We advertise a new method of preliminary orbit determination for space debris using radar observations, which we call Infang†. We can perform a linkage of two sets of four observations collected at close times. The context is characterized by the accuracy of the range ρ, whereas the right ascension α and the declination δ are much more inaccurate due to observational errors. This method can correct α, δ, assuming the exact knowledge of the range ρ. Considering no perturbations from the J2 effect, but including errors in the observations, we can compare the new method, the classical method of Gibbs, and the more recent Keplerian integrals method. The development of Infang is still on-going and will be further improved and tested.

We propose a strategy to attack the problems of orbit determination arising from the large number of short arcs. The method uses a solution of the linkage problem depending on the first integrals of the Keplerian motion.

Yarkovsky-Radzievskij effect exceeds the Poynting-Robertson effect in the perturbing action on particles larger than 100 μm. We obtained formulae for averaged changes in a meteoroid's Keplerian orbital elements and used them to estimate dispersion in the Geminid meteoroid stream. It was found that dispersion in semi-major axis of the model shower increased nearly three times on condition that meteoroids rotation is fast, and the rotation axis is stable.

The entry of small celestial bodies such as cometary nuclei, asteroids and their large fragments, into a planetary atmosphere is accompanied by an “explosion”, i.e., sudden rise in brightness and the generation of a “blast” shock wave, like the 2013 Chelyabinsk event. Fully analytic approach to the phenomenon is developed taking into account aerodynamic crushing of the body and transversal expansion of the crushed mass, that leads to impulse generation of hot plasma and a “blast” shock wave in the thin “exploding” layer.

Close encounters of Near Earth Objects (NEOs) with large asteroids are a possible source of systematic errors in trajectory propagations and asteroid mitigation. It is, thus, necessary to identify those large asteroids that have to be considered as perturbers in NEO orbit modeling. Using the Standard Dynamical Model we searched for encounters between the 1649 numbered Near Earth Asteroids (NEAs) and 2191 large asteroids having sizes greater than 20 km. Investigating the 21st century A. D. we have found 791 close encounters with 195 different large asteroids that lead to a substantial scattering of NEOs.

Two methods are briefly stated for finding the preliminary orbit of a small celestial body from its three or more pairs of angular measurements and the corresponding time instants. The methods are based on using the approach that we previously developed for constructing the intermediate orbit from a minimum number of observations. This intermediate orbit allows for most of the perturbations in the motion of the body under study. The methods proposed use the Herget's algorithmic scheme that makes it possible to involve additional observations as well. Using the determination of orbits of some asteroids as examples, we compare the results obtained by applying the Herget multiple-observation algorithm and the proposed methods. The comparison shows that the proposed methods are an efficient means for studying perturbed motion. They are especially advantageous if applied to high-precision observational data covering short orbital arcs.

Both analytical and numerical results are used to study high-order resonance regions in the vicinity of Molnya-type orbits. Based on data of numerical simulations, long-term orbital evolution are studied for objects in highly elliptical orbits depending on their area-to-mass ratio. The Poynting–Robertson effect causes a secular decrease in the semi-major axis of a spherically symmetrical satellite. Under the Poynting–Robertson effect, objects pass through the regions of high-order resonances. The Poynting–Robertson effect and secular perturbations of the semi-major axis lead to the formation of weak stochastic trajectories.

Planar motions of a triangular body and a massive point under the action of mutual Newtonian attraction are studied. For the first formulation the triangle is assumed to be composed of three massive points. For the second formulation it is constructed with three homogeneous rods. Some partial solutions are observed within the analysis of the geometry of mass distribution.

The investigation is motivated by the problem of motion of spacecrafts near asteroid-like celestial objects possessing irregular mass distribution. Comparison of dynamical effects for two types of mass distribution is another goal of the research.

Problems appearing because of irregularities in mass distributions have been known for a long time. Certain approaches to the description of motions under attraction as well as qualitative particulars of dynamics are discussed by Demin (1963), Burov & Karapetyan (1995), Buchin & Burov & Troger (2008), Burov & Guerman & Sulikashvili (2010), Kholshevnikov & Kuznetsov (2011), Beletsky & Rodnikov (2011) and Scheeres (2012).

