Even if complicated, can the gravitational field of a uniform toroid of radii $R$ and $r$ be calculated with the Gauss theorem? I know that we can guess the gravitational field of a RING but I have never seen if the field of an axisymmetric doughnut can be estimated with the aid of the Gauss flux theorem. Can it be done?
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Is this helpful? Gravitational force due to a ring – Quillo Oct 14 '23 at 16:18
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Related: https://www.aleph.se/andart/archives/2014/02/torusearth.html It's a slightly modified rotating torus. – PM 2Ring Oct 14 '23 at 16:37