A New Determination of the Fundamental Frequencies in our Solar System

Lhotka, Christoph and Dvorak, Rudolt (2006) A New Determination of the Fundamental Frequencies in our Solar System. In: 4th Austrian-Hungarian Workshop on Celestial Mechanics Edited by Á. Süli, F. Freistetter, A. Pál. Publications of the Astronomy Department of the Eötvös University (18). ELTE Sokszorosítóüzeme, Budapest, pp. 33-46.

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Abstract

In this investigation we integrated the orbits of the planets of our Solar System over 1 billion years (-500 million back and 500 million into the future) based on the Newtonian model of the Solar System including the 8 major planets Mercury to Neptune. For the integration we used the very stable and highly precise Lie-Integration method. The output of the simulation were the osculating orbital elements, stored every 66,6 years. We transformed the data set to Laplace-Lagrange variables and analyzed it using windowed fourier transformation with a windowsize of 10 million years, overlapping with 1 million years. In this paper we present the maximum and minimum values of the orbital elements of the planets and give the time varying fundamental frequencies of all eight planets.

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