Question

Does friction exist in case of the rotation of the moon around the earth? If no, then why?

Answer 1

Gravity pulls the Earth in its orbit, and centrifugal force holds it out. The centrifugal force on the Earth is just a result of the Earth moving in a curved path around the Sun. It doesn’t slow down because there isn’t any friction. After all, in space, there’s nothing to have friction with.

Similarly, gravity puts the moon in its orbit during rotation and centrifugal force help moon to rotate around the earth. Friction doesn't exist in case of the rotation of the moon.
Now the reason is why it doesn't exist?

Friction is a force that opposes motion between any surfaces that are touching.Friction occurs because no surface is perfectly smooth. Rougher surfaces have more friction between them.

When moon is rotated around the earth, there is no object or obstacle present on the axis of moon to create any friction. That's why there is no friction in case of rotation of moon around the earth.