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I'm curious, though, what you get as an answer when you consider the case
where the two bodies are *not* rotating. I predict you will get the result
that there are two opposing tidal bulges even in that case, simply from
the gravitational force gradient. Therefore textbooks shouldn't imply that
rotation is the *sole* cause of the bulges. However, it would be
interesting to compare the size of the non-rotational bulges, with the
size of them when the system is rotating, to see which cause is the
predominant one for the bulges.