When the earth pull the object towards itself it exert a force on object due to which the object starts falling towards earth at a fast speed of course, due to the object, a force is being applied on earth in the form of reaction, that is, the object pulls the earth towards itself with the same force. Due to this force, the earth moves rapidly towards the object but we don't experience this motion that is the earth doesn't fall towards the object because according to Newton's second law, the acceleration produced in the object when force is applied is equal to inversely praprotional to its mass. The mass of earth is much greater than that of the object. The acceleration produced in the earth is negligible compared to acceleration produced by the object. Therefore, the object falls towards the earth. Earth does not fall towards the object.
