• methods: data analysis;
  • methods: numerical;
  • celestial mechanics;
  • planets and satellites: dynamical evolution and stability;
  • stars: individual: Kepler-11


The Kepler-11 planetary system hosts at least six transiting super-Earth planets detected through the precise photometric observations of the Kepler mission (Lissauer et al.). In this paper, we re-analyse the available Kepler data, using the direct N-body approach rather than an indirect transit timing variation method as employed in the discovery paper. The orbital modelling in the realm of the direct approach relies on the whole data set, not only on the mid-transits times. Most of the results in the original paper are confirmed and extended. We constrained the mass of the outermost planet g to less than 30 M. The mutual inclinations between orbits b and c as well as between orbits d and e are determined with a good precision, in the range of [1°, 5°]. Having several solutions to the four qualitative orbital models of the Kepler-11 system, we analyse its global dynamics with the help of dynamical maps. They reveal a sophisticated structure of the phase space, with narrow regions of regular motion. The dynamics are governed by a dense net of three- and four-body mean motion resonances, forming the Arnold web. Overlapping of these resonances is a main source of instability. We found that the Kepler-11 system may be long-term stable only in particular multiple resonant configurations with small relative inclinations. The mass–radius data derived for all companions reveal a clear anticorrelation between the mean density of the planets and their distance from the star. This may reflect the formation and early evolution history of the system.