Question

the earth and moon equally attract each other so why the moon goes towards earth

Answer 1

because the mass of moon is less than of the Earth

Answer 2

The earth and moon are attracted to each other and orbit the center of mass between the two (barycenter). It is about 2,900 mile from the center earth toward the moon. Then there is the tidal effect between the two, that is causing the moon to slow down and move to a higher orbit. So the moon is slowly moving away from earth and will someday (assuming nothing else happens) will leave the orbit of earth.
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