What is the effect of gravitational force on an object?
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Although the gravitational force the Earth exerts on the objects is different, their masses are just as different, so the effect we observe (acceleration) is the same for each. The Earth's gravitational force accelerates objects when they fall. It constantly pulls, and the objects constantly speed up.
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The gravitational force between two objects is "directly proportional to the product of their masses" and "inversely proportional to the square of the distance between their centers".
So the force of gravity between Earth and other objects of different masses is different. Since this force is always attractive, it's principal effect is to pull that object towards itself.
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