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Originally Posted by JohnD
the whole object travels at the speed required to keep in orbit a point of the same mass at the position of its 'centre of gravity', or mass centre. A part of the object further out from the mass centre is travelling at the same speed but that is too fast for the wider orbit ... and as the Earth is flexible, it bulges, towards AND away from the Moon.
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You forget that the Earth does not orbit the Moon: it orbits the barycentre of the Earth-Moon system. This is only 1,600 km beneath the Earth's surface. This means that the point on the Earth's surface
closest to the Moon is
closer to the barycentre than is the Earth's centre of mass; but as it is travelling at the same speed, it's going too
slowly for its orbit, and so should (according to your argument) spiral in towards the barycentre
away from the Moon. In fact, the opposite happens: it bulges out towards the Moon and away from the barycentre.