Direct Solar Radiation Pressure Research Articles

The circumsolar dust complex and solar magnetic field

New model calculations for the dynamical evolution of dust particles at several solar radii around the Sun are presented. We choose a fractal aggregate consisting of either silicate or carbon as a representative of dielectric and absorbing fluffy particles. We take into account a large array of forces and effects acting on the dust particles—solar gravity, direct solar radiation pressure, Poynting-Robertson effect, sublimation, and the Lorentz force, with a special emphasis given to the latter. The Lorentz force was computed on the base of modeled grain’s charges and a model of the actual solar magnetic field from 1976 to 1996. We have investigated the dynamics of individual grains, obtained radial and vertical density profiles of different-sized particles, and used the computed dust density distributions to calculate the expected F-corona brightness during the periods of weak and strong magnetic field. We have found that the solar magnetic field and its variations do not affect the dynamics and spatial distribution of carbon aggregates, which are thought to produce the peak features of the near-infrared F-corona brightness that were sometimes observed. On the other hand, the variations of the solar magnetic field may alter the latitudinal distribution of silicate aggregates. However, the effect is not strong enough to account for the observed temporal variations in the brightness. Thus we can rule out the correlation between the appearance or disappearance of a peak feature and the solar activity cycle.

The Effect of Direct Solar Radiation Pressure on a Spacecraft of Complex Shape

The canonical equations of motion of a spacecraft of complex shape under the joint effects of earth oblateness and direct solar radiation pressure are formulated. The shape of the satellite is modeled as an axisymmetric body plus despun antenna emitting or receiving a radio beam which is suitable to describe the main effects for the telecommunication satellites. The attitude of the satellite is assumed stabilized such that the axis of the symmetric part be along the tangent to the orbit. The Hamiltonian is developed in terms of the Delaunay elements augmented so as to remove the time dependence of the Hamiltonian.

Global lunar gravity recovery from satellite-to-satellite tracking

A feasibility study is presented of high resolution and accuracy determination of the global grayity field of the Moon from a combination of low-low satellite-to-satellite range-rate observations and conventional tracking from stations on Earth. The European Moon ORbiting Observatory (MORO) mission, studied as a candidate for the third mediumsized science mission (M3) under the European Space Agency's Horizon 2000 scientific programme, is adopted for the simulation purposes. Global coverage and mapping of the fine details of the gravity field is achieved by satellite-to-satellite tracking (SST) of a small sub-satellite deployed by MORO in its 100 km polar orbit, whereas the long-wavelength features are obtained from Earth-based tracking. The combination of SST and Earth-based tracking therefore represents a powerful tool over a wide range of wavelengths. Moreover, tracking from Earth provides a clear reference for the satellite orbits, which are hard to determine from SST data only. The baseline mission proposal foresees a co-orbiting satellite pair in which the two satellites follow each other in essentially the same orbital plane with only a small spacing in time. The MORO gravimetry experiment requirements prescribe a surface level radial acceleration accuracy of a few mGal with a surface resolution of 50–100km. A number of satellite tracking configurations has been investigated and the influence of noise and systematic errors has been studied. Using perfect measurements and in the absence of systematic model errors the gravity field of the Moon, assumed to be pertectly represented by the 60 × 60 Lun60d model of Konopliv et al. (1993) with a surface resolution of 91 km, has been recovered with a radial acceleration accuracy better than 0.003 mGal using a 3° in-plane satellite spacing. Introducing uncorrelated random noise to the tracking links and a 10% model error in the direct solar radiation pressure model, still an accuracy better than 5 mGal can be achieved. Finally, it is shown that a small angular separation in right ascension of the ascending node of the orbital planes of MORO and its sub-satellite adds extra cross-track information to the SST range-rate signal and thus enables better determination of high sectorial and near-sectorial terms of the gravity field.

