When I was in grad school in astronomy, one of my professors told me "many a promising young researcher has run their career aground on the rocky shores of tides."
The mathematics involved in the theory of tides are formidable. Even in homogeneous, tidally locked systems things can get complicated very quickly.
But tides are nevertheless very important. One two objects pass very close to each other, tidal effects are substantial and can actual destroy one of the objects: https://en.wikipedia.org/wiki/Tidal_disruption_event
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