Because the Moon is orbiting the Earth every month, in addition to the Earth rotating every day. By the time the Earth rotates once, the Moon has moved ~1/28 of the way around its orbit, which is a big enough difference to be visible in the sky.
The Earth’s orbit creates the same effect for the Sun, but the longer length of the orbit (365+ days) makes it less noticeable from day to day.
Because the Moon is orbiting the Earth.
The daily movement of the Moon is because of the Earth’s rotation. The Earth takes 24 hours to complete a rotation.
The Moon’s orbit around the Earth is 28 days, so longer, but short enough that you can notice the difference from day to day. By the time 24 hours have gone by, the Moon has moved ahead in its orbit a bit, so instead of being in the same spot it’s a little bit further ahead
It’s orbiting very close to us so it seems to move relatively quickly against the background of stars. It moves its own width every hour in front of the stars. Actually the stars go around the sky fastest, returning to the same position every 23h56m. The sun comes next at 24h00m and the moon’s at 24h50m. So, in some ways, the moon is actually the slowest-moving object in the sky.
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