Pythagorean 3-Body Problem With Osculating Orbits

The osculating orbit of an object in space is the gravitational Kepler orbit that it would have if perturbations were not present. For each body exactly one osculating orbit exists in any moment of time, represented by the thin lines in the animation. The actual motion of the bodies is calculated numerically, the osculating orbits are calculated independently for each step, using only the masses, current positions and velocities of all 3 bodies. Axis ticks are astronomical units. Mass ratio blue/red/yellow: 3/4/5. Thanks for watching, Michael Dörr & Volker Dörr P.S. initial conditions: m = { 3, 4, 5 }, r = { { 1, 3, 0 }, {-2, 1, 0 }, { 1,-1, 0 } }, v = { { 0, 0, 0 }, { 0, 0, 0 }, { 0, 0, 0 } } The differential equations ready to use for numerical solvers as found in Matlab, Mathematica and others can be found here: And here is an excerpt from our Mathematica code that shows how we plot the primary trajectories: