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which will be some elliptical motion.
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By the way,
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Mr. Newton did not have math guys he could go to.
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Not only did he formulate laws of gravitation,
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he also invented calculus
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and he also learned how to solve the differential equation for calculus.
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He probably felt that nobody around was doing any work,
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because all the thing was given to this one person.
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It's really amazing
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that what Newton did in the case of gravity
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was to find the expression for this.
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A few years earlier he had also gotten this law.