Perturbations of a spheroidal satellite due to direct solar radiation pressure

The orbital accelerations of certain balloon satellites exhibit marked oscillations caused by solar radiation impinging on the surface of the satellites, which, once spherical, have assumed a spheroidal shape producing a component of force at right-angles to the Sun-satellite direction. Given the characteristics and orientation of the satellite, the equations of force are determined by the formulae of Lucas. Otherwise the phase-angle and magnitude of the right-angle force are determined by trial and error, or best-fit techniques. Using a variation of the approach developed by Aksnes, a semi-analytical algorithm is presented for evaluating the perturbations of the Keplerian elements by direct solar radiation pressure on a spheroidal satellite. The perturbations are obtained by summing over the sunlit part of each orbit and allow for a linear variation in the phase-angle. The algorithm is used to determine the orbital accelerations of 1963-30D due to direct solar radiation pressure, and these results are compared to the observed values over two separate periods of the satellite's lifetime.     

Perturbations of a close-earth satellite due to sunlight diffusely reflected from the Earth

A semianalytical method has been developed to calculate the radiation-pressure perturbations of a close-Earth satellite due to sunlight reflected from the Earth. It is assumed that the satellite is spherically symmetric and that the solar radiation is reflected from the Earth according to Lambert's Law. To account for the increasing reflectivity of the Earth toward the poles, its albedo is assumed to have a latitudinal dependence given bya=a ₀ +a ₂ sin². The effect of the terminator on the perturbations has been neglected. The perturbations within a particular revolution are given analytically, while the long-range perturbations are obtained by accumulation.     

Approximate Analytical Theory of Satellite Orbit Prediction Presented in Spherical Coordinates Frame

A comparative review of analytic theories for the motion of Earth satellites in quasi-circular orbits written in the spherical coordinate frame is presented. The theory of motion is developed for satellites in quasi-circular and quasi-equatorial orbits subjected to geopotential, luni-solar and solar radiation pressure force perturbations. The intermediate orbit is Keplerian and the equations of motion are solved by the Lyapunov–Poincaré small parameter method. Both resonant and non-resonant cases are considered. The results can be useful for the development of a complete theory of weakly eccentric orbits.     

Perturbations of a close-Earth satellite due to sunlight diffusely reflected from the Earth

A semianalytic method has been developed to calculate the radiation-pressure perturbations of a close-Earth satellite due to sunlight reflected from the Earth. The assumptions made are that the satellite is spherically symmetric and that the solar radiation is reflected from the Earth according to Lambert's Law with uniform albedo. By using expressions for the components of the radiation-pressure force due to Lochry, the expressions for the perturbations of the elements were developed into series in the true anomalyv. The perturbations within a given revolution can be obtained analytically by integrating with respect tov while holding all slowly varying quantities constant. The long-range perturbations are then obtained by accumulating the net perturbations at the end of each revolution.     

The effect of solar radiation pressure on the orbit of a cylindrical satellite

The effect of solar radiation pressure on the orbits of cylindrical satellites is considered. The cylinder is assumed to reflect radiation both specularly and diffusely. The resultant forces on a stationary cylindrical satellite are given. The evolution of the satellite's orbit is described for two particular modes of rotation. In both cases the satellites are assumed to be in circular Sun-synchronous orbits.     

A hybrid mode of diffuse and specular reflector for computation of the emergent radiation by the adding method

A method of computing the diffuse reflection and transmission radiation from an inhomogenous, plane-parallel planetary atmosphere bounded by the hybrid surface of a diffuse and specular reflector is discussed by using the addition method. If the atmosphere is simulated by a number of homogeneous sublayers, the radiation diffusely reflected and transmitted by the atmosphere can be expressed in terms of the diffuse reflection and transmission matrices of radiation of sublayers (Laciset al., 1974; Takashima, 1973, 1975). With this method (Takashima, 1975), the troublesome treatment due to the effect of polarity of radiation is overcome. Moreover, if the surface reflects radiation in accordance with the Lambert law as well as a quite arbitrary phase matrix (Takashima, 1974), the addition method can be easily extended. It is shown in this paper that the addition method is suitable for numerical computation even if the surface reflects light according to the hybrid mode of the diffuse and specular law (Uenoet al., 1974; Mukai, 1976).On leave from the Meterological Research Institute, Tokyo, Japan.     

