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10/12/1684 Newton's derivation of Kepler's laws from his theory of gravity

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Gravitation Keplers 1st Law

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Physics - Universal Law of Gravitation – Part 1

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Kepler’s First Law of Motion - Elliptical Orbits (Astronomy)

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Newton's Law of Gravitation Explained

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The Laws of Gravity

De motu corporum in gyrum gave important mathematical derivations relating to the three relations now known as "Kepler's laws". Halley reported the communication from Newton to the Royal Society in 1684. After further encouragement from Halley, Newton went on to develop and write his book Philosophiæ Naturalis Principia Mathematica.