Re: why isn't gravity infinite?

Hello Craig,

You have a very interesting question. The answer, in a nutshell is that 
you have exceeded the capacity, and violated the warranty of Newton's Law 
of Universal Gravitation":)

The formula, Newton's Law of Universal Gravitation:
 F = GmM/r*r
can be used to calculate the gravitational attraction between two bodies.

F = the gravitational force between the two bodies, in dynes
G = The gravitational constant = 6.668 x10 dynes cm g
m = mass of small body (grams)
M = mass of large body (grams)
r = distance between the center of mass of the two bodies (cm)

As you wisely noted, as the "r" in the denominator of the equation 
approaches zero, the force should become infinite.  This formula is 
really accurate ONLY when applied to bodies separated by relatively large 
distances, so that the mass of the bodies can be considered "point" 
masses (Their size and geometry can be ignored.). 
[note added by MadSci Admin: The gravitational force from SPHERICALLY
SYMMETRIC bodies CAN be accurately computed by considering it to arise
from all their mass located at the center, as long as the other body is
outside the first one.]

Because your scenario has large bodies inside each other, this formula
will not apply.  

You can visualize the reality of your scenario, and see why the formula 
fails:  If every particle of mass of one body attracts every particle of 
mass of the other, your small body in the center 
will surrounded by the mass of the ringed body, and "pulled" in all 
directions.  This would tend to cancel the gravity effect and make the 
attraction closer to zero instead of infinity!

Many formulas used in science are simplified to be practical in their 
use.  When formulas are simplified, there will be something 
called "boundary conditions", that limits and specifies the application 
of the formula.  In our case, the boundary conditions of Mr. Newton's 
formula is to have "point masses" of the bodies, as described above.

If formulas were not simplified for practical use, many would be so 
difficult, that solutions would take days instead of minutes, involving 
complex mathematics.  

The attached link might be a help in learning more about the physics of 
gravity. 
http://abyss.uoregon.edu/~js/ast221/lectures/lec08.html

I hope that this helps!

Sincerely,

Jay Shapiro