Exact solution of a triaxial gyrostat with one rotor

The problem of the attitude dynamics of a triaxial gyrostat under no external torques and one constant internal rotor, is a three degrees-of-freedom system, although thanks to the existence of integrals of motion it can be reduced to only one degree-of-freedom problem. We introduce coordinates to represent the orbits of constant angular momentum as a flow on a sphere. This representation shows that the problem is equivalent to a quadratic Hamiltonian depending on two parameters. We find the exact solution of the orbits in terms of elliptic functions. By making use of properties of elliptic functions we find the solution at each region of the parametric partition from the solution of one region. We also prove that heteroclinic orbits are planar curves.     

On a semi-inverse problem in the motion of gyrostat satellites

In this paper we study the equilibrium orientation of a gyrostat satellite in the gravity field of a point mass. Direct problem is to find all possible equilibrium orientation when the relative angular momentum vector is given. Inverse problem is to find this relative angular momentum in order to obtain equilibrium in a given orientation. Semi-inverse problem is solved here when some parameters (but not all) giving orientation of the satellite are chosen arbitrarily, giving for what choices real solutions occur.     

Dynamics and control of dual-spin gyrostat spacecraft with changing structure

We study the motion of the free dual-spin gyrostat spacecraft that consists of the platform with a triaxial ellipsoid of inertia and the rotor with a small asymmetry with respect to the axis of rotation. The system with perturbations caused by a small asymmetry of the rotor and the time-varying moments of inertia of the rotor is considered. The dimensionless equations of the system are written in Serret–Andoyer canonical variables. The system’s phase space is described. It is shown that changes in the moments of inertia of the gyrostat leads to the deformation of the phase space. The internal torque control law is proposed that keeps the system at the center point in the phase space. The effectiveness of the control is shown through a numerical simulation. It’s shown that the uncontrolled gyrostat can lose its axis orientation. Proposed internal torque keeps the initial angle between the axis of the gyrostat and the total angular momentum vector.     

Translatory-rotatory motion of a gyrostat in a newtonian force field

The paper deals with a system made of two gyrostats attracting one another according to Newton's law. The Hamiltonian is expressed in the modified canonical variables of Delaunay and Serret-Andoyer. After straightforward eliminations and changes of variables, the problem is integrated in a particular case to the first order of perturbation by means of an infinitesimal contact transformation.     

Asteroids with satellites: Analysis of observational data

The volume of observational information on asteroids and trans-Neptunians with satellites has significantly increased in recent years. In this paper we study the dependence of asteroid duplicity on the main physical parameters of the primary: the size and rotation rate. The proportion of binary asteroids is shown to grow rapidly with the rotation rate of the primary. The pattern of dependence between asteroid duplicity and size is more complex, with peaks in the area of small (<10 km) and large (>100 km) bodies. Noteworthy is the small number of binaries among typical-sized asteroids (10–150 km). All the orbits of asteroidal satellites whose rotation direction is known are shown to be prograde and have small eccentricities and inclinations.     

Rotational evolution of a symmetric gyrostat with visco-elastic bars around the center of mass in a circular orbit

The motion of a gyrostat in a circular orbit in a Newtonian field of force is considered. The gyrostat has four homogeneous viscoelastic bars attached to it. Rotation of the symmetric rotor inside the rigid body is statically and dynamically balanced. Bending deformations of the bars, accompanied by dissipation of energy, are the cause of the evolution of the system's rotational motion. Approximate equations describing this evolution are derived, together with averaged equations in Andoyer variables.     

Liapunov stability of spinning satellites with long flexible appendages

The equations of motion are derived for the case of a spinning satellite which has a central rigid body, and long flexible appendages which are nominally in the spin plane. The major-axis theorem is found to be necessary, but not sufficient for this case, and appropriate sufficiency criteria are derived from a Liapunov function. The results are presented in a form amenable to satellite design.     

