Fourier analysis of planet trajectories and the Copernican model of the solar system

Details Fourier analysis of planet trajectories and the Copernican model of the solar system Fourier analysis of planet trajectories and the Copernican model of the solar system

Jun 2003

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003rmxf...49..283p&link_type=abstract

Revista Mexicana De Fisica, vol. 49, no. 3, p. 283-289.

Physics

Scientific paper

The most important models before newtonian mechanics and the law of gravitation were stablished by Kepler and Copernicus. The relation between Newton's theory and Kepler's laws of planetary motion is widely discussed in textbooks; however, the relation with the model of Copernicus, where the position of a planet as a function of time is described as combination of circular motions, is usually avoided. In this work we use two simple and useful numerical techniques to show that this relation is easily performed. We use the algorithm of Verlet to solve the differential equations, not in polar coordinates as is usually done, but in cartesian coordinates, we also use the fast Fourier transform method to analyse the time series that in a natural way generate the deferent and epicicles of the Copernicus' model.

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