As has been pointed out, to understand tides you have to realise its a dynamic problem which must be framed appropriately as two revolving extensible bodies rotating about their common cm. The problem with the poor professor's paper is that it is quite simply unintelligent to include the range variation of gravity as its very small perturbing effect relative to a constant model is less than trivial when compared to the other forces acting and the inherent limitations of the model. That's what was meant by another poster when he said the beginning of the paper was wacky and not worth the read. He is entirely correct on that. I must have another look at it to see if he includes coriolis forces: I doubt he understands that either.
So can someone now explain this variable gravity theory of tides to me as opposed to the standard theory ?