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As I understand, the Moon is following Earth's curved space. If that's the case, shouldn't the Moon have no rotation if it's tidally locked, and only appear to have rotation?


If the Earth suddenly disappeared, would the Moon still rotate every 28 days?

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  • $\begingroup$ If the earth suddenly disappeared, the moon wouldn't rotate every 28 days. $\endgroup$ Feb 22, 2015 at 19:47
  • $\begingroup$ There are two rotations involved in a tidally-locked system. There is the rotation of the moon about its own axis, and the rotation of the moon around the Earth. Which rotation are you asking about? $\endgroup$
    – Brionius
    Feb 22, 2015 at 19:49
  • $\begingroup$ @Brionius im talking only about the moon's own rotation on its axis $\endgroup$ Feb 22, 2015 at 19:50
  • $\begingroup$ In your other question you seem to be trying to reason about the rotation of an extended body in terms of GR geodesics. It is worth noting that the individual pieces of an extended body are not free-falling: there are forces between them which means that no individual bit can be assumed to move on a geodesic. $\endgroup$ Feb 22, 2015 at 19:51
  • $\begingroup$ This is a special case of Will an object falling into Earth's orbit start spinning?. I think the question can be simplified to whether a gyroscope located at the centre of the Moon would rotate relative to the rest of the Moon. $\endgroup$ Feb 22, 2015 at 19:57

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Yes, the moon does rotate. In a tidally locked system, the angular speed of the rotation of the satellite about its own axis is equal to the angular speed of the rotation of the satellite about its primary.

Thus, the moon has an angular speed about the Earth of 1 cycle / 28 days, and an angular speed of 1 rotation / 28 days about its own axis; this is why we only see one face of the moon.

The moon itself moves along a geodesic, however the individual particles that make up the moon as they rotate about the moon's axis of rotation do not.

If you took away the Earth magically, the geodesic the moon would subsequently take through spacetime would resemble a straight line. However, absent some external torque that slows the moon down, the pieces of the moon would continue rotating around the moon's axis; the centripetal force that maintained their circular motion was not the Earth's gravity, but the Moon's gravity, which is still present.

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  • $\begingroup$ the moon can appear to rotate on its axis with 0 angular speed in GR can it not? if it follows earth's curvature of space. am i missing something? $\endgroup$ Feb 22, 2015 at 20:18
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    $\begingroup$ @user2914191 Again, what you are missing is that the bits of the moon not at the center are not moving along geodesics. The fact of tidal forces is enough to establish that. $\endgroup$ Feb 22, 2015 at 21:28

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