The Moon orbits the Earth such that the same side always faces the Earth. Determine the ratio of the Moon's spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)

Step-by-step solution

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The Moon possesses both spin and orbital angular momentum. However, the Moon orbits the Earth, facing the same side always. Therefore, its spin angular velocity = orbital angular velocity.

It is known that the radius of the Moon is

Also, the distance between the Earth and the Moon is . Let’s consider that M is the mass of the Moon.