Exercises in historical mathematics (Example)

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Name Professor Course Date Historical calculations 3. Aristarchus was a Greek astronomer and mathematician born on the island of Samos Greece around 310 BC. He was the person who first came up with the concept of the earth revolving around the sun and the sun being in the middle of the universe. Research and explain his calculations in your own words using Aristarchus' initial data. According to the initial Aristarchus data he employed many modern geometric methods in models designed to measure of the semi-major axis of its orbit". Newton's form of Kepler's law relates the distances masses and the orbital periods of two orbiting objects. p2=4π2G(M1+M2).a3Where P is their orbital period a is the distance between their centers M1 and M2 are the masses of the two objects while G is the gravitational constant. Mj=4π26.67.10-11. (15303752).4214490003=1.89.1027kgWork cited Nauenberg Michael. "The Reception of Newton's Principia." arXiv preprint arXiv:1503.06861 (2015). Walker Philip. A history of applying mathematics to physics. School of Mathematics University of Leeds. [...]

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I need the second part of the assignment. Questions 3 and 4. Only apply if you can. 2 Historical calculations In these questions, you will be required to research and to explain, in your own words and using modern notation, some significant astronomical calculations from history. Your mark will be based on the accuracy and detail that you provide. 3. In On the sizes and distances of the sun and moon, Aristarchus of Samos estimated the size and distance-fromEarth of the Sun and Moon, relative to the size of the Earth. His text has been translated into English. a) Research and explain his calculations in your own words, using Aristarchus’ initial data. b) Two pieces of his initial data were wildly inaccurate: better values would be 1 6 ◦ for the small angle in the triangle between the Sun, Moon and Earth, and 1 2 ◦ for the angular diameter of the Sun. How would Aristarchus’ results, with these improved data, compare against modern values? 4. Galileo’s observations of Jupiter in 1610 sparked a wave of new science among astronomers. a) One piece of Jupiter-based science, from 1676, was Ole Rømer’s use of eclipses of one of Jupiter’s moons, Io, to estimate the speed of light. Explain his insight, and his calculation. Illustrate your answer with data. b) In Principia Mathematica (1687), Bk. III Prop. 8, Newton applied Kepler’s third law to calculate the mass of Jupiter relative to the mass of the Earth. Explain, in your own words and using relevant formulae and data, how Newton could calculate the mass of Jup