Cloud coverage aspects of the albedo effect

We discuss some details of the cloud coverage aspects of the albedo effect — the pressure of the radiation reflected by the Earth — on the motion of an artificial satellite. We focus on modeling of the Earth's surface reflection and propagation of the radiation through the atmosphere. We adopt analytical models of these phenomena from radiative transfer theory, in contrast to earlier approaches, based on the fitting of satellite photometry data. We perform several computations based on the accepted models for the ERS-1 and MACEK satellites to test the hierarchy of importance of the effects investigated. In the case of the MACEK mission (which carried a precision accelerometer on board) this information might be essential when interpreting the data.     

A new treatment of the albedo radiation pressure in the case of a uniform albedo and of a spherical satellite

The purpose of this paper is to present a model for the radiation pressure acceleration of a spherical satellite, due to the radiation reflected by a planet with a uniform albedo. A particular choice of variables allows one to reduce the surface integrals over the lit portion of the planet visible to the satellite to one-dimensional integrals. Exact analytical expressions are found for the integrals corresponding to the case where the spacecraft does not "see" the terminator. The other integrals can be computed either numerically, or analytically in an approximate form. The results are compared with those of Lochry (1966). The model is applied to Magellan, a spacecraft orbiting Venus.     

On some new aspects of the photo-gravitational Copenhagen problem

We deal with some new aspects of the photo-gravitational Copenhagen case of the restricted three-body problem; more particularly, the distribution and the attracting domains of the stationary solutions of small particles that move in the neighborhood of two major bodies with equal masses when one or both primaries are radiation sources with constant luminosity. Under these conditions, each particle is subjected not only to gravitational forces but to the radiation emitted from the primaries as well.     

On the albedo of the interplanetary dust

The zodiacal light brightness and measured spatial density of the interplanetary dust lead to a mean geometric albedo of 0.24 for the dust particles near 1 AU; whereas the composition of collected micrometeroids suggests a geometric albedo ?0.1. The data do not support the very low albedo (?0.01) proposed by A. F. Cook [Icarus33 (1978), 349–360]. The evidence is against a change in the mean particle albedo between 0.1 and 2 AU. Beyond 2 AU the data are unclear and a change in albedo is not ruled out.     

On some group-theoretical aspects of the study of non-radial oscillations

Group-theoretical techniques are used for the analysis of non-radial oscillations of spherical stars, for the classification and the study of the splitting of the modes under the influence of rotation, tides and magnetic fields, as well as for ellipsoidal configurations. The general conclusions are compared with the analytical and numerical results which have up to now been worked out only for artificial models.     

On some transonic aspects of general relativistic spherical accretion on to Schwarzschild black holes

The equations governing general relativistic, spherically symmetric, hydrodynamic accretion of polytropic fluid on to black holes are solved in the Schwarzschild metric to investigate some of the transonic properties of the flow. Only stationary solutions are discussed. For such accretion, it has been shown that real physical sonic points may form even for flow with   γ <4/3  or   γ >5/3  . The behaviour of some flow variables in the close vicinity of the event horizon is studied as a function of specific energy and the polytropic index of the flow.     

First-order theory of satellite attitude motion application to HIPPARCOS

This work aims at finding an analytic solution corresponding to the attitude evolution in space of a satellite submitted to disturbing torques. This paper presents a basic frame applicable to any perturbed rotation satellite, and a method of resolution leading to a formal solution which is given here to the first order. Thus, the main problem is the slow rotation of a body with three unequal axes of inertia, essentially submitted to a dominant solar radiation pressure torque, with the axis pointing far away from a position of equilibrium. The comparison of the results with a numerical integration based upon a HIPPARCOS model is convincing.     

On the artificial satellite theory

Some of the basic ideas of an analytical orbiter theory which is being developed by Hubert Claes in Namur are presented.The theory is based on the Lie transform technique and will be expressed in a closed form up to second order. The inclusion of additional terms of the third order (expanded in power series of the eccentricity) will be considered.Special attention is being given to the choice of the elements and to the final form of the theory. Three main criteria are used. The removal of the virtual singularities of small inclination and eccentricity. The simplicity of the final form of the theory once the elements have been given their numerical values. The numerical stability of the evaluation of the theory.     

