Does earths gravity pull the moon toward it?

Does earths gravity pull the moon toward it?
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The force of gravity (simple theory) is equal to the product of the masses of the two objects and the square of the distance between them, times the gravitation constant of the universe. The Earth pulls on the moon, enough to pull it towards Earth, but no enough to make it fall. The force is only enough to keep it falling, but moving around at a speed that is countered by the curvature of the Earth. It is also pulling on us, which causes tides. Gravity is the natural force that brings masses together. It is relatively weak when compared to other forces, but it adds up with larger masses.
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