Undergrad Gravitation In Higher Dimensions

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Gravitation in higher dimensions is believed to follow a 1/d^(n-1) law, differing from the 3D case where a uniformly dense sphere's gravitational attraction is equivalent to a point mass at its center. For dimensions greater than three, this equivalence does not hold, prompting a search for the results in those scenarios. The discussion seeks to use the known 3D integration case as a model to understand higher-dimensional gravitation. A suggestion to search for the "gravitational shell theorem" was provided as a helpful resource. Understanding these concepts is crucial for exploring gravitational dynamics in n-dimensional spaces.
Hornbein
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It is assumed that gravitation in n dimensions would follow an approximate 1/d^(n-1) law. In our 3D world the attraction of a uniformly dense sphere is the same as if all the mass were concentrated at its center. I have read for n>3 this is not so. I want to find out what the result would be. I think I can do it if I have the common n=3 integration case as a model. I tried an Internet search but could not guess the correct search term. Any help?
 
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Hornbein said:
It is assumed that gravitation in n dimensions would follow an approximate 1/d^(n-1) law. In our 3D world the attraction of a uniformly dense sphere is the same as if all the mass were concentrated at its center. I have read for n>3 this is not so. I want to find out what the result would be. I think I can do it if I have the common n=3 integration case as a model. I tried an Internet search but could not guess the correct search term. Any help?
Google "gravitational shell theorem".
 
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Likes Vanadium 50, jim mcnamara, Hornbein and 1 other person
renormalize said:
Google "gravitational shell theorem".
Bingo.
 

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