TITLE: Derivation of Inverse Square Law
QUESTION [0 upvotes]: Is there a mathematical derivation of the inverse square law that doesn't depend on geometry or empirical data fitting?

REPLY [1 votes]: Here is an incredibly simple derivation of the the inverse square law for gravity which shows how it must rely on geometry..
A simple way to think about the gravitational field of an object is to imagine a fixed number of "lines of force" that radiate from the object evenly into space. 
Let's suppose the number of lines of force produced by an object is directly proportional to its mass, so..
n=k*m
where n is the number of lines of force produced by the mass m and k is a constant.
Now assume the density of the lines at any given point in space represents the strength of the gravitational field at that point. So at a distance r from the object the density of the lines of force is..
n/(surface area of the sphere of radius r)
which is n/(4*pir^2)=km/(4*pir^2)=Gm/(r^2) 
where G=k/4*pi is a constant.
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