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ERIC Number: EJ860651
Record Type: Journal
Publication Date: 2009-May
Pages: 6
Abstractor: As Provided
Reference Count: 11
ISSN: ISSN-0143-0807
A Simple Derivation of Kepler's Laws without Solving Differential Equations
Provost, J.-P.; Bracco, C.
European Journal of Physics, v30 n3 p581-586 May 2009
Proceeding like Newton with a discrete time approach of motion and a geometrical representation of velocity and acceleration, we obtain Kepler's laws without solving differential equations. The difficult part of Newton's work, when it calls for non-trivial properties of ellipses, is avoided by the introduction of polar coordinates. Then a simple reconsideration of Newton's figure naturally leads to an explicit expression of the velocity and to the equation of the trajectory. This derivation, which can be fully apprehended by undergraduates or by secondary school teachers (who might use it with their pupils), can be considered as a first application of mechanical concepts to a physical problem of great historical and pedagogical interest. (Contains 11 footnotes and 1 figure.)
Institute of Physics Publishing. The Public Ledger Building Suite 929, 150 South Independence Mall West, Philadelphia, PA 19106. Tel: 215-627-0880; Fax: 215-627-0879; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education; Secondary Education
Audience: Teachers
Language: English
Sponsor: N/A
Authoring Institution: N/A
Identifiers - Location: France