Long-periodic and secular perturbations to the orbit of a spherical satellite due to direct solar radiation pressure

A theory is developed for the perturbations to the orbit of a spherically symmetric satellite which accounts for the changes in the perigee and nodal positions and the variations of the Sun-Earth distance and direction over an orbital revolution. The theory is semi-analytical, the equations of motion being integrated with respect to time over the sunlit period of each orbital revolution. Long-periodic and short-periodic perturbations may be treated separately, and this is important for long-term analyses in terms of mean elements where short-period terms are averaged or omitted.

Long-periodic and secular perturbations to the orbits of Explorer 19 and Lageos due to direct solar radiation pressure

A theory for the long-term variations in the orbit of a spherically symmetric satellite due to direct solar radiation pressure is tested using two satellite orbit analyses. The first of these analyses is in terms of mean elements for the balloon satellite Explorer 19. The results are compared with the expected theoretical variations with short-period terms omitted. The second analysis utilises satellite laser ranging observations of the geodetic satellite, Lageos. A novel long-term analysis technique is developed primarily for laser ranging studies. The technique is tested along with the solar radiation pressure perturbation theory by comparing the results from the theory and the analysis.

Model of non-gravitational perturbations for CESAR experiment with MACEK accelerometer

Non-gravitational perturbations have recently achieved great interest among the theoreticians in satellite dynamics. Both short- and long-term residual phenomena in many space missions are connected with the non-gravitational effects. However, our theoretical understanding of such phenomena is rather limited. In many cases, only rough phenomenological models are available. In situ (instantaneous) measurements of the non-gravitational effects have thus great importance for checking our theoretical concepts. Microaccelerometer MACEK (embodied in the CESAR mission) is devoted to such measurements with expected threshold up to 5 × 10 −11 m/s 2. Model of the non-gravitational phenomena developed for the data analysis of the MACEK device include two principal parts: (i) atmospheric drag and lift model, (ii) radiation pressure model. With the aid of developed theory we assume to be able to fulfil the principal goal of the mission: the determination of the distribution and variations of the thermospheric density. Radiative effect package includes: (i) direct solar radiation pressure, with emphasis of theEarth shadow penumbra transitions; (ii) pressure of the Earth reflected/scattered sunlight (‘the albedo effect’), with special attention to the atmospheric phenomena and finite cone pattern of the specular reflection on the ocean surface; (iii) pressure of the Earth thermal (IR) radiation.

Radiative forces and LAGEOS' orbit

The orbit analysis of LAGEOS satellite has resulted into the discovery and/or reassessment of several very small sources of perturbation on satellite orbits. The analysis of orbital arcs of duration ranging from one month to several years has revealed that perturbative effects are present, having unpredicted long-term or secular components down to the 10 −12 m/s 2 acceleration level. It was soon realized that those perturbations have a non-gravitational origin. In recent years, we have devoted some effort to the physical modelling of radiative perturbations, caused by momentum exchanges with an appropriate radiative field, and have considered their potential role in the analysis of LAGEOS orbit residuals. These perturbations include: (i) direct solar radiation pressure; (ii) radiation pressure from the Earth's emitted/reflected/diffused radiation flux; (iii) the so-called thermal thrust force. The main results of this work are reviewed, discussing its relationships with models developed by other research groups. In particular, we present a list of the physical processes which still appear to need more detailed and realistic modelling to reach a better understanding of LAGEOS dynamics at the 10 −12 m/s 2 level.

Key features of a satellite skin force modelling technique by means of Monte-Carlo ray tracing

With the increasing accuracy requirements on precise orbit prediction (e.g. for geodetic satellites like ERS-1), the accurate modelling of non-gravitational forces has become an important factor. The key features of a skin force modelling software shall be described which has been implemented by MATRA under ESA contract. The software covers free-molecular aerodynamics, direct and indirect solar radiation pressure effects (diffuse and specular earth albedo, and earth IR), and is supported by state-of-the-art environmental models, and spacecraft geometry and thermo-optical surface models.

