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Rearing Its Ugly Head: The Cosmological Constant and Newton's Greatest Blunder
by Hieu D. Nguyen (Rowan University)This article originally appeared in:
American Mathematical Monthly
Subject classification(s): Mathematical Physics | Applied Mathematics | Ordinary Differential Equations | Differential and Difference Equations
Applicable Course(s): 4.18 Applied Math (Math Modeling) | 4.16 Partial Differential Equations | 4.11 Advanced Calc I, II, & Real Analysis | 3.6 Differential Equations
This article is part of the Mathematics of Planet Earth 2013 Collection. In this article the author discusses Einstein's use of the cosmological constant in his theory of relativity and compares that "blunder" with Newton's faulty calculation of the advance of the moon's apsis, or line of extreme position, as it orbits the earth. Nguyen argues that Newton's use of solar attraction as a harmonic force term is equivalent to Einstein's cosmolgical constant term from the perspective of Newtonian mechanics. The author's demonstration of Newton's calculation follows Chandrasekhar's proof and is "quite accessible to undergraduate students and ideal as an application topic in a sophomore-level differential equations course." The presentation emphasizes Newton's Revolving Orbit Theorem.
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