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ERIC Number: EJ851828
Record Type: Journal
Publication Date: 2009-Sep
Pages: 8
Abstractor: As Provided
Reference Count: 13
ISBN: N/A
ISSN: ISSN-0143-0807
Had the Planet Mars Not Existed: Kepler's Equant Model and Its Physical Consequences
Bracco, C.; Provost, J.P.
European Journal of Physics, v30 n5 p1085-1092 Sep 2009
We examine the equant model for the motion of planets, which was the starting point of Kepler's investigations before he modified it because of Mars observations. We show that, up to first order in eccentricity, this model implies for each orbit a velocity, which satisfies Kepler's second law and Hamilton's hodograph, and a centripetal acceleration with an r[superscript -2] dependence on the distance to the Sun. If this dependence is assumed to be universal, Kepler's third law follows immediately. This elementary exercise in kinematics for undergraduates emphasizes the proximity of the equant model coming from ancient Greece with our present knowledge. It adds to its historical interest a didactical relevance concerning, in particular, the discussion of the Aristotelian or Newtonian conception of motion. (Contains 3 figures and 15 footnotes.)
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: info@ioppubusa.com; Web site: http://www.iop.org/EJ/journal/EJP
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A