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Calculus Be Used To Prove Kepler's Three Laws Of Planetary Motion?

1450 Words6 Pages

Question: “How can differential and integral calculus be used to prove Kepler’s Three Laws of Planetary Motion?”
Introduction
Considered one of profound intimacy, the relationship between mathematics and physics has been a subject of study of great importance to mathematicians, physicists, philosophers and historians since their conception, and the two fields have constantly stimulated each other, promoting the creation of new knowledge. For instance, during the seventeenth century, many of the most important mathematical advances were motivated by the study of physics. One such advancement was the creation and development of calculus, which was primarily the result of a demand for a more advanced mathematical language that could be used to handle and describe a new set of physical phenomena and dynamics. Moreover, when studying natural phenomena, physicists have two main methods for producing scientific knowledge: the scientific method, in which the physicists …show more content…

More specifically, the research question is: “How can differential and integral calculus be used to prove Kepler’s Three Laws of Planetary Motion?”, and this question will be explored through the use of variable manipulation, vectors, and differential and integral calculus in the polar coordinate framework. In addition, in order to prove them, I have written my own original proof for each respective law applying principles of calculus and variable manipulation until the laws can be proven to be true, and I will be describing the process/method of each proof and explaining what each step means. Furthermore, this essay will demonstrate the interdisciplinary relationship between mathematics (Calculus) and science (Astrophysics), as well as the application of mathematics and how it is present in the real world, especially in

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