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From the book "The Science of Interstellar" by Kip Thorne. On Chapter 4 of the book, there is a diagram on the explanation of moon's gravity influence on Earth's ocean. Tidal Gravity

Where diagram A is labeled as the "Usual Viewpoint" and diagram B is labeled as "Earth's Viewpoint" In my mind experiment, I have thought diagram A is what tidal gravity supposed to look like yet I do not understand how scientists come up with diagram B.

In the book, it explains as

"With their[diagram A]'s average subtracted away; that is, it feels a stretch toward and away from the moon, and a squeeze on its lateral sides"

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  • $\begingroup$ It's hard to answer your question without knowing your background. Do you know Newton's laws of motion? Do you know about vector addition? Do you know about the distinction between an inertial frame of reference and a noninertial one? $\endgroup$ – Ben Crowell May 27 '17 at 21:50
  • $\begingroup$ @BenCrowell I do understand Newton's Laws of Motion, I do know vector addition, and I do understand the difference. Just pretend I am one of your student. $\endgroup$ – Raze May 28 '17 at 1:12
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Subtract from the above diagram, which is not the 'usual' viewpoint, but the point of view from the moon. It simply derives from the vectorial identity for the force of gravity, that the moon exerts on any fluid particle on Earth $\vec F_g = - \frac{GM_{moon}}{r^3} \cdot \vec r$, where $\vec r$ is the moon-centric radius vector.

To get to the earth-centric view (B), you subtract the average, which is the central arrow at Earth's center in the moon-centric view (A). Subtraction here means vectorial subtraction of course, if you need help with that this link might help.

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