ABSTRACT
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 have 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 might be empty due to the gravitational perturbation of the Sun. However, in 1961, the Polish astronomer, Kazimierz Kordylewski found two bright patches near the L5 point, which might refer to an accumulation of interplanetary particles. Since then, this formation has been called the Kordylewski dust cloud (KDC). Until now, only a very few computer simulations have studied the formation and characteristics of the KDC. To fill this gap, we have investigated a three-dimensional four-body problem consisting of the Sun, Earth, Moon and one test particle, 1 860 000 times separately. We mapped the size and shape of the conglomerate of particles that have not escaped from the system sooner than an integration time of 3650 d around L5. Polarimetric observations of a possible KDC around L5 will be presented in a following second part to this paper.
