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0 pointsmusgravepeter8y ago0 comments

Yes, that does work. In the literature this is called a "heirarchical system"

The very simplest version is called the Euler problem. Two fixed masses and a third moving in the "dipole field". All the solutions can be explicitly determined (although only in terms of e.g. Jacobi elliptic functions and other elliptics). There's a book "Integrable Systems in Celestial Mechanics" by Mathuna.

I recently added the Euler problem to my iOS app ThreeBody: https://appadvice.com/app/threebody-lite/951920756

Some day I'll get around to adding these 600 solutions...

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adrianratnapala8y ago

Right, but this dipole solution will neglect the perturbation of the third body on whatever is creating the dipole. Fair enough, because we expect the effect to be tiny.

But still you would have to unpack that dipole approximation to figure out if this perturbation will slowly change it in ways that do something significant in the long run.

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