On the effects of a sudden change in the albedo of the Earth

Acquisition by the upper atmosphere of some 10¹⁴ gm of cometary dust would have major implications on the Earth's climate. Pluvial activity would increase dramatically as temperature differences between sea and land widened. Global distribution of precipitation would be controlled by the density of the dust in the atmosphere; for a partially reflective blanket, a fraction of solar energy would still reach ground level creating new climatic zones. The totally undecomposed state of the interiors of Siberian Mammoths and the curious distribution, often uphill, of erratic boulders point to unbelievably sudden and severe conditions at the onset and possibly end of a glacial period. We suggest that a reflective blanket of particles could produce such conditions.     

On the effect of the eccentricity of a planetary orbit on the stability of satellite orbits

The effect of the eccentricity of a planet’s orbit on the stability of the orbits of its satellites is studied. The model used is the elliptic Hill case of the planar restricted three-body problem. The linear stability of all the known families of periodic orbits of the problem is computed. No stable orbits are found, the majority of them possessing one or two pairs of real eigenvalues of the monodromy matrix, while a part of a family with complex instability is found. Two families of periodic orbits, bifurcating from the Lagrangian points L₁, L₂ of the corresponding circular case are found analytically. These orbits are very unstable and the determination of their stability coefficients is not accurate, so we compute the largest Liapunov exponent in their vicinity. In all cases these exponents are positive, indicating the existence of chaotic motions     

Qualitative features of the evolution of some polar satellite orbits

Two special cases of the problem of the secular perturbations in the orbital elements of a satellite with a negligible mass produced by the joint influence of the oblateness of the central planet and the attraction by its most massive (or main) satellites and the Sun are considered. These cases are among the integrable ones in the general nonintegrable evolution problem. The first case is realized when the plane of the satellite orbit and the rotation axis of the planet lie in its orbital plane. The second case is realized when the plane of the satellite orbit is orthogonal to the line of intersection between the equatorial and orbital planes of the planet. The corresponding particular solutions correspond to those polar satellite orbits for which the main qualitative features of the evolution of the eccentricity and pericenter argument are described here. Families of integral curves have been constructed in the phase plane of these elements for the satellite systems of Jupiter, Saturn, and Uranus.     

On the perturbations of a close-Earth satellite due to lunar inequalities

The lunar disturbing function for a close-Earth satellite is expressed as a sum of products of harmonics of the satellite's position and harmonics of the Moon's position, and the latter are expanded about a rotating and precessing elliptic orbit inclined to the ecliptic. The deviations of the Moon from this approximate orbit are computed from Brown's lunar theory andthe perturbations in satellite orbital elements due to these inequalities are derived. Numerical calculations indicate that several perturbations in the position of the satellite's node and perigee have magnitudes on the order of one meter.The author is supported in part by a National Science Foundation Graduate Fellowship.     

Out-of-plane equilibrium points in the elliptic restricted three-body problem under albedo effect

The aim of this research is to show the significant effects of albedo on the existence of out-of-plane equilibria in the elliptic restricted three-body problem under an oblate primary model. We computed out-of-plane equilibria numerically and graphically for different values of the parameters μ, α, e, k and σ where μ, α, e, k and σ are mass parameter, albedo factor, eccentricity, ratio of the luminosity of smaller primary to luminosity of bigger primary considered as constant and oblateness factor due to smaller primary, respectively. Further, we examined the stability of out-of-plane equilibria and found that these equilibria are unstable in linear sense for all parameters μ, α, e, k and σ. Finally, the three-dimensional periodic orbits are analyzed for different values of albedo factor α and oblateness factor σ.     

Formation of satellite and ring systems: Comparatve aspects

There are four systems of a massive central body with a regularily structured satellite system in the Solar system: the planetary system and the satellite systems of Jupiter, Saturn and Uranus. Comparable structures in these four systems can be understood as indications for comparable processes of origin and formation. It is the aim of this paper to describe comparable properties, and to discuss possible physical processes in pre-satellite disks which can be the cause for this comparability.     

Observation and analysis of some recent Galilean satellite phenomena

Five well observed recent mutual phenomena (1 occultation, 4 eclipses) of the Galilean satellites have been analysed and four fitting parameters determined for each event.The times of mid-minima are well determined in all cases (generally to within a second or two), but the separation and velocity parameters depend on the penumbral illumination modelling. For this reason, parameters derived from eclipses are somewhat less well determined than from occultations.Taken together with the dependence on the inherent surface reflection properties of the rearward satellite, the results indicate that Asknes et al.'s (1984) suggestion of order 0.01 arcsec accuracies on positional determinations from mutual phenomena data represents rather a lower limit to the real errors in most cases.     

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.