Subject: Surface Gravity to tell actual force one object has on another?

I was asked a question, my teacher counted it wrong, but she can’t explain why 
it’s wrong.  Would you please tell me if I did this right, and if not, what I 
did wrong?

QUESTION AND ANSWER BELOW

Imagine that the moon were twice its current distance from the Earth.  By how 
much would the moon's tidal force on the Earth change?  What implacation does 
this have for tides on the Earth as the moon moves away from the Earth? 
The moon's gravitational force is 1/6 the Earths.  Earth's is 9.8 (m/s)/s at 
the surface.  So the moon's acceleration at the surface is 9.8/6= 1.63 (m/s)/s 
The moon is approximately 60 earth diameters from us right now, so.... 
60^2=3600 
Now to find the force the moon has on the Earth we need to take 
1.63/3600=4.5*10^-4 (m/s)/s 
Double the distance to 120 and.... 
120^2=14,400 
1.63/14,400= 1.13*10^-4 (m/s)/s 
As you can see, gravitation is much gets much weaker as you move out, so the 
tidal force would be much weaker as well.  As the moon's distance increases 
from the Earth, the tidal force should weaken as the inverse square of the 
distance

Re: Surface Gravity to tell actual force one object has on another?