Multiwavelength focusing with the Sun as gravitational lens

The light deviation caused by the gravitational potential in the vicinity of the sun could be used as a means of focussing radiation that cannot be focussed easily otherwise. The gravitational lens formed by the sun is not stigmatic, but does have the advantage of being achromatic and acts identically on all types of mass-less radiations. For a source at infinity, its geometrical characteristics present a “caustic” line starting at 550 astronomical units (UA) downstream from the sun. In a plane perpendicular to that caustic line, images of distant objects are formed.The perturbations by the solar corona plasma will significantly blur electromagnetic radiation for wavelengths longer than those of the IR domain. At shorter wavelengths, for example the γ domain, the focussing process could lead to 10⁸ amplification factors. In order to reach the regions where images are formed, long distance space missions are necessary. Once launched, missions of this type would be dedicated to a single field. Some possible targets are considered, such as Sagitarius A observed in X and γ rays.In this paper we study the point spread function (PSF) of the sun as a gravitational lens. Taking into account perturbations by the planets, the non sphericity of the sun and coronal plasma index, we derive limits within which such observations could be possible.     

Is Nereid a binary satellite?

If real, Nereid's recently observed large photometric variations (Schaefer and Schaefer, 1988) can be explained by modelling this Neptunian satellite as a quasi-contact binary system made of two similar, ellipsoidal components distorted by their mutual tides. Both the amplitude and the likely periodicity of the observed luminosity changes are consistent with the binary model, provided Nereid's density is close to 1 g cm^–3 (similar to that of most outer solar system satellites). The assumed binary would be probably stable against Neptune's gravitational perturbations, and its origin - as already suggested for a few suspected binary asteroids, like 624 Hektor (Weidenschilling, 1980; Farinella et al., 1982) - could be due to rotational fission following a catastrophic impact. During the Neptune encounter due for August, 1989, Voyager 2's cameras will provide images adequate to confirm, or disprove, the binary model.     

Numerical theory of the motion of Jupiter’s Galilean satellites

A numerical theory of the motion of Jupiter’s Galilean satellites was constructed using 3767 absolute observations of the satellites. The theory was based on the numerical integration of the equations of motion of the satellites. The integration was carried out by Everhart’s method using the ERA software package developed at the Institute of Applied Astronomy (IAA). Perturbations due to the oblateness of the central planet, perturbations from Saturn and the Sun, and the mutual attraction of the satellites were taken into account in the integration. As a result, the coefficients of the Chebyshev series expansion for coordinates and velocities were found for the period from 1962 to 2010. The initial coordinates and velocities of the satellites, as well as their masses, the mass of Jupiter, and the harmonic coefficient J ₂ of the potential of Jupiter, were adjusted. The resulting ephemerides were compared to those of Lieske and Lainey.     

Are plasma satellites present among chromospheric lines?

From a study of the chromospheric lines listed by Pierce (1968, 1973) indications have been found that first-order plasma satellites appear sometimes as a pair of faint chromospheric emission lines in such places where forbidden lines, mainly of metals, should be located. Second-order satellites are indicated sometimes by an asymmetry in the emission wings of stronger lines, either with respect to intensity or with respect to distance from the line centre and, if so, with the remote wing of diffuse shape. Finally diffuse faint lines, appearing in somewhat greater distances from strong chromospheric lines, suggest the appearance sometimes of fourth-order plasma satellites. All the three types of satellites give electron densities of the order of 10¹² cm^?3. Traces of possible absorption satellites are found also for some of the lines in the solar spectrum. In this connection special attention is drawn to a few faint solar lines located near the wavelengths of corona emission lines. The observational evidence is discussed on the bases of recent theoretical research by Drawin and Truong-Bach (1982a, b).     

Reflectance model for densely packed media: Estimates of the surface properties of the high-albedo satellites of Saturn

Interpretation of photometric and polarimetric observations of atmosphereless celestial bodies faces the problems connected with both the insufficient accuracy and level of details in groundbased observations and the current state of the theory of the multiple scattering of light. In application to sparse media, where the electromagnetic waves, propagating between the scatterers, can be considered as spherical (the socalled far-field approximation), this theory is rather well developed for both the diffuse and coherent components of the scattered radiation. In this paper, we show that this theory can be also successfully applied to the measurements of polarization of light scattered by densely packed, though nonabsorbing or weakly absorbing, media. For this purpose, we calculated the models for a semi-infinite layer of the medium composed of randomly oriented clusters of spherical particles and compared them with the data of laboratory and astronomical measurements. The potential of the present approach is illustrated by an example of the interpretation of the polarization measurements of the ice satellites of Saturn—Rhea and Enceladus—which allowed some properties of the surface of these celestial bodies to be estimated. In particular, the ratio of the surface area that makes no contribution to the negative polarization of light reflected at small phase angles to the area producing the negative polarization branch was found. Under the assumption of the same albedo of these areas, this ratio turned out to be 3.31–3.66 and 1.7–3.8 for Rhea and Enceladus, respectively. For Enceladus, it is difficult to obtain a sufficiently narrow range of the estimated parameters, since the number of measurement points in the phase dependence of polarization of this satellite is small. For the surface of Rhea, the estimated packing density of particles, participating in the opposition effects, is approximately 15%, while their smallest size is of the order of the wavelength of visible light.     

