Three Body Orbits

Families / Belgrade classes

Sequence VIII orbits

The eighth sequence of the Belgrade gallery, recovered from its archived pages; three orbits that appear in no other catalogue.

Sequence VIII orbits are periodic solutions of the planar three-body problem. The atlas holds 3 of them, with periods from 39.61 to 74.39, all with equal masses; none is linearly stable. They come from Dmitrašinović, Hudomal, Shibayama & Sugita (2018), Linear stability of periodic three-body orbits with zero angular momentum and topological dependence of Kepler’s third law. Every orbit is precomputed to machine precision and plays one period at a time; open one to watch it, nudge it or rate it.

Dmitrašinović, Hudomal, Shibayama & Sugita (2018). Linear stability of periodic three-body orbits with zero angular momentum and topological dependence of Kepler’s third law. Journal of Physics A 51, 315101 (link)

See them on the mapOpen VIII.8.A

All 3 orbits

VIII.8.A, a periodic three-body orbitVIII.8.AT 39.61VIII.10.A, a periodic three-body orbitVIII.10.AT 48.89VIII.15.B, a periodic three-body orbitVIII.15.BT 74.39