In the circular case of the coplanar Restricted Three-body Problem, we studied how the family of quasi-satellite (QS) periodic orbits allows to define an associated libration center. Using the averaged problem, we highlighted a validity limit of this one: for QS orbits with low eccentricities, the averaged problem does not correspond to the real problem. We do the same procedure to L3, L4 and L5 emerging periodic orbits families and remarked that for very high eccentricities ${\cal F}_{L_4}$ and ${\cal F}_{L_5}$ merge with ${\cal F}_{L_3}$ which bifurcates to a stable family.

To study an asteroid family it is crucial to determine reliably the list of its members, i.e. to reduce the number of interlopers as much as possible. However, as the number of known asteroids increases fast it becomes more and more difficult to obtain robust list of members of an asteroid family. To cope with these challenges we are proposing a new approach that may help to significantly reduce presence of interlopers among the family members.

A set of 29 low order secular resonance relations in the near-Earth satellite dynamics has been obtained and their influence on dynamic evolution of objects has been investigated on time intervals of 100 years. The analysis of the results shows that secular resonances are very common phenomena in the near-Earth orbital space. Sharp resonances are concentrated in the orbital space areas where the semi-major axes a ⩾ 20000 km and the inclinations i ⩾ 50○. In some areas objects have several secular resonances. The superposition of several secular resonances or orbital and secular resonances are the source of randomness in the motion of objects.

The problem of the origin of asteroids residing in the Jovian first-order mean motion resonances is still open. Is the observed population survivors of a much larger population formed in the resonance in primordial times? Here, we study the evolution of 182 long-lived asteroids in the 2:1 Mean Motion Resonance, identified in Brož & Vokrouhlické (2008). We numerically integrate their trajectories in two different dynamical models of the solar system: (a) accounting for the gravitational effects of the four giant planets (i.e. 4-pl) and (b) adding the terrestrial planets from Venus to Mars (i.e. 7-pl). We also include an approximate treatment of the Yarkovksy effect (as in Tsiganis et al.2003), assuming appropriate values for the asteroid diameters.

In recent years, a rare class of asteroids has been discovered by Cellino et al. (2006), with its distinguishing characteristic being the anomalous polarimetric properties of its members. Named Barbarians, after (234) Barbara, the prototype of the class, these asteroids show negative polarization at unusually high phase-angles compared to normal asteroids. Motivated by the fact that some of the few discovered Barbarians seemed to be related to the Watsonia asteroid family, Cellino et al. (2014) performed a search for more Barbarians among its members. A positive result of this search led to the conclusion that Watsonia is indeed an important repository of Barbarian asteroids. Based on these findings, we decided to analyze this family in detail.

Satellite systems are often seen as mini-planetary systems, and they are as various and complex. The Earth has one single satellite of more than one percent of its own mass, but the giant planets have many, some of them tiny. They constitute fascinating, interacting, evolving, and dynamically complex systems. While irregular satellites, having inclined and eccentric orbits, are supposed to be captured, it was generally admitted that regular satellites, having circular orbits in the equatorial plane of their host planet, formed in the gas and dust circum-planetary disk that surrounded giant planets at the time of their formation, more or less similarly as planets formed in the proto-planetary disk around their host star. Here, we propose an alternative mechanism for the formation of regular satellites: the spreading of a dynamically cold disk of solids beyond the Roche radius of a planet.

