I have tried looking at various sources and Wikipedia articles. I also checked some Q&As here at StackExchange but I couldn't quite grasp how the formula for the height of tides is derived when we consider just the influence of the moon on a static ocean. The formula I am talking about is $$h \propto \frac{M_\text{moon}R^4}{Md^3}. $$

I know this is pretty basic. I am coming from the online edX class on Relativity and Astrophysics offered by Cornell. This is the link to the note provided for the video that they used to describe the derivation. I am a little confused. Can anyone post a step by step derivation of this formula.

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    $\begingroup$ Tides are way more complex than this. See physics.stackexchange.com/q/121830/109928. $\endgroup$ – Stéphane Rollandin May 22 '18 at 11:37
  • $\begingroup$ Thanks, Stephane but I had already seen that thread. I know tides are very complex. And talking only about the moon, we haven't touched the effect of the sun and earth's spin on the tides. But my main objective is to understand the most basic concept of static tides. Right now, I am interested in how this approximate formula is derived. I have seen some derivation but they were pretty unclear. $\endgroup$ – Breamhall May 22 '18 at 14:10
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    $\begingroup$ "However, this is not my actual motive. I want to understand the basic concept of tidal forces." Err, then why not ask about that? $\endgroup$ – dmckee May 22 '18 at 19:02
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    $\begingroup$ Your title should summarize your question. If your question is where the tidal force comes from and why it points in funny directions, ask that. If your question is how to get the expression for the vector tidal force, ask that. If your question is how to obtains the expression for the static equilibrium height of a liquid under the influence of the tidal force (what you have in your question right now is the maximum of that distribution), ask that. What you are asking for right now is a very complicated problem (which is why your instructor introduced "Boring World" in the first place). $\endgroup$ – dmckee May 23 '18 at 18:40
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    $\begingroup$ Okay. I will change my question to "Deriving the expression for the static equilibrium height of liquids under tidal force". Is that fine? Also you know the answer dmckee. So why not post it? $\endgroup$ – Breamhall May 24 '18 at 2:25

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