Not trusting a non certified EDU site I focused my sight on a science formula that has an explanation.
In doing so, applying a mathmatical rule of thumb and a mathmaticians rule. At least this time,
F=(GMm)/R
^{2}=mg
Where G is the gravitational constant, M is the mass of the Earth, m is the mass of the object, and R is the distance between the of the two objects (in this case, the distance is between you and the center of the Earth.)
Therefore it could be assumed that the closer you are to the center of the Earth (the lower the elevation), the stronger the force of gravity.
If I remember correctly the lowest place in the U.S. is Death Valley at -282 ft (-85.9536m). Given that the mean radius of the Earth is 6.37*106m, we could calculate g, acceleration due to gravity, in Death Valley using the equation above:
g=((6.673*10
^{-11})(5.98*10
^{24}))/(6.37*10
^{6}-85.9536)
^{2} =9.834565215 m/s
^{2 } Where
G=6.673*10
^{-11}M=5.98*10
^{+24}Compare this to the gravitational field calculated using the mean radius: 9.834299811 m/s
^{2 } As you can see, the difference is so small, it is insignificant.
http://www.physlink.com/education/askexperts/ae375.cfm=======================
According to the formula, digging a hole to the center of the earth M and m is constant.
F will increase indirectly porportional to the radius of distance to the center.
Then, at the center, the radius becomes so small approaching zero, by La H'opitals rule F approaches infinity? Not zero as suggested.
I should say little g instead of big F since little m cancels out.