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Two star systems: http://en.wikipedia.org/wiki/Circumbinary_planet - not exactly what you asked, but I think it's as close as real systems will get. The example you give, 2 planets orbiting each other is easy, two objects will tend to orbit each other but when you have 3 objects, it gets a bit more complicated, unless the 3rd one is distant and orbits ...


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Your question is very unclear. As long as the orbit is bound (i.e. the total energy is negative), then there is a unique closed orbit solution (see Bertrand's theorem). There will be no 'transient' part of the solution.


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What is the most populated/numerous stellar system in which the orbits of all objects are known? The answer is none. Other than our own solar system, astronomers don't know if they know all of the large bodies (aka planets) orbiting any given star system. Presumably other star systems have asteroids, comets, and other stuff. The orbits of those small bodies ...


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According to Vokrouhlicky et al. 2015 Yarkovsky forces can be measured for small bodies with diameters up to 30-40 km. The largest object they have in their list of Yarkovsky detections is 4179 Toutatis with a diameter of (only) 2.8 km. I am not aware if Yarkovsky forces have been measured on anything larger than asteroids.


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I have done a lot more research into this and found an answer. It comes down to solving Kepler's Equation, and my main references are: Kepler's equation and the Equation of Centre which gives an iterative method for solving the equation, and Determination of Position in Orbits which has the formulae for calculating orbital coordinates. Here is the ...



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