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I've been looking into the tidal mechanism for a binary star system and seem to have hit a brick wall. In the literature (see below), little explanation is given to justify the equations (9.60), (9.61) and (9.62). I would be grateful if someone could talk me through where these equations came from, as my efforts to find a complete and concise explanation online have thus far been fruitless. Note that I've had to cut some of the text at the top where the page turns over, but this is just a brief introduction to the use of Legendre polynomials in providing a tide raising part of the potential.

enter image description here Eldridge and Tout, The Structure and Evolution of Stars, 2019

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    $\begingroup$ Can you cite the source of your screenshot? It's always important to credit the original source of borrowed material, and it's possible it will help someone formulate an answer. It looks like it might be The Structure and Evolution of Stars doi.org/10.1142/p974 January 2019 by J J Eldridge and Christopher A Tout. Is that right? Note, the passage is viewable here: books.google.com/… $\endgroup$ – uhoh Sep 21 at 4:44
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    $\begingroup$ Yes, that's right. $\endgroup$ – user29126 Sep 21 at 15:33
  • $\begingroup$ looks good, thanks! $\endgroup$ – uhoh Sep 22 at 0:30

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