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Since the discovery in 1772 of the triangular Lagrange points L4 and L5 inthe gravitational field of two bodies moving under the sole influence of mutualgravitational forces, astronomers found a large number of minor celestialbodies around these points of the Sun-Jupiter, Sun-Earth, Sun-Mars andSun-Neptune systems. The L4 and L5 points of the Earth and Moon may be emptydue to the gravitational perturbation of the Sun. However, in 1961 Kordylewskifound two bright patches near the L5 point, which may refer to an accumulationof interplanetary particles. Since that time this formation is called theKordylewski dust cloud (KDC). Until now only a very few computer simulationsstudied the formation and characteristics of the KDC. To fill this gap, weinvestigated a three-dimensional four-body problem consisting of the Sun,Earth, Moon and one test particle, 1860000 times separately. We mapped the sizeand shape of the conglomeratum of particles not escaped from the system soonerthan an integration time of 3650 days around L5. Polarimetric observations of apossible KDC around L5 are presented in the second part of this paper.

monthly notices of the royal astronomical society

Celestial Mechanics and Polarization Optics of the Kordylewski Dust  Cloud in the Earth-Moon Lagrange Point L5 Part I. 3D Celestial Mechanical  Modelling of Dust Cloud Formation