Hello! This is quite a complicated question, and is known by the big phrase ‘gravitational time dilation’…a bit of a mouthful 🙂
It is something that Albert Einstein first described and is a very strange effect where clocks that are next to a massive object (earth, moon, sun) will run more slowly than clocks far away. In fact, anything that has mass will make a clock run more slowly. So, the watch on your wrist runs more slowly because it is close to your body. This kind of physics is very weird but very fun to study, even professional scientists (including myself) get confused by it!
So yes, because of the moon’s gravitational pull (the moon has mass), it increases our time. Only by a tiny tiny amount though, the Earth does the same, and increases it by a larger amount.
It’s also true that the clock in your class room is running more slowly than the clock on the international space station – this is because the space station is further from Earth. You and your teacher are literally aging more slowly than those astronauts. Very strange indeed!
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