Determination of the area and mass distribution of orbital debris fragments

An important factor in modeling the orbital debris environment is the loss rate of debris due to atmospheric drag and luni/solar perturbations. An accurate knowledge of the area-to-mass ratio of debris fragments is required for the calculation of the effect of atmospheric drag. In general, this factor is unknown and assumed values are used. However, this ratio can be calculated for fragments for which changes in the orbital elements due to atmospheric drag as a function of time are known. This is the inverse of the technique used to determine the atmospheric density from the decay of satellites with accurately known area-to-mass ratios. These kinds of propagation programs are routinely used in predicting the decay of an orbiting vehicle. In this work the area-to-mass ratio of about 2600 fragments arising from the breakup of 24 artificial satellites have been determined. An analysis of the data on about 200 objects (rocket bodies, scientific satellites, etc.) with known mass, size, and shape has also been made. The value of the radar cross-section (RCS), as measured by the Eglin radar operating at 70 cm wavelength, has been correlated to the effective area of these objects. The measurements of the area-to-mass ratio of these objects then provide a calibration of the actual to the calculated mass. It has been shown that the debris mean mass, m, is related to the mean effective area, A, by a power law relation, m = k A ^1.86. However, for a given effective area the mass distribution is very broad. Moreover, the cumulative mass distribution, N(>m), can be expressed as N(>m) = D(m + b), where D, b, and c are constants. The asymptotic slope, c, of low intensity explosions is on the average lower than the slope for high intensity explosions, but there is considerable spread of this slope in each class. Part of the flattening, as indicated by the finite value of the parameter, b, can be understood as arising out of the spread in the RCS values due to the tumbling motion of the fragments and effects related to the detectability of the fragment by the Eglin radar. It has been established that the mass in a given breakup calculated using this technique is in good agreement with the expected mass value. These results can be used in modeling the breakups of other artificial earth satellites and safety analysis.     

Thermal force effects on slowly rotating, spherical artificial satellites-I. Solar heating

The heating of a spinning artificial satellite by natural radiation sources such as the Sun and the Earth results in temperature gradients arising across the satellite's surface. The corresponding anisotropic emission of thermal radiation leads to a recoil force, commonly referred to as “thermal force”. A quantitative theory of this effect is developed, based on more general assumptions than used so far, to model such radiation forces on spherically symmetric LAGEOS-like satellites. In particular, the theory holds for any ratio of the three basic timescales of the problem: the rotation period of the satellite, the orbital period around the Earth, and the relaxation time for the thermal processes. Thus, the simplifying assumption of a comparatively fast rotational motion is avoided, which will fail for LAGEOS within the next decade, owing to magnetic dissipation effects. A number of predictions about the future behaviour of non-gravitational long-term orbital perturbations of LAGEOS become possible with the new theory. In particular the Yarkovsky-Schach thermal force effects are studied arising as a consequence of the solar radiation flux onto the satellite, periodically interrupted by eclipses. Starting on about year 2005, the orbital perturbation effects predicted by the new theory are substantially different from those inferred in the fast-rotation case. This holds not only for the long-term semimajor axis effects, but also for eccentricity and inclination perturbations.     

A general model of the planetary radiation pressure on a satellite with a complex shape

The purpose of this paper is to present a general model for the acceleration exerted on a spacecraft by the radiation coming from a planet. Both the solar radiation reflected by the planet and the thermal emission associated with its temperature are considered. The planet albedo and the planet emissive power are expanded in spherical harmonics with respect to an equatorial reference frame attached to the planet. The satellite external surface is assumed to consist of a juxtaposition of planar surfaces. A particular choice of variables allows to reduce the surface integrals over the lit portion of the planet visible to the satellite to one-dimension integrals.     

