We concentrate on the traditional model of capture from the Oort Cloud. We improve the method of calculation of captured comet populations by combining large numbers of accurate orbit calculations with Monte Carlo methods. As a first step in the development of a Monte Carlo code we calculate accurate probabilities for changes of orbit in a single planet-comet encounter. These will be later used to study the orbital evolution of the Oort Cloud comets when multiple encounters take place.

We argue that Hyperion may act as a reasonably effective source of dust in the Saturnian system. Hypervelocity impacts of interplanetary grains and of dust particles from the outermost moon Phoebe should produce impact ejecta from Hyperion’s surface, an appreciable share of which would escape into the planetocentric orbits. Though the particles would initially be locked in a strong 4:3 mean motion resonance with Titan so that encounters with this satellite would be prohibited, the solar radiation pressure and especially plasma drag force destroy the resonant locking. Once the resonance is broken, the orbits become unstable and experience multiple close approaches to Titan. Using numerical integrations, we performed a statistical study of the grain trajectories and found that most of the grains larger than ~ 5 μm will finally collide with Titan, smaller particles down to ~ 1 μm will escape out of the system, and still smaller (submicrometer) particles will rapidly collide with Saturn. First order estimates of the dust influx to Titan are also made; they show that the upper limit of the income rate of the Hyperion particles is comparable with the direct influx of interplanetary grains.

We compare the two current representations (TASS and that of Harper and Taylor) of the motion of Mimas, Enceladus, Tethys, Dione, Rhea, Titan, Hyperion and Japetus. Although both theories produce almost the same (o-c) residuals with the available observations, we show that they may give positions significantly different at dates corresponding to a gap in the distribution of these observations. In the interval 2000–2020 (corresponding to the CASSINI mission) these differences can reach 5000 km for Mimas, 8000km for Hyperion, 6 000 km for Japetus. So, to test a theory of motions it is necessary to use other criteria among which the most important ones are its dynamical consistency and its internal accuracy.

Clementine II is a Department of Defense (DoD) and industry interplanetary mission designed to flyby several asteroids and release science probes that will impact these asteroids. Candidate asteroids were identified and a nominal and backup mission was chosen from these candidates. The mission design is discussed and the baseline encounters are presented. A backup mission is briefly described. A mass breakdown for the baseline mission is provided as well as the proposed mission sensors. The final encounter approach B-Plane errors are determined and analyzed. A final summary of the Clementine II mission is presented.

We consider initial determination of asteroid orbits in the case of small numbers of observations and short observational arcs. For asteroids having long arcs, we can assess the orbital uncertainties with the help of the covariance matrix that, in the phase space of the orbital elements, defines a set of probability ellipsoids. In initial orbit determination, because of the nonlinear characteristics and multiple solutions of the inversion problem, we cannot readily use the covariance matrix to estimate the orbital uncertainties. However, by computing the eigenvalues and eigenvectors of the formal correlation matrix (that is, by deriving the eigenorbits), we can discern the most indeterminate orbital elements. Here we solve the eigenproblem for 17 single-apparition asteroids.

The orbits of 6807 numbered minor planets on the time interval 1975–2010 have been integrated. The possibility of determining masses for asteroids with close encounters with each other has been investigated, including several kinds of situations. The importance of the observational time arc, as well as the distribution of observations, for determining the masses are shown. The mass of asteroid (24) Themis from its perturbations on asteroid (2296) Kugultinov, and the mass of (10) Hygiea from its perturbations on (1259) Ógyalla have been determined.

Lunar motion serves for a number of important tests of the relativity theory. Although the final quantitative results come out from the direct numerical treatment of the lunar laser ranging data, the analytical solutions yield important keys for understanding sensitivity of the lunar motion on diverse effects. In the last few years, important relativistic phenomena, notably the equivalence principle violation and the preferred direction effects, have been reexamined using detailed Hill-Brown type theories. Surprising amplification of the former effect, indicated also from the numerical tests, has been explained by intricate coupling with the tidal deformation of the lunar orbit. Similar treatment proved that the lunar motion hides potentially a high-quality test of the preferred frame effects. In both cases, fundamental resonances of the problem cause singular amplification of the effects for particular lunar-like orbits.