The Roche radius is defined as the distance from a planet beyond which self-gravity is stronger than tidal forces, allowing gravitationally bound aggregates to form, and satellites to exist. Saturn's rings are inside the Roche radius, which is why they don't coalesce into one single object. However, like any astrophysical disk in Keplerian rotation, they spread. Once material reaches the Roche limit, it should accrete into moonlets. These moonlets migrate outwards, repelled by tidal interactions with the rings and Saturn. We showed with numerical simulations that the small and mid-sized moons of Saturn formed this way, which explains their young age and composition (Charnoz et al.2010, 2011). Analytical calculations show that the formation of satellites from a ring of solids spreading beyond the Roche limit takes place in 2 phases: (i) the continuous regime, in which only one satellite forms (this regime prevailed for the moon-forming disk around the Earth); (ii) the pyramidal regime, in which a series of moons form, migrate outwards, merge. . . In this regime, the satellites should follow a precise mass-distance relation, which matches that of the Saturnian system, confirming that it formed this way. It also fits the Uranian and Neptunian systems, suggesting that these planets used to have massive rings that gave birth to their regular satellites, and vanished (Crida & Charnoz (2012)).

Refinements of this model, applications to planetary systems, and a recent likely observation of this process will be discussed in conclusion.

The presence of a co-orbital companion induces the splitting of the well known Keplerian spin-orbit resonances. It leads to chaotic rotation when those resonances overlap.

In this work we discuss the elusive Kordylewski clouds – dust matter in the neighborhood of the Lagrange libration points L4, L5 of the Earth-Moon system. On the base of restricted planar circular four body problem we get some proof for possibility of existence of four such clouds and some rule to predict the optimal moments of time for their observation.

The “Grand Tack” model proposes that the inner Solar System was sculpted by the giant planets' orbital migration in the gaseous protoplanetary disk. Jupiter first migrated inward then Jupiter and Saturn migrated back outward together. If Jupiter's turnaround or “tack” point was at ~ 1.5 AU the inner disk of terrestrial building blocks would have been truncated at ~ 1 AU, naturally producing the terrestrial planets' masses and spacing. During the gas giants' migration the asteroid belt is severely depleted but repopulated by distinct planetesimal reservoirs that can be associated with the present-day S and C types. The giant planets' orbits are consistent with the later evolution of the outer Solar System.

Here we confront common criticisms of the Grand Tack model. We show that some uncertainties remain regarding the Tack mechanism itself; the most critical unknown is the timing and rate of gas accretion onto Saturn and Jupiter. Current isotopic and compositional measurements of Solar System bodies – including the D/H ratios of Saturn's satellites – do not refute the model. We discuss how alternate models for the formation of the terrestrial planets each suffer from an internal inconsistency and/or place a strong and very specific requirement on the properties of the protoplanetary disk.

We conclude that the Grand Tack model remains viable and consistent with our current understanding of planet formation. Nonetheless, we encourage additional tests of the Grand Tack as well as the construction of alternate models.

In the standard model of core accretion, the cores of the giant planets form by the accretion of planetesimals. In this scenario, the evolution of the planetesimal population plays an important role in the formation of massive cores. Recently, we studied the role of planetesimal fragmentation in the in situ formation of a giant planet. However, the exchange of angular momentum between the planet and the gaseous disk causes the migration of the planet in the disk. In this new work, we incorporate the migration of the planet and study the role of planet migration in the formation of a massive core when the population of planetesimals evolves by planet accretion, migration, and fragmentation.

Growth barriers, including the bouncing, fragmentation and radial drift problems, are still a big issue in planetesimal and thus planet formation theory. We present a new mechanism for very rapid planetesimal formation by sweep-up growth. Planetesimal formation is extremely fast in the inner protoplanetary disk where the growth rate exceeds the radial drift rate, leading to local planetesimal formation and pile-up inside of 1 AU. This scenario is very appealing particularly in the context of explaining the low mass of Mars, as well as the formation of recently discovered multi-transiting systems with tightly-packed inner planets.

We develop numerical tools to detect and quantify the mass and area for all structures of a protoplanetary disk with different optical depths. We consider two planets of 0.1 MJ. They are initially at 12.5 and 20 AU embedded in a viscous disk, where planetary mass accretion and migration are allowed. We find a gap region with optically thick streams, this region is characterized by an optically thin filling factor near to 1. Additionally, we generate the Spectral Energy Distribution of each structure of the disk considering silicate dust. Our tools are useful to identify the locations of structures and sub-structures as possible sites where the material is accumulated.