SEARCH FOR CHAINS OF RESONANCES IN THE COMPACT PLANETARY SYSTEM KEPLER-51

Abstract

We consider the compact three-planetary system Kepler-51 and search for resonance chains within the errors of determining the orbit periods from observations.To determine the resonant combinations of the semi-major axes of the orbits, the ratio of the mean motions of neighboring planets was represented as a segment of a sequence of convergent fractions.We have shown that the planetary system Kepler-51 evolves outside the low-order resonant chains .