How do I develop physical intuition for the tidal force?

[Simfish]

I know that it corresponds to the 1/r^3 term in the Taylor series expansion of the gravitational force. But Taylor series expansions can't give me any physical intuition. By physical intuition, I mean that I want to know why the coefficients for the 1/r^3 term are the way they are.

 

[zhermes]

There is a better way (in my opinion) to think about it:
Consider the 'stretching' (force difference) on the two radially-opposite ends of a body (say, length 'l') near another far more massive body (mass 'M'). Make the assumption that the distance between the two objects ('R') is much larger than the size of the smaller body; e.g. $$l << R$$