Effects of high velocities on photoionization lines

We have treated formation of spectral lines in a commoving frame where photoionization is predominant over collisional processes. We have assumed that the radiation field for causing photoionization is a function of Planck function. We have also considered the situation in which the continuum contributes to the radiation in the line. In all the models the quantityB/A (ratio of outer to inner radii) is kept equal to 10 and the total optical depth is taken to be 10³. The velocity is assumed to be varying according to the lawdV/dτ ∼ < 1/τ whereτ is the optical depth (τ > 0) in the given shell. The velocities at the innermost radius (r =A) are set equal to 0 and at the outermost radius (r =B), the maximum velocities are taken to be 0, 1, 3 and 10 Doppler units. The calculated line profiles are those seen by an observer at infinity.P Cygni-type profiles are observed in the case of a medium with no continuum absorption. For a medium with continuum absorption double peaked asymmetric profiles are noticed when the velocities are small; the two emission peaks merge into a single asymmetric peak for larger velocities.     

The effect of surface characteristics on diffuse reflection radiation at λ=0.40 μm

The diffuse radiation in the upward direction at the top and at an internal level of an inhomogeneous atmosphere is computed at =0.40 m. The surface is assumed to reflect light in accordance with a hybrid mode of a diffuse and specular reflector. The objective is to estimate the effect of underlying surface characteristics in terms of the diffuse radiation field. By making use of these results, accuracy in monitoring the atmospheric aerosols would be increased for the use of remote sensing satellite techniques. Junge power lawv ^*=3 is adopted for the size distribution of aerosols (1963), while the data given by McClatchyet al. (1971) is used for the number density of aerosols with height distribution. It is noted from the computations that the diffuse reflection radiation is affected by the surface characteristics, even if the albedo of the surface is a fixed constant and very small.On leave from the Meterological Research Institute, Tokyo, Japan.bl]References     

A spherical model for computing polarized radiation in Titan's atmosphere

The Huygens descent through Titan's atmosphere in January 2005 will provide invaluable information about Titan's atmospheric composition and aerosol properties. The Descent Imager/Spectral Radiometer (DISR) will perform upward and downward looking radiation observations at various spectral ranges and spatial resolutions. To prepare the DISR data interpretation we have developed a new model for radiation transfer in Titan's atmosphere. The model solves for the full three-dimensional polarized radiation field in spherical geometry. However, the atmosphere itself is assumed to be spherically symmetric. The model is initialized with a fast-to-compute plane–parallel solution based on the doubling and adding algorithm that incorporates a spherical correction for the incoming direct solar beam. The full three-dimensional problem is then solved using the characteristics method combined with the Picard iterative approximation as described in Rozanov et al. (J. Quant. Spectrosc. Radiat. Transfer 69 (2001) 491). Aerosol scattering properties are calculated with a new microphysical model. In this formulation, aerosols are assumed to be fractal aggregates and include methane gas absorption embedded into the extinction coefficient. The resulting radiance of the model atmosphere's internal field is presented for two prescribed DISR wavelengths.     

Satellite theory

In this paper dynamical characteristics of satellites are outlined by classifying the satellites into three categories according to the values of the solar tidal factor (n/n)² which is the disturbing factor due to the sun and the oblateness factor of the primary planetJ ₂/a ². For inner satellites (n/n)² is much smaller thanJ ₂/a ² and there are several pairs among them, for which the mean motions are commensurable to each other, and for some of them secular accelerations in the mean longitudes have been detected. For outer satellites (n/n)² is much larger and the solar perturbations are dominant. For intermediary satellites the motion of the pole of the orbital plane is not so simple as those of the satellites of the other categories.     

Radial HI profiles at the periphery of galactic disks: The role of ionizing background radiation

Observations of neutral hydrogen in spiral galaxies reveal a sharp cutoff in the radial density profile at some distance from the center. Using 22 galaxies with known HI distributions as an example, we discuss the question of whether this effect can be associated exclusively with external ionizing radiation, as is commonly assumed. We show that before the surface density reaches δ _HI ≤ 0.5 M _⊙ pc⁻² (the same for galaxies of different types), it is hard to expect the gas to be fully ionized by background radiation. For two of 13 galaxies with a sharp drop in the HI profile, the “steepening” can actually be caused by ionization. At the same time, for the remaining galaxies, the observed cutoff in the radial HI profile is closer to the center than if it was a consequence of ionization by background radiation and, therefore, it should be caused by other factors.     

Spherically symmetric cosmological perturbations in the de Donder gauge (II)

In the framework of a previously developed procedure the evolution of small spherically symmetric perturbations in a homogeneous R-W-F universe is analyzed. It turns out that the evolution tendency is mainly predicted by the state of the cosmic background. In the radiation dominated period the universe does not stimulate growing processes, a perturbation will be in a frozen state or it will diffuse. It is found that a dust dominated universe stimulates the perturbation masses to grow. The rate of this cosmic affected growing process is proportional to (R)^–1/2 (R being the scale factor). Consequently almost all galaxies were formed at the beginning of the dust dominated era.