The capture of the Moon represents a very unique event in the history of the solar system (Singer, 1968; Goldreich et al., 1975; Goldreich, 1966). The Moon formed separately in a heliocentrical orbit similar to the Earth’s and was later captured by the Earth. The capture of the Moon defines also a severe heating event where the Earth’s kinetic energy of rotation is largely dissipated by the mechanism of tidal friction.

A corrected tidal theory (Singer, 1977) leads to a dramatically different result of MacDonald’s theory (MacDonald, 1964) suggesting lunar capture from a prograde orbit.

Information about the structure of lunar interior and evolution could be obtained from measurements of lunar free librations, gravitational field, dissipation etc. In this paper the precision of determining free librations from Lunar Laser Ranging (LLR) data are estimated. Using the observing data from four telescopes for eighteen years, the amplitudes and phases of free librations, and ratios of the moments of inertia of the Moon were determined.

Some results of analysis of lunar ranging data of 1969–1995 are presented. A relevant dynamic theory has been constructed by numerical integration of the equations of motion of the major planets and the Moon and of lunar libration equations. To make the dynamical theory completely self-consistent an optional approach is tested in which the equations of Earth rotation are integrated simultaneously. Partial derivatives with respect to estimated parameters are also obtained by numerical integrations of variational equations. Preliminary results of evaluation of a large set of parameters involved in the lunar ranging data are presented.

The present precision of VLBI observations for the Earth rotation, the accuracy of time measurement realised with modern atomic clocks, and the necessity to obtain precise definition of reference systems and links between them, imply that we compute in the near future more accurate ephemerides, based on general relativity theory (GRT), in accordance with the recent IAU resolutions (IAU, 1992). This paper is dedicated to the presentation of semi-analytical integration of the motion of bodies in the Solar system which completes the theories built at the Bureau des Longitudes by (Bretagnon and Francou, 1988), with some applications in the determination of coordinate time scales links.

A brief description of a problem-oriented language SLON for ephemeris and dynamical astronomy and a corresponding programming system ERA is given. In the frame of the system the user has easy access to an embedded universal program package to process high precision positional observations of Solar system bodies as well as of artificial Earth satellites.

The construction of long-term numerical ephemerides of the Sun, major planets and the Moon is based essentially on the high-precision numerical solution of the problem of the motion of these bodies and polynomial representation of the data. The basis of each ephemeris is a mathematical model describing all the main features of the motions of the Sun, major planets, and Moon. Such mathematical model was first formulated for the ephemerides DE/LE and was widely applied with some variations for several national ephemeris construction. The model of the AE95 ephemeris is based on the DE200/LE200 ephemeris mathematical model. Being an ephemeris of a specific character, the AE95 ephemeris is a basis for a special edition “Supplement to the Astronomical Yearbook for 1996–2000”, issued by the Institute of the Theoretical Astronomy (ITA) (Glebova et al., 1995). This ephemeris covering the years 1960–2010 is not a long ephemeris in itself but the main principles of its construction allow one to elaborate the long-term ephemeris on an IBM PC-compatible computer. A high-precision long-term numerical integration of the motion of major bodies of the Solar System demands a choice of convenient variables and a high-precision method of the numerical integration, taking into consideration the specific features of both the problem to be solved and the computer to be utilized.

A numerical theory of motion of the inner planets and Jupiter is presented. The numerical ephemerides were compared with the set of American and Russian radar observations of planets, obtained during 1961–1995 (nearly 60000 observations), together with range measurements of Martian landers Viking-1,-2 and Mariner-9 tracking data.

The main fitted parameters were the elements of Mercury, Venus, Earth, Mars, the Astronomical Unit, the scale corrections to the reference surface of planets and variability of the gravitational constant. The parameters of Mars rotation, coordinates of Viking landers, elements and the mass of Jupiter, the masses of the three asteroids were evaluated from Viking landers observations.

