  Since the discovery in 1772 of the triangular Lagrange points L4 and L5 in
the gravitational field of two bodies moving under the sole influence of mutual
gravitational forces, astronomers found a large number of minor celestial
bodies around these points of the Sun-Jupiter, Sun-Earth, Sun-Mars and
Sun-Neptune systems. The L4 and L5 points of the Earth and Moon may be empty
due to the gravitational perturbation of the Sun. However, in 1961 Kordylewski
found two bright patches near the L5 point, which may refer to an accumulation
of interplanetary particles. Since that time this formation is called the
Kordylewski dust cloud (KDC). Until now only a very few computer simulations
studied the formation and characteristics of the KDC. To fill this gap, we
investigated a three-dimensional four-body problem consisting of the Sun,
Earth, Moon and one test particle, 1860000 times separately. We mapped the size
and shape of the conglomeratum of particles not escaped from the system sooner
than an integration time of 3650 days around L5. Polarimetric observations of a
possible KDC around L5 are presented in the second part of this paper.
