Direct Solar Radiation Pressure Research Articles

Fundamental physics measurements with Galileo FOC satellites and the Galileo for science project. II. A box wing for modeling direct solar radiation pressure and preliminaries orbit determinations

Fundamental physics measurements with Galileo FOC satellites and the Galileo for science project. II. A box wing for modeling direct solar radiation pressure and preliminaries orbit determinations

Heliotropic orbits at asteroid 99942 Apophis: Considering solar radiation pressure and zonal gravity perturbations

Heliotropic orbits are ideal for low-altitude science orbits around asteroids since they can maintain long lifetimes by balancing perturbations from the asteroid's non-spherical gravitational field and the direct solar radiation pressure. In this study, Lagrange Planetary Equations and averaged disturbing potentials are applied to investigate the region around the asteroid Apophis where long-lifetime maintenance-free heliotropic orbits may exist. Based on both singly-averaged and constrained doubly-averaged disturbing potentials, the equations of motion in the orbital elements are derived, considering perturbations from the J2, J3, J4 term and solar radiation pressure including simple shadowing. The possible existence zones of heliotropic orbits at the asteroid Apophis (99942) are obtained with a semi-analytical method, applying the heliotropic and frozen conditions to the motion equations. In addition, consideration of the J4 term is found to diminish the maximum of a, e, i of the possible existence zones. The analysis in this paper helps us to quickly determine the distribution of possibly long-lifetime heliotropic orbits in the a-e-i space at a low computational cost.

Analysis of the orbital evolution of space debris using a solar sail and natural forces

Since the launch of the first artificial satellite around the Earth up to the present date, various non-functional objects are orbiting the Earth, such as deactivated satellites, satellite components, rocket bodies, among others. These objects can collide with operational satellites or other debris, generating a cloud of smaller particles. Space agencies are concerned about the current scenario of the space environment. If we continue as we are the number of objects in orbit will make it difficult to operate safely in the space environment. So space exploration may become unsustainable (ESA (2020)). In this work, the orbital evolution of these objects that are located in the geostationary orbit (GEO) is analyzed. In the mathematical model we consider the main disturbing forces, such as the direct solar radiation pressure (SRP), the perturbation of the third body (Sun and Moon) and the Earth oblateness. The SRP is the most relevant perturbation for objects with larger area-mass ratio. Knowing this, the possibility of using a solar sail is considered to help to clean the space environment. The main natural environmental perturbations that act in the orbit of the debris are considered in the dynamics. Such forces acting in the solar sail can force the growth of the eccentricity of these objects in the GEO orbit. Several authors have presented models of the solar radiation pressure considering the single-averaged model. But, doing a literature research, we found that the authors consider the Earth around the Sun in a circular and inclined orbit. Our contribution to the SRP model is in developing a different approach from other authors, where we consider the Sun in an elliptical and inclined orbit, which is valid for other bodies in the solar system when the eccentricity cannot be neglected. The expression of the SRP is developed up to the second order. We found that the first-order term is much superior to the second-order term, so the quadrupole term can be neglected. Another contribution is the approach to identify the initial conditions of the perigee argument (g) and the longitude of the ascending node (h), where some values of the (g,h) plane contribute to amplify the eccentricity growth. In the numerical simulations we consider real data from space debris removed from the site Stuff in Space. The solar sail helps to clean up the space environment using a propulsion system that uses the Sun itself, a clean and abundant energy source, unlike chemical propellants, to contribute to the sustainability of space exploration.

Spacecraft orbital stability zones around asteroid 99942 Apophis

In this work, we study spacecraft orbital motion around potentially “dangerous” near-Earth asteroid (99942) Apophis under the combined effects of perturbations from the third-body gravity, asteroid's non-spherical gravitational field, and the direct solar radiation pressure, incorporating possible asteroid's shadow crossings. To identify possibly stable orbital zones around Apophis, we vary initial conditions of the semimajor axis, inclination, and the longitude of ascending node. The stability is defined in terms of spacecraft lifetime in orbits without collisions or escapes. We have found two regions of stable orbits (initially circular) with a lifetime of up to 3 years: the one with small initial radii (about 400 m), lying close to the modified Laplace plane, the other with initial radii of 1.5–2.5 km, lying near the terminator plane. We also compared the cases accounting for full factors to those without shadows to see the influence of eclipse on the stable orbits. Results demonstrate the importance of considering the asteroid's shadow effect in the long-term orbital evolution - the eclipse may significantly change spacecraft lifetime (in years) at low orbits.

