2007, Vol.10, No.2, pp.105-115

The paper reviews the important role of resonances for the structure of planetary systems. After a short introduction into the basics of the orbital dynamics of motion in resonances we describe the dynamics of our planetary system and also of extrasolar planetary systems. Up to now more than 147 are known with 170 planets. In our system the planets move on quite regular orbits with small eccentricities although it was found that the motion is chaotic on very large time scales, which surpasses the age of the Solar System. This quasi regularity is not true for the small bodies: the main belt of asteroids between Mars and Jupiter with gaps for special values of the semimajor axes on one hand and on the other hand with families of many small bodies, is sculpted due to the presence of mean motion resonances with Jupiter. In extrasolar systems the planets are - rather surprisingly - found to move sometimes on very high eccentric orbits. Because of our still limited observational techniques using indirect methods most of them are massive planets comparable to the size of Jupiter. One of our aims is to find theoretically zones where additional terrestrial planets could move in such a system. Because of the mostly large eccentricities the resonances are, in contrary to our planets, essential for the stability of the orbits, and may protect or destroy an orbit. In multiple planetary systems we concentrate on the stability of their orbits. A very interesting new result is that most of these multiple planetary systems with high eccentric orbits move in resonances with a special configuration which protects them from close encounters although there orbits are crossing. A special chapter is devoted to possible terrestrial planets in the 1:1 resonance with a Jupiterlike planet in extrasolar planetary systems.
Key words: extrasolar planetary systems, resonances

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