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Newton had been interested in math his entire life, and at the age of 24 he made his first major contribution to society. “ Newton began to treat the areas under curves kinetically, as areas swept out by a moving line. From the idea of motion he derived the term 'fluxional', to describe this method, something we now call calculus.” (http://www.bbc.co.uk/history/historic_figures/newton_isaac.shtml)
With his new methods, Newton was able to calculate the area inside a shape with curved sides, and to calculate the rate of change of one thing with respect to another. Newton’s discovery left the mathematical world in awe as he stunned mathematicians with his new theories and methods.
With his mathematical accomplishments under this belt, Newton took an interest in motion and what forces impact it. After studying a book by Galileo on how things fell to earth, and also studying work by Johannes Kepler, who taught how planets circle the sun, Newton starting to question what kept planets in orbit, or more specifically, what kept the moon from crashing with the earth or the sun? Although many people say that his questions were answered while sitting under an apple tree and having an apple fall on his head. “This alleged accident supposedly prompted him to imagine that perhaps all objects in the Universe were attracted to each other in the same way the apple was attracted to Earth.
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“ Newton’s Law of Universal Gravitation states that every particle in the Universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.”(Serway) The picture below illustrates the Law of Universal Gravitation. "Newton concluded that the centripetal force of the Moon or of any planet must decrease as the inverse square of its distance from the center of its motion. For example, if the distance is doubled, the force becomes one-fourth as much."( http://euler.ciens.ucv.ve/English/mathematics/newton.html)
Newton not only came up with the Law of Universal Gravitation, he also developed the three laws of motion. The four laws were all introduced and explained in Principia Mathematica, a book he wrote in 1687, which is considered one of the greatest scientific books ever written.
Newton ’s First Law of Motion: A body at rest remains at rest or a body in motion remains in motion unless acted on by an external force.
Newton ’s Second Law of Motion: When viewed from an inertial reference frame, the acceleration of an object is directly proportional to the net force action on it and inversely proportional to its mass. In mathematical terms: ∑ F=ma where ∑ F is the net force acting on an object, ‘m’ is the mass of an object, and ‘a’ is the acceleration of an object.
Newton ’s Third Law of Motion: For every action force there is an equal and opposite reaction force.