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The Geometry of Planetary Orbits and Ellipses
Moti Ben-Ari
2024
Everyone "knows" that Kepler discovered that the orbits of the planets are ellipses and everyone "knows" that Newton showed that a planet in an elliptical orbit is subject to the force of gravity that is inversely proportional to the square of the distance from the Sun. Although I knew these facts, I had never seen them demonstrated until I read Calculus in Context by Alexander J. Hahn.
This document is a tutorial on the planetary orbits with an emphasis on proofs using Euclidean geometry. Although Newton invented the calculus and used it to study motion, from the time of the Greeks, proof meant proof by geometry. Newton's proof requires a depth of knowledge of Euclidean geometry and conic sections that is no longer studied today.
The tutorial is intended to enrich the learning of mathematics by secondary-school students and students in introductory university courses. The prerequisites are a good knowledge of Euclidean geometry along with some trigonometry, a bit calculus and Newton's laws of motions.
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Rights Information
This work has been claimed by Mordechai Ben-Ari.
Downloads
- 12 - pdf (CC BY-SA) at Unglue.it.
Keywords
- Mathematics
- Mathematics / Geometry
- Science
- Science / Gravity
Links
web: https://github.com/motib/orbitsEditions