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Please refer to the image below: Earth and moon's tidal bulge

My question is, why doesn't Earth's leading tidal bulge (encircled in the green circle 1) pull on the moon's tidal bulge (encircled in green circle 2), leading to a force $F_{1,2}$, and consequently a torque on the Moon's tidal bulge, leading it to start spinning as shown in the image. This spinning direction would be opposite of the original direction of the Moon's spin, which got retarded and eventually stopped due to tidal interactions over billions of years.

Please note: I know that Earth's tidal bulge causes the Moon as a whole to increase its velocity which is causing the Moon to be drifted away from the Earth, but that is not what my question is.

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    $\begingroup$ Are you able to do some back of the envelope math to determine how much of an effect this may actually have? I have not done so myself, but my guess is that the effect is so tiny as to be completely negligible and thus the answer to your question. $\endgroup$
    – zephyr
    Oct 7, 2020 at 20:25
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    $\begingroup$ @zephyr That's my guess too. I haven't done the math though. So asked this question to ensure that I wasn't missing anything conceptually here. $\endgroup$
    – Shikhin Mehrotra
    Oct 7, 2020 at 20:28

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why doesn't Earth's leading tidal bulge (encircled in the green circle 1) pull on the moon's tidal bulge

It does....

leading to a force, and consequently a torque

There's nothing here that will give an ongoing torque.

Because of the Earth's high rotational speed and lag in response to forces, the earth's bulge stays displaced from the direction of net gravitational pull.

You have drawn the moon's bulge directly in line with the Earth's center. But in fact it would be pointed at the net gravitational pull direction, which includes the earth's bulge. Since the moon's rotation does not carry its distortion away from that line, there is no net torque in either direction. (I'm ignoring libration and long-term changes in rotation due to orbit raising).

So, the Earth's bulge is continuously displaced due to rotational mismatch, while the moon's bulge is not. If the moon's bulge were directed at earth's center, then there would be a temporary torque and the moon's orientation (in this non-inertial frame) would appear to pendulum back and forth, not a consistent torque that would get it spinning. (Again, I've completely ignored libration effects and assumed a circular orbit for simplifications).

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  • $\begingroup$ This answered my query completely. Thanks! $\endgroup$
    – Shikhin Mehrotra
    Oct 18, 2020 at 20:01
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It does. But it also transfers momentum to the moon which raises the orbit.

The two effects mirror each other. One tends to slow the moon's rotational speed, the other tends to raise the orbit of the moon. The consequence is that the month gets slightly longer, but the same face of the moon continues to point towards Earth.

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