What causes the gravitational force to increase as a star collapses?

The strength of a gravitational force depends on how much mass is involved, and how far away from it you are. For very dense objects, a lot of mass is concentrated in a very small region of space, so you can get very close to it. The force of gravity is defined as:



          G M m
F  =    --------
            2
           R

And for an object with a density of D and a radius of r, you get

          4       3
M = D x  --- pi  r
          3 

so that by substitution:

        Gm       4         3
F   =  -----  x ---  pi   r   D
         2       3
        R

and so in terms of density:

                       3
     4 pi G m         r
F = -----------  D  -----
         3             2
                      R

If you are outside the body, R is greater than r and the entire body acts like a point mass located at R = 0. If you are inside the body, R = r and the force you feel depends on the total mass in the sphere inside your radial position from the center. The force of gravity actually decreases inside such a body as you approach its center, no matter how dense it is.
Copyright 1997 Dr. Sten Odenwald
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