Other
Scientific paper
Jan 1981
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981zamm...61....1m&link_type=abstract
Zeitschrift für angewandte Mathematik und Mechanik, vol. 61, Jan. 1981, p. 1-6. In German.
Other
Celestial Mechanics, Resonance, Solar Orbits, Three Body Problem, Circular Orbits, Gravitational Effects, Planetary Gravitation, Secular Variations
Scientific paper
The considered investigation is concerned with the relationship between celestial mechanics and the theory of vibrations. Attention is given to the existence of a combination resonance in the planetary system, taking into account an excitation frequency near the difference or sum of two natural frequencies. Motions in a plane are considered. It is assumed that two planets are in nearly circular orbits with respect to a large central body (sun). The planets produce mutually gravitational effects on each other. The perturbations can be divided into periodic perturbations and secular perturbations. Only the secular perturbations provide information regarding the long-term behavior of the system. The motions of the planets of the solar system related to secular perturbations occur in time periods of more than ten thousand years. It is shown that this phenomenon of celestial mechanics, which has been known for a long time, is actually related to combination resonance.
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