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Newton's Law of Universal GravitationIsaac Newton compared the acceleration of the moon to theacceleration of objects onearth. Believing that gravitational forces were responsible for each,Newton was able todraw an important conclusion about the dependence of gravity upon distance. Thiscomparison led him to conclude that the force of gravitationalattraction between theEarth and other objects is inversely proportional to the distanceseparating the earth'scenter from the object's center. But distance is not the only variable effecting themagnitude of a gravitational force. In accord with Newton'sfamous equationFnet= m*aNewton knew that the force which caused the apple's acceleration(gravity) must bedependent upon the mass of the apple. And since the force acting to cause the apple'sdownward acceleration also causes the earth's upward acceleration(Newton's third law),that force must also depend upon the mass of the earth. So forNewton, the force ofgravity acting between the earth and any other object is directly proportional to the massof the earth, directly proportional to the mass of the object, andinversely proportional tothe square of the distance which separates the centers of the earthand the object.
But Newton's law of universal gravitation extends gravity beyond earth. Newton's law ofuniversal gravitation is about theuniversalityof gravity. Newton's place in theGravityHall of Fameis not due to his discovery of gravity, but rather due to hisdiscovery thatgravitation is universal.ALLobjects attract each other with a force of gravitationalattraction. This force of gravitational attraction is directlydependent upon the masses ofboth objects and inversely proportional to the square of thedistance which separates theircenters. Newton's conclusion about the magnitude of gravitationalforces is summarizedsymbolically as