Three Body Orbits

Families / Li–Liao classes

Moth IVa.2.A, unequal masses

The stable moth IVa.2.A continued to unequal masses: one body a little lighter or heavier than the other two, and the orbit stays stable.

Moth IVa.2.A, unequal masses are periodic solutions of the planar three-body problem. The atlas holds 7 of them, with periods from 7.134 to 7.865, for several mass ratios; all of them are linearly stable. They come from Li, Li & Liao (2021), One family of 13315 stable periodic orbits of non-hierarchical unequal-mass triple systems. Every orbit is precomputed to machine precision and plays one period at a time; open one to watch it, nudge it or rate it.

Li, Li & Liao (2021). One family of 13315 stable periodic orbits of non-hierarchical unequal-mass triple systems. Science China Physics, Mechanics & Astronomy 64, 219511 (doi)

See them on the mapOpen Moth IVa.2.A

All 7 orbits

Moth IVa.2.A, a periodic three-body orbitMoth IVa.2.A m₁ = 0.960T 7.134 stableMoth IVa.2.A, a periodic three-body orbitMoth IVa.2.A m₁ = 0.970T 7.233 stableMoth IVa.2.A, a periodic three-body orbitMoth IVa.2.A m₁ = 0.980T 7.334 stableMoth IVa.2.A, a periodic three-body orbitMoth IVa.2.A m₁ = 0.990T 7.436 stableMoth IVa.2.A, a periodic three-body orbitMoth IVa.2.A m₁ = 1.010T 7.646 stableMoth IVa.2.A, a periodic three-body orbitMoth IVa.2.A m₁ = 1.020T 7.754 stableMoth IVa.2.A, a periodic three-body orbitMoth IVa.2.A m₁ = 1.030T 7.865 stable