The general equilibria of a spinning satellite in a circular orbit

Let a rigid satellite move in a circular orbit about a spherically symmetric central body, taking into account only the main term of the gravitational torque. We shall investigate and find all solutions of the following problem: Let the satellite be permitted to spin about an axis that is fixed in the orbit frame; the satellite need not be symmetric, the spin not uniform, and the spin axis not a principal axis of inertia. The complete discussion of this type of spin reveals that the cases found by Lagrange and by Pringle - and the well-known spin about a principal axis of inertia orthogonal to the orbit plane — are essentially the only ones possible; the only further (degenerate) case is uniform spin of a two-dimensional, not necessarily symmetric satellite about certain axes that are orthogonal to the plane containing the body and to the orbit of the satellite around the central body.     

The orbital dust torus as an enveloping surface of a family of trajectories of isotropically ejected particles

Meteorite impacts onto a small satellite lead to the ejection of a regolith mass, which is much greater than the impactor mass, into cosmic space. Assume that an isotropic ejection with velocities smaller than the maximum possible velocity b took place at the time moment t ₀. Since the orbital periods are unequal, the particle trajectories will densely fill a certain domain D. The same domain will be filled after an explosion of an artificial satellite moving in a high orbit. One to three months later, the node and pericenter longitudes will be distributed over the entire circle and the domain D will become a body of revolution, a topological solid torus. We examine the domain of possible particle motion and its boundary S immediately after the impact event (an unperturbed case) and the same domain under the assumption that the initial longitudes of nodes and pericenters were already a result of considerable changes (a perturbed case). In both cases, we managed to construct the domain D and its boundary S analytically: parametric equations containing only relatively simple functions were obtained for S. The basic topologic and differential-geometric properties of S were studied completely.     

Regular precessions of a gyrostatic satellite in a circular orbit

In the present paper, the regular precessions about the mass center are studied, for a Volterra-type gyrostatic satellite in a circular orbit under a Newtonian force field. All the possible regular precessions are determined.     

Dust torus formed by particles ejected from a celestial body at an arbitrary point of its elliptic orbit

Dust comnplexes make one of the components of the Solar System. The surface shape of a typical dust complex consisting of particles ejected by a celestial body is found analytically, under reasonable assumptions (the main one being the smallness of perturbations). Parametric equations of the surface are obtained. The main properties of the surface are established and studied. Singular points are found, and the topological type of the surface as a whole and in the vicinity of the singular points (one conic points and one constriction) is examined.     

On the true circular orbit of a satellite

The osculating orbit of a planetary satellite moving in the equatorial plane of the central body under the influence of a rotational symmetric perturbation force is elliptical in first order approximation even if the true orbit is always circular. The satellite motion is influenced by a resonance effect due to this perturbing force. An inclined true satellite orbit cannot be circular.     

Dynamical friction on a satellite of a disk galaxy: The circular orbit

In a previous paper, we have studied dynamical friction during a parabolic passage of a companion galaxy past a disk galaxy. This paper continues with the study of satellites in circular orbits around the disk galaxy. Simulations of orbit decay in a self gravitating disk are compared with estimates based on two-body scattering theories; the theories are found to give a satisfactory explanation of the orbital changes. The disk friction is strongly dependent on the sense of rotation of the companion relative to the rotation of the disk galaxy as well as on the amount of mass in a spherical halo. The greatest amount of dynamical friction occurs in direct motion if no spherical halo is present. Then the infall time from the edge of the disk is about one half of the orbital period of the disk edge. A halo twice as massive as the disk increases the infall time four fold. The results of Quinn and Goodman, obtained with a non-self-gravitating method, agree well with our experiments with massive halos (Q ₀ 1.5), but are not usable in a more general case. We give analytic expressions for calculating the disk friction in galaxies of different disk/halo mass ratios.     

Resonant attitude instabilities for a symmetric satellite in a circular orbit

The roll-yaw attitude motion of a spinning symmetric satellite in a circular orbit is investigated with particular emphasis on the behavior near resonance. Resonance in circular orbit occurs if there is a low-order commensurability between the coupled roll-yaw attitude frequencies. For the so-called Delp region where the Hamiltonian describing the linearized attitude oscillations is not positive definite, there can exist, near resonance, a simultaneous growth or decay of the energy of the two normal modes. Two sections of the resonance line ₂=3 ₁ permitting the largest effects are determined and the equations of motion are integrated numerically as a check on the resonance theory. In particular, resonance-induced instabilities are confirmed.     

On the periodic solutions of a rigid dumbbell satellite in a circular orbit

The aim of the present paper is to provide sufficient conditions for the existence of periodic solutions of the perturbed attitude dynamics of a rigid dumbbell satellite in a circular orbit.     

Stability of numerical method as applied to motion in a circular orbit

In this paper we discuss the numerical stability of Cowell's method when applied to the Keplerian circular motion. The critical stepsize h_m is given for the PE, PECE and CE algorithms of various orders. A comparison of our results with others' shows our method to be more precise.     

Motion of a space station. I

In this first part of the work we develop the equations of motion of a triaxial space station in orbit around the oblate Earth. A first order solution of the problem is presented and the method of complete integration of the system is outlined up to second order of approximation. The zero order part of the Hamiltonian includes both the kinetic and potential energy (Earth's Newtonian attraction) of the station, while the motion in the vicinity of a specific configuration is assumed.The solution leads to deviations on the attitude introduced by the oblateness of the Earth. Such attitude is an exact solution of the equations of the station when its center of mass moves in an elliptic Keplerian orbit.The explicit expressions of the complete solution, discussion of other possible effects on the motion and numerical comparisons will be presented in the second part of the work.     

