Yes. The moon is slowly moving away from Earth as well at a rate of 3.78cm a year (that’s the same speed our fingernails grow apparently!). This is because the Moon is losing some of it’s orbital energy in making tides on Earth and a larger orbit has less orbital energy.
One other interesting thing is that the Moon rotates at the same speed as it orbits Earth – i.e. the same side always faces us. This is called “tidal locking” or “synchronous rotation”. The tidal forces (a different force of gravity on one side of the Moon to the other) caused the Moon a long time ago to be stretched very slightly in the direction facing the Earth (today, it’s a nearly perfect sphere, if you ignore the craters, etc). As the Moon rotated, this effect kept dragging the longer side of the Moon back towards the Earth. Eventually, the rotation of the Moon was slowed down so that it always faced the Earth.
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