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I got a bit confused while studying the tropical and sidereal years. I noticed that the Earth's precession is in the opposite direction than that of a top's precession, when their rotational direction is the same.

In other words, if you spin the top clockwise, its precession is going to be clockwise too. While Earth's precession is just the opposite.

Could someone please explain how that is?

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A top's precession is caused by torque from the point not being aligned with the center of gravity, this tends to try to get the top to rotate away from the stable axis.

In the case of Earth, the oblateness interacts with the sun's, moon's, and Jupiter's gravity to try to align the axis of rotation perpendicular to orbital plane. This is a torque that tries to rotate the earth towards the stable axis.

Since the torque is in the opposite (relative) direction, the precession is also in the opposite (relative) direction.

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