9.81, the accepted constant for the acceleration due to gravity, only works at 6374313.131 meters away from the center of gravity of the earth. Just saying this for measurement's sake.
That would be about 400 something miles from the center of the earth? So your saying a large mass can only have a mamimun effect at a specific distance?
No no no...9.81 is the accepted acceleration due to gravity, because people are too lazy to do the crazy math that you would have to do(recalculate the acceleration, etc.(there are more examples)), actually, a large mass has max. effect of 10^- infinity meters.