Perturbations of the orbit of Explorer 19 due to solar radiation

The orbit of the balloon satellite, Explorer 19, is analysed to determine the effects of direct solar radiation pressure over one revolution of the satellite (111 min) for MJD 42822 and MJD 42966. At the earlier date, the satellite entered the Earth's shadow, presenting an opportunity to examine the effectiveness of two different shadow models. The reflectivity of the surface of the satellite was estimated from analysis of the variations in orbital eccentricity over a period of 236 days. Although many of the parameters associated with the shape and orientation of the satellite are unknown, the theory for a non-spherical satellite is applied using trial and error methods to determine the parameters of best fit. The paper concludes with an examination of the perturbations in orbital eccentricity and inclination due to incident, specularly reflected, and diffusely reflected radiation.

Combined solar radiation pressure and drag effects on the orbits of artificial satellites

A semi analytical theory is proposed to study the joint effects of direct solar radiation pressure and atmospheric drag on the orbit of an artificial Earth satellite. Making the solar radiation pressure equal to zero the problem is reduced to one already solved by Brouwer and Hori. The solutions are not equivalent, however, since in the Brouwer and Hori theory one has spurious Poisson terms.

Sun-synchronous orbits near critical inclination

The long period dynamics of Sun-synchronous orbits near the critical inclination 116.6° are investigated. It is known that, at the critical inclination, the average perigee location is unchanged by Earth oblateness. For certain values of semimajor axis and eccentricity, orbit plane precession caused by Earth oblateness is synchronous with the mean orbital motion of the apparent Sun (a Sun-synchronism). Sun-synchronous orbits have been used extensively in meteorological and remote sensing satellite missions. Gravitational perturbations arising from an aspherical Earth, the Moon, and the Sun cause long period fluctuations in the mean argument of perigee, eccentricity, inclination, and ascending node. Double resonance occurs because slow oscillations in the perigee and Sun-referenced ascending node are coupled through the solar gravity gradient. It is shown that the total number and infinitesimal stability of equilibrium solutions can change abruptly over the Sun-synchronous range of semimajor axis values (1.54 to 1.70 Earth radii). The effect of direct solar radiation pressure upon certain stable equilibria is investigated.

Earth satellite orbits with resonant lunisolar perturbations - II. Some resonances dependent on the semi-major axis, eccentricity and inclination

Earth satellite orbits resonant with respect to lunisolar gravity and direct solar radiation pressure perturbations are discussed with particular reference to those resonances satisfying commensurability conditions of the following form: ψ 4 = α ώ + γ (ώ p + Ṁ p ) ≈ 0 and ψ 5 = β Ω . + γ (ώ p + Ṁ p ) ≈ 0, where ω is the argument of perigee of the satellite’s orbit, Ω is the longitude of its ascending node, ω p is the argument of perigee of the lunar or solar orbits, and M p is the mean anomaly of the lunar or solar orbits; α, β and γ are integers. Certain simple relations are derived connecting the satellite’s semi-major axis, eccentricity and inclination; they must be satisfied, if the satellite is to exist in the commensurabilities ψ 4 ≈ 0 and ψ 5 ≈ 0. Tables are also given which contain the predominant resonant terms in the lunisolar gravity and direct solar radiation pressure disturbing function expansions for every commensurability of the type ψ 4 ≈ 0 and ψ 5 ≈ 0. Finally some important examples of these resonances are discussed.

Direct solar and earth-albedo radiation pressure effects on the orbit of Pageos 1

The orbit of the Pageos 1 balloon satellite has been investigated in detail over the early part of the balloon's lifetime. The analysis herein focuses on how Pageos's orbit was affected by direct solar and albedo radiation pressure. Near the end of the second year of the satellite's lifetime, anomalous behavior was found in the orbital acceleration. This behavior may be the result of a change in the shape of the satellite: Pageos's original spherical shape had become slightly oblate, spinning about a minor axis and precessing about the direction to the sun. In fact, we have been able to represent this effect quite well by accounting for a small component of force in the plane perpendicular to the sun and allowing this component to rotate about the solar direction. By analyzing the balloon-inflation process, attained with sublimating compounds, and the consequent variation of the satellite's mass due to leakage through the holes caused by micrometeoroid bombardment, we have evaluated the near-earth micrometeoroid-particle flux, which turns out to be 5×10−8 cm−2 sec−1. With the assumptions we made for the satellite's area-to-mass ratio and reflection coefficient, we would need a solar constant of 1.95 cal cm−2 min−1 to give a best-fit to our data.