Statistical analysis of favorable conditions for thermographic inspection of concrete slabs

Infrared thermography has been successfully applied as a remote non-destructive testing approach for access to the internal conditions of reinforced concrete bridge slabs. Due to the different thermal properties of concrete and air or water present in the subsurface defects, damaged areas can be detected by the thermal contrast recorded on the inspected concrete surface. Thus, inspections should be conducted at favorable conditions, where the highest thermal gradients facilitate damage detection. In this study, experimental models were created to simulate bridge slabs with different delamination patterns. A multivariate regression analysis was used to explain and predict the thermal behavior of the test samples using data collected at different weather conditions and different periods of the day and the year. Based on experimental and regression analysis, it was observed that environmental conditions have an important influence on the concrete surface temperature variation and, therefore, on thermal contrast. Within the scope of this study, time frames between 12:00 noon and 3:00 pm, with temperatures between 27.5 and 37.9 °C, a high level of direct solar radiation and low atmospheric pressure values set an ideal scenario for thermographic inspections in reinforced concrete bridge slabs under passive heating.

Uncertainty analysis on direct solar radiation pressure modelling for GPS IIR and Galileo FOC satellites

Solar Radiation Pressure (SRP) is one of the main perturbations that needs to be carefully considered for space missions requiring great precision in satellite’s orbit. The computation of SRP is related to both satellite’s geometry and surface material. SRP model is usually used in the estimation of satellite’s position in space. However, the quality of SRP model is not easy to be assessed in a straightforward way. In this study, we proposed an uncertainty analysis on satellite geometry and surface optical properties using GPS IIR and Galileo FOC spacecraft. We compared the SRP acceleration between simple box-wing and the detailed geometry model under the condition that the optical properties are set exactly the same. It showed that the average difference caused by satellite geometry is around 6.7% and 2% of the total SRP for GPS IIR and Galileo FOC. We also found that the irregular shape of satellites can be a source of the so-called “y-bias” in orbit modelling. In addition, the partial derivatives of SRP acceleration with respect to optical properties for complex satellite geometry are computed using ray tracing. The partials w.r.t optical properties on solar panels are larger than that on satellite bus due to the large area of solar panels. Furthermore, partials w.r.t reflectivity is about 10 times larger than that w.r.t specularity for both solar panels and satellite bus. For GPS IIR (mass 1100 kg) and Galileo FOC (mass 700 kg) satellites, if we require the uncertainty of SRP model be less than 0.1 nm·s-2, the standard deviation of optical properties has to be less than 0.001 on solar panels and 0.01 on satellite bus.

System-specific systematic errors in earth rotation parameters derived from GPS, GLONASS, and Galileo

The earth rotation parameters (ERPs) are time-variable global geodetic parameters with a purely geophysical origin. Theoretically, the estimates of these parameters should be independent of the satellite constellation used in GNSS processing. Nonetheless, clear differences in the time series of ERPs are noticed when using different GNSS constellations. In this study, GPS, GLONASS, and Galileo estimates of ERP have been extensively evaluated in search of system-specific signals. Some of the processing details, such as modeling of the direct solar radiation pressure and length of the orbital arc, also have an impact on the ERP estimates. The GPS-based polar motion estimates are of better quality than those based on GLONASS and Galileo, which are susceptible to deficiencies in the orbit modeling. On the other hand, we observe a systematic bias of GPS-based length-of-day (LoD) with respect to the IERS-C04-14 values with a mean offset of − 22.4 µs/day. The Galileo-based solutions are almost entirely free of this issue. The extension of the orbital arc in the GNSS processing from 1 to 3 days is superior for the quality of the ERPs, especially for pole coordinate rates and LoD. The spurious signals inherently influence the Galileo-based and GLONASS-based ERPs at the frequencies which arise from the resonance between the satellite revolution period and earth rotation, e.g., 3.4 days for Galileo and 3.9 days for GLONASS. These and the draconitic signals overshadow the GNSS-based ERP estimates. Although all the system-specific solutions are affected by the artificial signals, the combination of different GNSS mitigates most of the uncertainties and improves the ERP results.

