Abstract. CCD observations of comet C/1999 J2 (Skiff) were made at the Pik Terskol Observatory on September 15, 1999. The 2-m telescope equipped with the two-channel focal reducer of the Max-Plank-Institute for Aeronomy was used to study the cometary environment. In spite of the large heliocentric distance, 7.24 AU, a straight dust tail with fairly well defined boundaries was recorded. These data provide an opportunity to study the peculiarity of dust, that is not driven by water vapor. To fit the dust tail, a Monte Carlo model was developed. We trace the trajectories of about 10 7 sample grains to construct the detailed brightness distribution in the comet tail. The simulated isophote field and the observed one agree very well. In our model we also take into account the heliocentric dependence of the dust production rate and ejection velocity, and the dust ejection anisotropy. To transform the particle population to brightness in the modelled tail we calculate the scattering cross section of a separate particle using Mie theory. The age, ejection velocity, dust size distribution, minimum and maximum size of the involved dust particles have been derived from the model giving the best fit. The intensity map is in agreement with a flow of the slowly travelling icy grains. It has been determined that the age of the dust tail of comet C/1999 J2 (Skiff) was, at the moment of the observations, about 540 days and that the main reason for its appearance is likely phase transition from amorphous to crystalline water ice activated at the heliocentric distance of 8.6 AU.

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A restricted three-body problem for a dust particle, in presence of a spherical cometary nucleus in an eccentric (elliptic, parabolic or hyperbolic) orbit about the Sun, is considered. The force of radiation pressure and the PoyntingRobertson effect are taken into account. The differential equations of the particle's non-inertial spatial motion are investigated both analytically and numerically. With the help of a complex representation, a new single equation of the motion is obtained. Conversion of the equations of motion system into a single equation allows the derivation of simple expressions similar to the integral of energy and integrals of areas. The derived expressions are named quasiintegrals. Relative values of terms of the energy quasiintegral for a smallest, largest, and a mean comet are calculated. We have found that in a number of cases the quasiintegrals are related to the regular integrals of motion, and discuss how the quasiintegrals may be applied to find some significant constraints on the motion of a body of infinitesimal mass.