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).mfb said: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...Orodruin said: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...?Orodruin said: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?Ken G said: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.DarkStar42 said: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...?
Newton's shell theorem states that the gravitational force exerted by a spherically symmetric mass distribution on a particle outside of the distribution is the same as the force that would be exerted by the entire mass of the distribution at its center. This means that the gravitational force between two binary planets would be influenced by the combined mass and distance between the two planets, rather than just the individual masses.
Yes, Newton's shell theorem applies to all types of binary systems, including binary planet systems. As long as the two objects have a spherically symmetric mass distribution, the theorem will hold true.
Yes, Newton's shell theorem would cause changes in the orbit of binary planets. The combined mass and distance between the two planets would affect the gravitational force between them, potentially altering their orbits.
No, binary planet systems cannot exist without following Newton's shell theorem. This theorem is a fundamental law of gravity and applies to all objects with spherically symmetric mass distributions.
No, there are no exceptions to Newton's shell theorem for binary planet systems. As long as the two planets have spherically symmetric mass distributions, the theorem will accurately predict the gravitational force between them.