Earth satellite orbits with resonant lunisolar perturbations I. Resonances dependent only on inclination

Earth satellite orbits resonant with respect to lunisolar gravity and direct solar radiation pressure perturbations are discussed with particular reference to those resonances the occurrence of which is dependent only on the satellite’s orbital inclination. All types of lunisolar resonance orbits are first classified in terms of the general commensurability condition, which is then expressed as a function of the non-angular elements of the satellite’s orbit and certain parameters of the perturbing forces. Rules and constraints for ascertaining the predominant resonance terms in the disturbing function expansion for a given commensurability are also derived. Finally, the resonances dependent only on inclination are discussed. Criteria for determining their existence are found and the predominant resonant terms for every commensurability of this type are given. A num­ber of important examples of resonance orbits in this category are also discussed.

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 in the Anomalistic Period of Artificial Satellites Caused by the Direct Solar Radiation Pressure Centre for Astronomy and Space Sciences, Satellite Tracking Station No. 1132

AbstractApproximate formulae for the evaluation of the influence of direct solar radiation pressure (neglecting the POYNTING‐ROBERTSON effect) on the anomalistic period of artificial satellites with quasi‐circular and completely illuminated orbits are derived.

Satellite orbits perturbed by direct solar radiation pressure: General expansion of the disturbing function

An expression is derived for the solar radiation pressure disturbing function on an Earth satellite orbit which takes into account the variation of the solar radiation flux with distance from the Sun's centre and the absorption of radiation by the satellite. This expression is then expanded in terms of the Keplerian elements of the satellite and solar orbits using Kaula's method. The Kaula inclination functions are replaced by an equivalent set of modified Allan inclination functions. The resulting expression reduces to the form commonly used in solar radiation pressure perturbation studies (e.g. Aksnes, 1976), when certain terms are neglected. If, as happens quite often in practice, a satellite's orbit is in near-resonsnce with certain of these neglected terms, these near-resonant terms can cause changes in the satellite's orbital elements comparable to those produced by the largest term in Aksnes's expression. A new expression for the solar radiation pressure disturbing function expansion is suggested for use in future studies of satellite orbits perturbed by solar radiation pressure.

The influence of direct solar radiation pressure on the nodal period of artificial earth satellites

AbstractApproximate formulae for the evaluation of the effect of direct solar radiation pressure (neglecting the POYNTING‐ROBERTSON effect and shadow effect) on the nodal period of artificial Earth satellites with quasi‐circular orbits are derived. The cases of osculating elements considered in the ascending node and of circular orbits are studied.

Analytical study of the Earth's shadowing effects on satellite orbits

In this paper a new mathematical model is proposed for the study of the effects of the direct solar radiation pressure on the orbit of an artificial Earth satellite. The equations for the first order effects become canonical when a different definition for the orders of magnitude is adopted. This enables us the utilization of the method of Von Zeipel to eliminate all periodic terms. The model leads to the non-existence of pure secular perturbations owing to the direct solar radiation pressure on the metric elements: semi-major axis, eccentricity and inclination. Numerical examples built with an approximation for the shadow function show that the secular inequalities on the angle variables—longitude, perigee and node—are very small.

The utility of diffuse skylight measurements in characterizing low levels of particulate air pollution

Measurements of direct and diffuse solar radiation, surface temperature and vapor pressure, and atmospheric dust content were made at two localities on the outskirts of Phoenix, Arizona. On two days of light to moderate air pollution with different dust contents, but nearly identical amounts of precipitable water aloft, total transmittances of the atmosphere for the combined direct plus diffuse solar radiation were nearly identical, while ratios of diffuse to direct solar radiation were quite different. The utility of diffuse skylight measurements to provide a detailed characterization of light to moderate particulate air pollution episodes was thereby demonstrated.