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Since the moon is tidally locked to earth, what about center of mass and geometric center? How far from each other are they? Can a celestial body be tidally locked to an other one if its mass distribution is perfectly homogeneous (center of mass at the very same place of geometric center)

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Since the moon is tidally locked to earth, what about center of mass and geometric center? How far from each other are they?

They differ by about two kilometers.

Can a celestial body be tidally locked to an other one if its mass distribution is perfectly homogeneous (center of mass at the very same place of geometric center)?

Yes, but that condition is not what I would call "perfectly homogenous". What's needed is a non-spherical mass distribution. For example, a uniform density ellipsoidal body would have its center of mass and center of figure of coinciding, but would still be subject to torques. It's the moment of inertia that is key rather than the offset between center of mass and center of figure. An object whose center of mass and center of figure do not coincide necessarily has a non-spherical moment of inertia tensor.

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  • $\begingroup$ To add to this, it's the tidal bulge, not the moon's gravitational irregularity that lead to the tidal locking. A gravitational irregularity rotates around in circles. A tidal bulge stays in one place ahead of or behind the straight line between the Planet and Moon. That's not to say that the gravitational lumpiness has no effect. It has some. But the tidal bulge has a much greater effect in most tidal locking situations. $\endgroup$ – userLTK Jul 19 '17 at 17:06
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    $\begingroup$ @userLTK -- If you are writing about the Earth's tidal bulge, this (a) would have zero impact on a spherically symmetric Moon and (b) doesn't exist. The Moon, however, does have a frozen tidal bulge. $\endgroup$ – David Hammen Jul 19 '17 at 17:12
  • $\begingroup$ I was talking about how the tidal bulge in general is the feature that leads to tidal locking, not gravitational asymmetry. I thought that was relevant to the homogeneous question. $\endgroup$ – userLTK Jul 19 '17 at 17:31
  • $\begingroup$ @DavidHammen I don't believe that tides don't exist for a second. There are multiple issues I have with the answer you linked. Besides, if you just look around the web, you'll see extremely varying answers and opinions about tides so its a really hard thing to get a straight, correct answer on. Kind of like the question about what makes planes fly. $\endgroup$ – zephyr Jul 20 '17 at 14:50
  • $\begingroup$ @zephyr - I never wrote tides don't exist. I wrote that the tidal bulge doesn't exist. Laplace wrote pretty much the same thing when he came up with his dynamic theory of the tides. $\endgroup$ – David Hammen Jul 20 '17 at 16:43

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