Newton's Law of Gravitation - Derived From Scratch

Newton's Law of Gravitation - Derived From Scratch

A simple way to model the gravitational field of an object is to imagine a fixed number of "lines of force" that radiate from the object evenly into space.

Assumption #1
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.

Assumption #2
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 a sphere of radius r) which is..

n/(4*pi*r^2)=k*m/(4*pi*r^2)=G*m/(r^2)

where G=k/4*pi is a constant.

This is Newton's famous law of gravitation. G is called the "universal gravitational constant". I think the more interesting thing here is the 1/(r^2) term.

I wonder if this simple method could be modified to give Einsteinian gravity, meaning the General Relativity model of gravity?

Content written and posted by Ken Abbott abbottsystems@gmail.com