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Central force fields and Kepler's laws

Published online by Cambridge University Press:  18 June 2018

Luis Blanco ,
María García-García ,
Joaquín Gutíerrez  and
Andrea Rios
Luis Blanco
Affiliation:
Undergraduate, Escuela Técnica Superior de Ingenieros Industriales, Universidad Politécnica de Madrid, Madrid (Spain) e-mail: luis.blanco.diaz@alumnos.upm.es
María García-García
Affiliation:
Undergraduate, Escuela Técnica Superior de Ingenieros Industriales, Universidad Politécnica de Madrid, Madrid (Spain) e-mail: mariademadriguera@hotmail.com
Joaquín Gutíerrez
Affiliation:
Departamento de Matemáticas, Escuela Técnica Superior de Ingenieros Industriales, Universidad Politécnica de Madrid, C. José Gutiérrez Abascal 2, 28006 Madrid (Spain) e-mail: joaquin.gutierrez.alamo@gmail.com
Andrea Rios
Affiliation:
Undergraduate, Escuela Técnica Superior de Ingenieros Industriales, Universidad Politécnica de Madrid, Madrid (Spain) e-mail: andrea_michelle.laz@hotmail.com
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Extract

In this survey we give very simple proofs of Kepler's Laws and other facts about central force fields using only Newton's second law, Newton's law of universal gravitation, basic notions of vector calculus, and an elementary double integral.

Hopefully, this article will help undergraduate students of mathematics and engineering who wish to understand these fundamental scientific discoveries.

In many textbooks (see, for instance, [1, 2, 3, 4, 5]), Kepler's Laws are obtained using conservation of energy and angular momentum, differential equations, mobile reference systems, or notions not so well-defined such as differentials or ‘infinitesimal elements’. Some of the arguments appear to be rather involved if one is not accustomed to them, whereas the proof of Kepler's Laws may actually be obtained from quite simple facts.

Type
Articles
Information
The Mathematical Gazette , Volume 102 , Issue 554 , July 2018 , pp. 270 - 279
Copyright
Copyright © Mathematical Association 2018 

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