The reaction force to this pull is the force with which the object pulls on the Earth. This force also has a magnitude mg, and it has a direction opposite to that of the force with which the Earth pulls on the object.
This is an example of the Third Newton's Law, which states that when two objects interact, they act on each other with the forces that are opposite in direction and equal in magnitude. In other words, the Third Newton's Law states that every action causes a reaction. This is one of the laws on which classical mechanics is based. In the case of the gravity, as in the given example, both the Earth and the object exert a gravitational force equal mg on each other.
The resultant motion of the objects is described by the Second Newton's Law: F = ma. Here, a is the acceleration. While the forces acting on the Earth and the object are equal in magnitude, the mass of the Earth is much, much larger than the mass of the object, so its acceleration due to this force will be much, much smaller. Therefore, we can observe the motion of the objects due to the gravitational attraction of the Earth, but not the other way around.
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