Long-term motion of resonant satellites with arbitrary eccentricity and inclination

A first-order, semi-analytical method for the long-term motion of resonant satellites is introduced. The method provides long-term solutions, valid for nearly all eccentricities and inclinations, and for all commensurability ratios. The method allows the inclusion of all zonal and tesseral harmonics of a nonspherical planet.We present here an application of the method to a synchronous satellite includingonly theJ ₂ andJ ₂₂ harmonics. Global, long-term solutions for this problem are given for arbitrary values of eccentricity, argument of perigee and inclination.     

Orbital history of the Martian satellites with inferences on their origin

Recent Viking results indicate the Martian satellites are composed of carbonaceous chondritic material, suggesting that Phobos and Deimos were once asteroids captured by Mars. On the other hand, the low eccentricities and inclinations of their orbits on the equator of Mars argue against that hypothesis. This paper presents detailed calculations of the tidal evolution of Phobos and Deimos, considering dissipation in both Mars and its satellites simultaneously and using a new method applicable for any value of the eccentricity. In particular, including precession of the satellites' orbits indicates that they have always remained close to their Laplacian plane, so that the orbital planes of Phobos and Deimos switched from near the Martian orbital plane to the Martian equator once the perturbations due to the planetary oblateness dominated the solar perturbations, as they do presently. The results show that Deimos has been little affected by tides, but several billion (10⁹) years ago, Phobos was in a highly eccentric orbit lying near the common plane of the solar system. This outcome is obtained for very reasonable values of dissipation inside Mars and inside Phobos. Implications for the origin of the Martian satellites are discussed.     

The Kα complex of He-like iron with dielectronic satellites

It is shown that the dielectronic satellites (DES) dominate X-ray spectral formation in the 6.7-keV K α complex of Fe  xxv at temperatures below that of maximum abundance in collisional ionization equilibrium T _m. Owing to their extreme temperature sensitivity, the DES are excellent spectral diagnostics for     in photoionized, collisional or hybrid plasmas; whereas the forbidden, intercombination and resonance lines of Fe  xxv are not. A diagnostic line ratio GD ( T ) is defined including the DES and the lines, with parameters from new relativistic atomic calculations. The DES absorption resonance strengths may be obtained from differential oscillator strengths, possibly to yield the     column densities. The DES contribution to highly ionized Fe should be of interest for models of redward broadening of K α features, ionized accretion discs, accretion flows and K α temporal-temperature variability in AGN.     

Mapping the substructure in the Galactic halo with the next generation of astrometric satellites

We run numerical simulations of the disruption of satellite galaxies in a Galactic potential to build up the entire stellar halo, in order to investigate what the next generation of astrometric satellites will reveal by observing the halo of the Milky Way. We generate artificial DIVA , FAME and GAIA halo catalogues, in which we look for the signatures left by the accreted satellites. We develop a method based on the standard Friends-of-Friends algorithm applied to the space of integrals of motion. We find this simple method can recover about 50 per cent of the different accretion events, when the observational uncertainties expected for GAIA are taken into account, even when the exact form of the Galactic potential is unknown. The recovery rate for DIVA and FAME is much smaller, but these missions, like GAIA , should be able to test the hierarchical formation paradigm on our Galaxy by measuring the amount of halo substructure in the form of nearby kinematically cold streams with, for example, a two-point correlation function in velocity space.     

Prediction of satellites in Earth's gravitational field with axial symmetry using Burdet's regularized theory

In this paper, economical and stable recurrence formulae for the Earth's zonal potential and its gradient for Burdet's regularized theory will be established for any number N of the zonal harmonic coefficients. A general recursive computational algorithm based on these formulae is also established for the initial value problem of Burdet oscillator for the prediction of artificial satellites in the Earth's gravitational field with axial symmetry. Applications of the algorithm for the problem of the final state prediction are illustrated by numerical examples of three test orbits each for two geopotential models corresponding to N = 2 and N = 36.A final state of any desired accuracy is obtained for each case study, a result which shows the flexibility of the algorithm.Dept. of Astronomy, KAU     

A comparison of some observations of the Galilean satellites with Sampson's tables

