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That formula for the area is geometric; the exponent couldn't possibly be anything other than 2.
 
That formula for the area is geometric; the exponent couldn't possibly be anything other than 2.
 
ON THE OTHER HAND, this is all in Newtonian gravity.  In GR, a derivation of the exponents works similarly, but the possibility of them being slightly off 2 is equally remote, that is, 0, but even then, GR is not an ultimate formulation of gravity.  Who knows how the world really works. [[User:JacobB|JacobB]] 23:53, 1 October 2009 (EDT)
 
ON THE OTHER HAND, this is all in Newtonian gravity.  In GR, a derivation of the exponents works similarly, but the possibility of them being slightly off 2 is equally remote, that is, 0, but even then, GR is not an ultimate formulation of gravity.  Who knows how the world really works. [[User:JacobB|JacobB]] 23:53, 1 October 2009 (EDT)
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::: This question is a very interesting one, but I think you'll agree after pondering it further that there is no logical obstacle to observing a gravitational force that proportional to the inverse of, say, 2.0000001.  Math is fine for what it does, but mathematical elegance does not dictate physical laws.
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::: Invariably math/physics types initially insist that it must be precisely 2 in order to make the integrals work nicely.  But physical observation is what counts, and there is no logical obstacle to mathematical inelegance.  Thanks for discussing this.--[[User:Aschlafly|Andy Schlafly]] 23:56, 1 October 2009 (EDT)
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