We study the orbital evolution of dust particles in the region of exte
rior mean motion resonances with the Earth. The trajectories of the pa
rticles are integrated in the context of a seven-body problem (Sun, fi
ve major perturbing planets and the particle) with the solar radiation
and wind forces accounted for. Regions of stable resonant trapping ar
e identified in the e-omega plane for a sequence of first order j/(j 1) resonances. On the basis of these maps it comes out that particles
reaching the proximity of the Earth with high values of eccentricity
are trapped more frequently in low-j resonances. Results for different
particle sizes are presented. We have also integrated the orbits of p
articles for more than 10(5) yr by a procedure alternative to the dire
ct integration of the many-body problem, i.e. by introducing directly
in the equation of motion the position vectors of the planets as obtai
ned from the recent Richardson & Walker (1989) accurate numerical simu
lation of the full planetary system. A study of the trapping times has
been performed for different j/(j + 1) resonances and for different p
article sizes. The duration of the trapping phenomenon is regulated by
occurrence of close approaches with the Earth. For the 2/3 and 3/4 re
sonances, close approaches to Mars can also be important in forcing th
e particle out of resonance.