What if there is nothing for it to rotate around? If it's rotating around something, and there is no center of mass there, is it its own center of mass?
Should the eq of the movement of the moon should be like 354 not 28 cuz the moon orbits the earth multiple times during one month not just once every 28 days right ?
you would think so, but that's mostly caused by the rotation of the earth. It takes 28 days for the moon to travel around the earth one time, which is evident by the phases of the moon We see the moon "rise" and "fall" many times during that 28 day period because the earth itself is rotating, so we view the sun and moon as moving very quickly even though it's quite so. Similar to how the length of a day isn't the length of a year. a year is how long it takes for the earth to go around the sun, a day is how long it takes for the earth to rotate one time.