Submillimeter observations from space: A space station submillimeter facility (SSSF)

There are many important scientific problems to be attacked in the submillimeter wavelength region including the astrophysics of star formation, the dynamics of protoplanetary systems, the physics of interstellar gas, mass loss from stars, supernovae, the chemical evolution of galaxies, the star formation rates in galaxies, the astrophysics of active galactic nuclei, the deuterium abundance in different astrophysical environments, and the distribution of the cosmic background radiation. However, to effectively explore this wavelength range requires going into space since atmospheric absorption precludes most observations from the ground. As in most areas of astronomy, the twin needs for sensitivity and high redsolution indicate use of an imaging interferometer, but the needed baselines of a few tens-of-meters require a large physical structure. The planned Space Station will provide, for the first time, a platform which is large enough to accommodate a forefront submillimeter synthesis instrument. Such a telescope would open an entirely new wavelength regime to astronomy with the attendant possibilities for unexpected new discoveries.A submillimeter array would also be technically well suited for operation on the Space Station. Second-of-are resolution at submillimeter wavelengths requires only relatively short baselines; pointing accuracy and tracking stability requirements are relatively crude being determined by the single dish size rather than the array resolution; radio frequency interference (RFI) susceptibility is very low due to the large frequency separation from normal communications bands; emissions from co-orbiting debris, dust, gas, and water vapour are uncorrelated between interferometer elements; baseline stability requirements, while severe, are less stringent than for optical/IR interferometers and can almost certainly be satisfied for existing phase correction and phaseless image restoration techniques; and the technology for the dishes, mounts, receivers, LO/IF systems, and correlators either exists or is a reasonable extrapolation of what already is available on the ground.We consider the applications and possible design of a Space Station based submillimeter array which could be mounted along the main (Y) axis of the Space Station and use orbital revolution and precession to produce high-resolution synthesis mapping in much the same way ground-based linear arrays do by Earth rotation synthesis.     

Concept development for a space solar power station

This paper introduces a concept for the development of a space solar power station, starting from the manufacture of a photoemissive panel to the creation of a prototype of an industrial power plant. Balloon systems play a special role both in the testing of the power plant and in the operation of prototypes of solar power stations.     

Distributions of boulders ejected from lunar craters

We investigate the spatial distributions of boulders ejected from 18 lunar impact craters that are hundreds of meters in diameter. To accomplish this goal, we measured the diameters of 13,955 ejected boulders and the distance of each boulder from the crater center. Using the boulder distances, we calculated ejection velocities for the boulders. We compare these data with previously published data on larger craters and use this information to determine how boulder ejection velocity scales with crater diameter. We also measured regolith depths in the areas surrounding many of the craters, for comparison with the boulder distributions. These results contribute to understanding boulder ejection velocities, to determining whether there is a relationship between the quantity of ejected boulders and lunar regolith depths, and to understanding the distributions of secondary craters in the Solar System. Understanding distributions of blocky ejecta is an important consideration for landing site selection on both the Moon and Mars.     

Approximate solutions of non-linear circular orbit relative motion in curvilinear coordinates

A compact, time-explicit, approximate solution of the highly non-linear relative motion in curvilinear coordinates is provided under the assumption of circular orbit for the chief spacecraft. The rather compact, three-dimensional solution is obtained by algebraic manipulation of the individual Keplerian motions in curvilinear, rather than Cartesian coordinates, and provides analytical expressions for the secular, constant and periodic terms of each coordinate as a function of the initial relative motion conditions or relative orbital elements. Numerical test cases are conducted to show that the approximate solution can be effectively employed to extend the classical linear Clohessy–Wiltshire solution to include non-linear relative motion without significant loss of accuracy up to a limit of 0.4–0.45 in eccentricity and 40–45\(^\circ \) in relative inclination for the follower. A very simple, quadratic extension of the classical Clohessy–Wiltshire solution in curvilinear coordinates is also presented.     

The distribution of ejected brown dwarfs in clusters

We examine the spatial distribution of brown dwarfs produced by the decay of small‐N stellar systems as expected from the embryo ejection scenario. We model a cluster of several hundred stars grouped into ‘cores’ of a few stars/brown dwarfs. These cores decay, preferentially ejecting their lowest‐mass members. Brown dwarfs are found to have a wider spatial distribution than stars, however once the effects of limited survey areas and unresolved binaries are taken into account it can be difficult to distinguish between clusters with many or no ejections. A large difference between the distributions probably indicates that ejections have occurred, however similar distributions sometimes arise even with ejections. Thus the spatial distribution of brown dwarfs is not necessarily a good discriminator between ejection and non‐ejection scenarios. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The contour of an orbit and a stable periodic orbit

We derive an equation that relates the contour of an orbit and a stable periodic orbit.     

The nature of protons ejected from the nuclei of extragalactic radio sources

We have estimated the proton injection flux from the nuclei of some typical extragalactic radio sources (EGRS). To do so, we have used measured values of radio luminosities from these sources and have assumed the proton-proton collision model as a source of relativistic electrons which give rise to radio emission. The estimated values of the proton flux is in fairly good agreement with theoretical estimates of cosmic-ray fluxes within the same range of energy. This lends support to the fact that the nuclei of EGRSs might be the site for the generation of primary cosmic rays.