Re: Why is the force of gravity stronger on the earth than the moon?

The force of gravity on an object is related to the mass of the objects and 
the distance between them squared.  So the force due to gravity will 
increase as the mass of the objects involved increases, and will decrease 
quickly as the objects are moved further apart.

The Earth's mass is about 81 time greater then the mass of the moon and 
the earth's radius is about 3.7 times greater then that of the moon.  So the 
greater mass of the Earth will increase the force of gravity on us compared 
to the moon, but because the Earth much bigger then the moon, we are 
farther from the center which decreases the effect of gravity on us.

Here is the math...
The force of gravity on the moon, Fm, is proportional to Mm/(Rm*Rm)
where Mm is the mass of the moon and Rm is the radius of the moon.  We 
can arbitrarily say that Mm and Rm both equal 1, so that the Fm is 1

The force of gravity on the Earth, Fe, has the same equation: Me/(Re*Re)
where Me is the mass of the Earth and Re is the radius of the earth.

We can no put in the numbers for the mass and radius of the Earth that I 
mentioned above to find out how the force of gravity on the earth 
compares to that of the moon:

Fe = Me/(Re*Re) = 81/(3.7*3.7) = 5.92

This means that we weigh almost 6 times more on earth as we do on the 
moon!
Hope this helps
Eric