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+------- Thread: The Geometry of Ellipses and Planetary Orbits [Ben-Ari] (/showthread.php?tid=1578)
The Geometry of Ellipses and Planetary Orbits [Ben-Ari] - mklabgr - 08-12-2026
The Geometry of Ellipses and Planetary Orbits
BY Mordechai Ben-Ari
Summary
The Geometry of Ellipses and Planetary Orbits by Mordechai Ben-Ari is an open-access textbook that explores the geometry of ellipses and their fundamental role in understanding planetary motion, using primarily secondary-school Euclidean geometry, analytic geometry, and trigonometry.
The book combines mathematical history with rigorous geometric proofs, covering the work of Apollonius, Kepler, and Newton, including Kepler’s laws, Newton’s geometric derivation of the inverse-square law, elliptical orbits, orbital computations, and Lagrange points.
It also examines methods for constructing ellipses and presents advanced results such as the Steiner inellipse, Marden’s Theorem, Pascal’s and Brianchon’s theorems, and Newton’s Ellipse Theorem, making the book both a historical account and a challenging introduction to the mathematics connecting geometry, gravitation, and planetary motion.
BOOK [FREE AS A PDF]