periodic three-body orbitYin-Yang III.15.BβT 54.64Yin-Yang III.15.Cα, a periodic three-body orbitYin-Yang III.15.CαT 88.44Yin-Yang III.15.Cβ, a periodic three-body orbitYin-Yang III.15.CβT 54.82Yin-Yang III.16.Aα, a periodic three-body orbitYin-Yang III.16.AαT 80.15Yin-Yang III.16.Aβ, a periodic three-body orbitYin-Yang III.16.AβT 74.85Yin-Yang III.18.Aα, a periodic three-body orbitYin-Yang III.18.AαT 84.86Yin-Yang III.18.Aβ, a periodic three-body orbitYin-Yang III.18.AβT 79.28Yin-Yang III.19.Aβ, a periodic three-body orbitYin-Yang III.19.AβT 86.40Yin-Yang III.21.Aβ, a periodic three-body orbitYin-Yang III.21.AβT 92.98