How do I develop physical intuition for the tidal force?

AI Thread Summary
To develop physical intuition for tidal forces, it's essential to understand the concept of 'stretching' due to gravitational differences on opposite ends of an object near a massive body. The discussion emphasizes that the gravitational force can be approximated using a Taylor series, particularly focusing on the 1/r^3 term. However, the coefficients of this term require a deeper understanding of the force differential experienced by the object. By considering the relationship between the size of the smaller body and its distance from the massive body, one can better grasp the nature of tidal forces. This approach provides a more intuitive framework for understanding how tidal forces operate in gravitational interactions.
Simfish
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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.
 
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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
 
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