Re: Gravity

The acceleration due to gravity, g, which is about 9.8 meters/sec^2 (about 
32 feet/sec^2) on the earth's surface, would be zero at the center of the 
earth.

To show this mathematically, the Physics textbook by Halliday and Resnick 
has an example in chapter 16 where one imagines that a tunnel is dug 
through the earth. The gravitational attraction of the earth for the object 
in this tunnel any distance r from the center of the earth is due to the 
attraction between  the object in the tunnel AND the portion of the matter 
making up the earth that could be viewed as in shells inside the position 
of the object in the tunnel.

The force of gravity is given by the equation:

   Force  = G Mass(earth) Mass(object)
            -------------------------              (Equation 1)
               r^2

where G is the other Gravitational constant, 6.67 x 10^-11 nt-m^2/kg^2,

Mass(earth) is the mass of the earth itself if you are on or above the 
   surface of the earth  but becomes the effective mass of the earth in 
   shells inside the position of the object in the tunnel,
     and 
r is the effective radius of the earth (how far from the center of the 
earth that the object is in the tunnel) 

So, assuming the earth has constant density (not totally correct, but other 
assumptions give similar results with more complicated algebra), the 
effective Mass of the earth, Mass(earth), that applies a gravitational 
attraction for our object within the tunnel into the earth would be:
 
Mass(earth) = (density) x 4 x pi x r^3 / 3     (Equation 2)

So, plugging equation 2 into equation 1, and dividing the r^3 by the r^2 in 
the denominator, we get

Force = G x (density) x 4 x pi x m x r / 3     (Equation 3)

So, the force of gravity on the object in the tunnel through the earth is 
directly proportional to the distance r that the object is from the center 
of the earth. 

At the center of the earth, the distance r is zero, and the force of 
gravity is zero. Since the force of gravity is also F = m g (g being the 
acceleration due to gravity that you asked about), if F = 0, then g is zero 
at the center of the earth.