the Moon moves about 3.8 cm away from the earth each year
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The mass of the earth is over 80 times the mass of the moon. A massive object will tend to capture less massive objects in its gravitational field.____________But consider this: if the moon happened to be the same general size and mass as earth, which would orbit which? You would observe them each orbiting around an invisible spot half way between them, their 'system' center of gravity otherwise called the 'barycenter'. They would effectively be orbiting around each other. As the moon becomes less massive, what determines the 'cut-off' between orbiting around each other and the smaller orbiting the larger? In fact it is still true that earth and moon are each orbiting their barycenter. Interestingly, the barycenter in this case is within the body of the earth, because the earth is so much more massive than the earth.
The moon's gravity is 1/6 the force of Earth's gravity, so you would weight 1/6 as much on the moon than on the Earth. For example, if you were 120 kg on Earth, you would be 20 kg on the Moon. (120 / 6 = 20)
It is because there is less gravitational force on the moon.
The moon's synodic period, the time it takes to come back to the same phase relative to the Earth and Sun, varies but, on average, is 29.53 days.
The gravitational effect of the moon causes both the high tide and low tides. The gravity of the moon attracts water which then is attracted by the much powerful force of the earth. These gravitational forces cause low and high tides.