Why is the moon moving away from the earth/why are the days getting longer?
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You’ve probably learned the moon causes the ocean tides. The moon’s gravity pulls on the oceans and causes it to bunch up a little bit. Well, more mass means more gravity. So this area of bunched up ocean has slightly more gravity, pulling back on the moon. As the Earth rotates and drags this bunched up water forward, that extra bit of gravity also pulls the moon forward a little bit. And a faster orbit also means a bigger orbit.
You know how you get pushed into the side of a car if it takes a turn too quickly? The earth is doing that to the moon.
But wait, there’s more. Newton’s third law states that for every action, there’s an equal an opposite reaction. As the Earth is pulling the moon forward, the moon is dragging backwards on the Earth’s rotation (aka longer days).
Eventually, they’ll meet in the middle and become tidally locked. The moon’s orbit will exactly match the Earth’s rotation. One side of the Earth will always see the moon, and the other side will never see it again. (Well, the death of the Sun will mean they’ll never survive to get to that point).
Same reason there are tides on Earth.
That same “pull” from the Moon which creates the tides on Earth also creates an pull on the Moon.
But the Earth is rotating faster than the Moon is orbiting. This makes the tidal bulge move ahead of the Moon at all times, which imparts a small but not insignificant increase in speed to the Moon’s orbit. (It also causes the Earth’s rotation to slow down in exchange)
And when an orbiting object increases it’s speed, it must also increase it’s altitude/distance.
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