An analysis is made of two series of photographic observations of the Galilean satellites of Jupiter. In the comparison of theory with observation, the aim of this work is to solve for systematic errors in the observations as well as those in the theory. The observations are those made by D. Pascu with the McCormick refractor during the apparition of 1967–1968 and with the 26" refractor of the U.S. Naval Observatory in 1973. Neutral density filters were used for magnitude compensation between the planet and the satellites as well as between the satellites themselves. Preliminary positions were derived by the trail/scale method using a scale value derived from scale plates taken during the observational program. The mean error of these observations is expected to be about ±0".10. The computed positions are those supplied by the Bureau des Longitudes and are based on Sampson's theory. Both intersatellary and planet-satellite positions were used in the comparison of theory with observation. The least squares adjustment included as unknowns, corrections to the longitudes, inclinations and scale for both observation types, and an additional periodic term to account for residual phase defect for the planet-satellite coordinates. The validity of the results is discussed in terms of the unknowns introduced, the correlations between them and the reduction of the residuals.     

Comparison of Sampson-Lieske theory of the Galilean satellites of Jupiter with observations

The aim of the present work is to compare photographic observations of the Galilean satellites of Jupiter with the theory developed by Sampson at the beginning of the century and corrected and implemented recently by Lieske.The comparisons between the observed and computed values give differences in geocentric angular distances of the order of 0.08 for modern observations (1968 to 1977) and of the order of 0.14 for older ones (1913 to 1928).These results lead to the suggestion that important long period defects still exist in the theory of Sampson-Lieske. This is not surprising, due to the difficulties of the computation of the long-period inequalities in mean longitudes, even in a first-order theory.Proceedings of the Conference on Analytical Methods and Ephemerides: Theory and Observations of the Moon and Planets. Facultés universitaires Notre Dame de la Paix, Namur, Belgium, 28–31 July, 1980     

Astrometric observations of the Uranian satellites with the Faulkes Telescope North in 2007 September

The results of astrometric observations of the main Uranian satellites taken with the Faulkes Telescope North are presented. A median filter algorithm was applied to subtract a scattered-light halo caused by Uranus. The Two-Micron All-Sky Survey (2MASS) and USNO-B1.0 were used as reference catalogues. The mean value of the differences between the equatorial coordinates of the satellites determined with 2MASS and USNO-B1.0 is close to 200 mas. A comparison of the observed equatorial coordinates of the satellites and their relative positions with ephemerides based on different combinations of theories of motion of Uranus and its satellites (DE405+GUST86, DE405+GUST06, INPOP+GUST86, INPOP+GUST06) was performed. The satellites' positions obtained with respect to 2MASS are in better agreement with theories. The values of (O−C) of the equatorial coordinates determined with the 2MASS are mainly less than 100 mas. The majority of (O−C) of relative positions are within ±50 mas. The mean values of the standard errors of (O−C) are within 20 to 60 mas.     

Some particularities in motion of retrograde satellites of Jupiter

Some peculiarities in the motion of retrograde satellites of Jupiter have been investigated. The intermediate orbits were obtained by approximated solution of differential equations before transformation by the Zeipel's method. These orbits are non-keplerian ellipses. For their construction the secular motion of nodes, perijoves, and essential periodic perturbations were taken into account.The eccentricities and inclinations of all the retrograte satellites change in a large range. The motion may happen in a region, which is located very near to the limit cases of our theory. For some satellites the sign of the constant, which characterizes the type of orbit, librating or circular, may change. In some cases the value of this constant may be close to zero. Then the motion of the longitude of perijove will reduce the speed and in some moment the circular orbit may change its direction.     

Astrometric observations of major satellites of Saturn with a 26-inch refractor

The results of observations of Saturn and its satellites with the 26-inch refractor at Pulkovo are presented. Over the observing period from January 2008 until May 2009, results were found from more than 5000 CCD frames suitable for measurement. On the basis of these frames, 183 positions of major satellites of Saturn (with the exception of Mimas) were obtained. The astrometric reduction was based on the Turner method, with the use of the UCAC2 catalog as a reference. The obtained equatorial coordinates of satellites were compared with the TASS 1.7 theory, and results of comparison are presented. The accuracy of observed positions is 0.05″ on average. Positions of Saturn, calculated on the basis of positions of satellites and their theoretical saturnocentric coordinates according to the TASS 1.7, and the differential coordinates of satellites relative to each other, are also given.