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Main Question or Discussion Point
Would the shell theorem prevent a binary planet system, with two ideally equal masses, structure etc?
I meant two planets of the same mass and make up(ideally).The shell theorem is true, and there are probably binary planets around (and Pluto/Charon are similar to a binary planet). Clearly not.
Why would you expect that?
yes, I think you're correct....I've jumped the gun again...The shell theorem holds for a spherically symmetric distribution. Your setup is not spherically symmetric.
or maybe I'm right(probably not....)...surely if the shell theorem holds for a whole sphere, it would also hold for a symmetrical two body system...?The shell theorem holds for a spherically symmetric distribution. Your setup is not spherically symmetric.
ok so I may well have jumped the gun, but is there still something to the idea?You are confusing the term "symmetric" (by which you mean a mirror symmetry) with "spherically symmetric" (which requires dependence on nothing but distance from a center point, no angular dependence). The latter is much more restrictive, and is the only time the shell theorem applies.
Your saying that because the second planet is outside the first planet, according to the shell theorem, the second planet exerts no gravitational force on the first planet, right? But in the shell theorem, the mass outside the shell is counter-balanced by the mass of the shell on the opposite side - it's spherically symmetric. In the two planet example, there's no mass on the other side of the first planet to counter-balance the gravitational attraction of the second planet.or maybe I'm right(probably not....)...surely if the shell theorem holds for a whole sphere, it would also hold for a symmetrical two body system...?