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A two-dimensional earthquake model that consists of a single block resting upon a slowly moving rough surface and connected by two springs to rigid supports is studied. Depending on the elastic anisotropy and the friction force three…
The three-body problem, which describes three masses interacting through Newtonian gravity without any restrictions imposed on the initial positions and velocities of these masses, has attracted the attention of many scientists for more…
One of the most remarkable instability zones in the Solar system are Kirkwood gaps in the asteroid belt. In this paper we analyze instabilities in the famous Kirkwood gap $3:1$ in the regime of small eccentricity of Jupiter. Mathematically…
An essential role in the asteroidal dynamics is played by the mean motion resonances. Two-body planet-asteroid resonances are widely known, due to the Kirkwood gaps. Besides, so-called three-body mean motion resonances exist, in which an…
More than 10% of extra-solar planets (EPs) orbit in a binary or multiple stellar system. We investigated the motion of planets revolving in binary systems in the frame of the particular case of the three body problem. We carried out an…
We investigate the multiple bifurcations in periodic orbit families in the potential field of a highly irregular-shaped celestial body. Topological cases of periodic orbits and four kinds of basic bifurcations in periodic orbit families are…
A method for determining the orbital parameters of interacting pairs of galaxies is presented and evaluated using artificial data. The method consists of a genetic algorithm which can search efficiently through the very large space of…
The orbital distributions of dust particles in interplanetary space are inferred from several meteoroid data sets under the constraints imposed by the orbital evolution of the particles due to the planetary gravity and Poynting-Robertson…
This paper presents synthetic observations of long-lived, coorbiting asteroids of Mercury, Venus, the Earth and Mars. Our sample is constructed by taking the limiting semimajor axes, differential longitudes and inclinations for long-lived…
The restricted three-body problem describes the motion of a massless particle under the influence of two primaries of masses $1-\mu$ and $\mu$ that circle each other with period equal to $2\pi$. For small $\mu$, a resonant periodic motion…
The richness of dynamical behavior exhibited by the rotational states of various solar system objects has driven significant advances in the theoretical understanding of their evolutionary histories. An important factor that determines…
A considerable amount of information regarding the processes that occurred during the accretion of the early planetesimals is still present among the small bodies of our solar system. A review of our current knowledge of the density of…
We investigate the problem of determining the shape of a rotating celestial object - e.g., a comet or an asteroid - under its own gravitational field. More specifically, we consider an object symmetric with respect to one axis - such as a…
It is well established that certain detached eclipsing binary stars exhibit apsidal motions whose value is in disagreement with with calculated deviations from Keplerian motion based on tidal effects and the general theory of relativity.…
A novel approach for solving equations of motion of finite-sized satellite supposed to be moving in a proximity and around the planet in the elliptic restricted three-body problem, ER3BP is presented in this semi-analytical investigation.…
The origin of Mars's small moons, Phobos and Deimos, remains unknown. They are typically thought either to be captured asteroids or to have accreted from a debris disk produced by a giant impact. Here, we present an alternative scenario…
A three-dimensional dynamical model for a galaxy hosting a BL Lacertae object is constructed. The model consists of a logarithmic potential representing an elliptical host galaxy with a bulge of radius $c_b$ and a dense massive nucleus.…
Gaia Data Release 3 contains accurate photometric observations of more than 150,000 asteroids covering a time interval of 34 months. With a total of about 3,000,000 measurements, a typical number of observations per asteroid ranges from a…
An asteroid pair consists of two unbound objects with almost identical heliocentric orbital elements that were formed when a single "rubble pile" asteroid failed to remain bound against an increasing rotation rate. Models suggest that the…
The population of known minor bodies in retrograde orbits ($i > 90 ^{\circ}$) that are classified as asteroids is still growing. The aim of our study was to estimate the dynamical lifetimes of these bodies by use of the latest observational…