The Navigation Ancillary Information Facility (NAIF) at Caltech’s Jet Propulsion Laboratory, acting under the directions of NASA’s Office of Space Science, has built a data system–named SPICE–to assist scientists in planning and interpreting scientific observations. SPICE provides geometric and some other ancillary information needed to recover the full value of science instrument data, including correlation of individual instrument data sets with data from other instruments on the same or other spacecraft.

The primary SPICE data sets are called “kernels.” One of these kernel types provides ready access to ephemerides of spacecraft, planets, satellites, comets and asteroids. A second kernel type provides a set of data specifying target body size, shape and orientation. These data are currently based primarily on IAU/IAG/-COSPAR models.

The SPICE system includes FORTRAN subroutines needed to read the kernel files and to calculate many common observation geometry parameters. Users integrate these SPICE “Toolkit” subroutines into their own application programs to compute needed information.

The application of CCD photometry to monitoring the light variations of very small asteroids has led to an explosion of data available, and perhaps as importantly, has made it possible to probe fainter, and hence smaller asteroids. In this paper, we review several new results from the analysis of such lightcurve data, much of it taken by the late W. Z. Wisniewski, a native of Poland who studied at Poznan University (Wisniewski et al., 1997).

At the time of the last close pass of the asteroid 4179 Toutatis by the Earth in 1992, it became apparent from radar observations that the asteroid was in a bizarre rotation state, and that the rotation rate was extremely slow. Harris (1994), re-evaluating the work by Burns and Safronov (1973) found that very small and slowly rotating asteroids can have a time scale of damping into a principal-axis rotation state which is long compared to their expected collisional lifetime, or for that matter, the age of the solar system:

We investigate simplified models of flat rotational motion of the coorbital satellites of Saturn, Janus and Epimetheus. We try to verify the hypothesis of chaotic rotation of the moons, caused by gravitational interaction between them. The possibility of parametric resonance in the librations of Janus is also investigated.

Dynamics of the rotational motion of the Earth and Moon is investigated numerically. Very convenient Rodrigues-Hamilton parameters are used for high-precision numerical integration of the rotational motion equations in the post-newtonian approximation over a 400 yr time interval. The results of the numerical solution of the problem are compared with the contemporary analytical theories of the Earth’s and Moon’s rotation. The analytical theory of the Earth’s rotation is composed of the precession theory (Lieske et al., 1977), nutation theory (Souchay and Kinoshita, 1996) and geodesic nutation solution (Fukushima, 1991). The analytical theory of the Moon’s rotation consists of the so-called Cassini relations and the analytical solutions of the lunar physical libration problem (Moons, 1982), (Moons, 1984), (Pešek, 1982). The comparisons reveal residuals both of periodic and systematic character. All the secular and periodic terms representing the behavior of the residuals are interpreted as corrections to the mentioned analytical theories. In particular, the secular rate of the luni-solar inclination of the ecliptic to the equator J2000.0 (–0027, with a mean square error 0000005) is very close to its theoretical value (Williams, 1994).

The study of lunar rotation has attracted considerable interest with the advent of the epoch of exploration of the Solar system by space technology. A series of works on an investigation of the lunar gravitational field carried out with the help of artificial lunar satellites have greatly advanced our possibility for that study. The problem concerning the landing on the lunar surface of spacecraft, and the creation of durable lunar bases, impose heavy demands on the accuracy of theoretical description of orbital and rotational motion of the Moon.

The development of the observational technology with the help of radio-and laser ranging (LLR) provides at the present time measurements of the distance to a given point on the Moon with an accuracy of about 2 cm, probably improved in the future to about 5mm (Banerdt, 1995). By using differential VLBI measurement with extragalactic radio sources angularly near the Moon, it should be possible to obtain routine estimates of angular position of the beacon to 0.1 mas from each observation (Baudry, 1995). Therefore, combining VLBI and LLR techniques will provide a means of achieving new objectives, and that calls for the development of the theories adequate to an accuracy for observations.

A new nutation series for a rigid Earth model was derived from a new and highly accurate tidal potential series. A new second order theory for the nutational amplitudes of rotation-, figure- and angular momentum-axis based on tidal amplitudes is formulated. Amplitudes larger than 0.45μas are taken into account leading to a series with 699 terms. The new series may serve as test of other ones that were recently published in the literature.