Inverse-Square Orbits Revisited

Author:

Rizcallah Joseph A.1ORCID,Shaar Yahya N.2

Affiliation:

1. School of Education, Lebanese University, Beirut, Lebanon

2. Institute of Physical Research and Technology, Peoples’ Friendship University of Russia, Moscow, Russia

Abstract

Kepler’s laws are an essential part of any mechanics course at the introductory level. They are commonly used to illustrate the power of Newton’s laws at explaining and predicting the motion of planets and comets around the sun. While the derivation of the second and third laws are outlined in every standard textbook, that of the first law (and the shape of orbits in general) is invariably omitted, due mainly to the insufficient proficiency of the targeted students in differential equations. The paper offers a workaround this difficulty. Assuming familiarity with the basic properties of conics and employing Newton’s law of universal gravitation, we manage to obtain, with very little calculus, the classic result: orbits are conic sections whose nature is determined by the body’s total energy.

Publisher

World Scientific Pub Co Pte Ltd

Subject

General Physics and Astronomy,General Mathematics,Education

Reference12 articles.

1. H. Goldstein, C. Poole and J. Safko , Classical Mechanics, 3rd edn. (Addison Wesley, San Francisco, 2001), pp. 86–98.

2. D. Morin , Introduction to Classical Mechanics: With Problems and Solutions (Cambridge University Press, Cambridge, 2008), VI–6.

3. H. D. Young and R. A. Freedman , Sear’s and Zemansky’s University Physics: With Modern Physics, 12th edn. (Addison-Wesley, San Francisco, 2008), pp. 396–399.

4. P. A. Tipler and G. Mosca , Physics for Scientists and Engineers, 6th edn. (W. H. Freeman and Company, New York, 2008), pp. 370–372.

5. D. L. Goodstein and J. R. Goodstein , Feynman’s Lost Lecture: The Motion of Planets Around the Sun (Norton, New York, 1996), pp. 145–170.

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