The moon accelerates or decelerates because the pull of gravity between it and the earth changes as it moves closer or farther from earth. As the moon orbits the earth, it moves closer in one half of its cycle and away in the other half. As the moon approaches the earth, mutual gravity increases its speed.
When the moon is moving away from the earth, the decreased gravity decelerates it, causing it to move slower. The moon's orbit around the earth is an ellipse whose center is 12,000 miles from the center of the earth. Subsequently, during each orbit, the distance between the moon and the earth varies by twice the 12,000 miles.
When the moon reaches its closest distance from the earth, or perigee, it’s moving at about 6 percent faster than its average speed. Conversely, when it’s farthest from the earth, or apogee, its speed reduces by 6 percent compared to its average speed.
The moon rotates on its axis, even as it revolves around the earth. Tidal coupling between the earth and the moon causes the latter’s rotational period of 27.3 days to coincide with its period for revolution. The tidal locking has the moon maintain the same side facing the earth.