Poynting-Robertson effect and capture of grains in exterior resonances   with planets
  Spherical meteoroids orbiting the Sun experience orbital decay due to the Poynting-Robertson effect and can become trapped in commensurability resonances with a planet. Detail conditions for trapping in the planar circular restricted three-body problem with action of solar electromagnetic radiation on spherical grain are presented. The results are given in terms of the radiation presure factor $\beta$.   In general, the greater value of $\beta$, the shorter capture time in a resonance. Captures of particles may be even several times longer than it is presented in literature. Analytical formula for maximum capture times is given.   Analytical theory for minimal capture eccentricities is presented. The obtained analytical results differ from those presented in the literature. However, the known analytical results are not very consistent with our detail numerical computational results for $\beta-$values 0.01 and 0.05 and for the planet Earth. Minimum eccentricities for captures into resonances are also smaller, even in order of magnitude, than the published values.   The presented results enable comparison with calculations for nonspherical particles. 
J. Klacka and P. Pastor