How is the gravitational field related to force?
Force and Newton’s Laws of Motion
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This is not an easy question to answer. Newton recognized the problem and had to develop a new mathematics, the integral calculus, to solve it. His argument, simplified, can be illustrated with a wooden button. Hold it at arms length in front of a window so you can see a tree. Note how much area the button covers on the tree. According to Newton, assuming that the button and tree were made of the same material, the force of attraction of the button on you is exactly the same as that of the part of the tree the button covers. The reason is that the effect of the button being closer is balanced by the much larger mass of the tree. Can you show that the area the button covers is r^{2} times the area of the button? The sum of the two forces is that of the sum of the masses of the button and the tree located at a distance halfway between the two.
As was described above, the force of gravity on an object is equal to the objectâ€™s mass times the gravitational field strength, expressed as F = mg. Thus if you have a mass of 70 kilograms (154 pounds), the force of gravity on you is 686 newtons.