Toward the 1-cm Galileo orbits: challenges in modeling of perturbing forces

Precise orbit determination demands knowledge of perturbing forces acting on the satellites of the Global Navigation Satellite Systems (GNSS). The metadata published by the European GNSS Agency for the Galileo satellites allow for the composition of the analytical box-wing model dedicated for coping with the direct solar radiation pressure (SRP), albedo, and infrared radiation (IR). Based on the box-wing model, we evaluated both the magnitude and the characteristic periods of accelerations caused by all the aforementioned forces. We assess which perturbations can be absorbed by the extended Empirical CODE Orbit Model (ECOM2) and what are the consequences of neglecting higher-order ECOM2 coefficients. In order to evaluate the impact of SRP, albedo, IR, and the navigation antenna thrust, we perform a series of precise Galileo orbit determination strategies for Galileo In-Orbit-Validation (IOV), Full Operational Capability (FOC), and two FOC satellites launched into eccentric orbits. The proposed box-wing model is capable of absorbing approximately 97% of the SRP in the Sun-satellite direction, whereas the rest can be mitigated by an additionally estimated small set of empirical parameters. The purely physical box-wing model does not fully handle satellite misorientation and re-radiation effects, such as Y-bias, solar panel rotation lag, that is the misalignment causing a constant acceleration perpendicular to the solar panel axis and the direction to the Sun. However, the box-wing model is especially crucial in terms of the absorption of the higher-order terms of SRP and stabilizes the orbit solutions during the eclipsing periods. Based on the SLR residual analysis, we found a systematic effect at the level up to 50 mm resulting from the omission of the high-order empirical orbit coefficients. We also found that the impact of the albedo, IR, and transmitter antenna thrust on the Galileo orbits reach the level of 5, 14, and 20 mm, respectively. Eventually, we obtain the overall accuracy of the Galileo-FOC orbits at the level of 22.5 mm, even for the eclipsing period for the solution which considers the box-wing model with the estimation of the constant empirical accelerations.

Species-Specific Shifts in Diurnal Sap Velocity Dynamics and Hysteretic Behavior of Ecophysiological Variables During the 2015-2016 El Niño Event in the Amazon Forest.

Current climate change scenarios indicate warmer temperatures and the potential for more extreme droughts in the tropics, such that a mechanistic understanding of the water cycle from individual trees to landscapes is needed to adequately predict future changes in forest structure and function. In this study, we contrasted physiological responses of tropical trees during a normal dry season with the extreme dry season due to the 2015–2016 El Niño-Southern Oscillation (ENSO) event. We quantified high resolution temporal dynamics of sap velocity (Vs), stomatal conductance (gs) and leaf water potential (ΨL) of multiple canopy trees, and their correlations with leaf temperature (Tleaf) and environmental conditions [direct solar radiation, air temperature (Tair) and vapor pressure deficit (VPD)]. The experiment leveraged canopy access towers to measure adjacent trees at the ZF2 and Tapajós tropical forest research (near the cities of Manaus and Santarém). The temporal difference between the peak of gs (late morning) and the peak of VPD (early afternoon) is one of the major regulators of sap velocity hysteresis patterns. Sap velocity displayed species-specific diurnal hysteresis patterns reflected by changes in Tleaf. In the morning, Tleaf and sap velocity displayed a sigmoidal relationship. In the afternoon, stomatal conductance declined as Tleaf approached a daily peak, allowing ΨL to begin recovery, while sap velocity declined with an exponential relationship with Tleaf. In Manaus, hysteresis indices of the variables Tleaf-Tair and ΨL-Tleaf were calculated for different species and a significant difference (p < 0.01, α = 0.05) was observed when the 2015 dry season (ENSO period) was compared with the 2017 dry season (“control scenario”). In some days during the 2015 ENSO event, Tleaf approached 40°C for all studied species and the differences between Tleaf and Tair reached as high at 8°C (average difference: 1.65 ± 1.07°C). Generally, Tleaf was higher than Tair during the middle morning to early afternoon, and lower than Tair during the early morning, late afternoon and night. Our results support the hypothesis that partial stomatal closure allows for a recovery in ΨL during the afternoon period giving an observed counterclockwise hysteresis pattern between ΨL and Tleaf.

Accounting for perturbing forces acting on Galileo using a box-wing model

In November 2017, the European Global Navigation Satellite System Agency (GSA) released geometrical and optical information for the Galileo satellites which allowed for the composition of a box-wing model whose main goal is absorption of the direct solar radiation pressure, earth’s albedo, and infrared radiation. In order to evaluate the efficiency of the box-wing model, we test solutions based solely on the empirical models, the pure analytical box-wing model, and a series of hybrid models including the box-wing with different sets of additionally estimated empirical parameters. The hybrid solution, which is based on the box-wing model and on a reduced number of estimated empirical parameters, substantially reduces variabilities of the satellite laser ranging (SLR) residuals, especially for the low elevation angles of the sun above the orbital plane (β), i.e., for eclipsing Galileo satellites. The standard deviation of SLR residuals for |β| < 12.3° decreases from 37 to 25 mm between the solution based on the ECOM2 and the hybrid solution, respectively. We found significant mitigation of the spurious geocenter signal in the Z component and its formal errors, when reducing the number of estimated empirical parameters, and a substantial reduction of the dependency between geocenter coordinates, the geometry of Galileo orbital planes, and the position of the sun. The hybrid box-wing solution with a reduced set of empirical parameters provides thus the best solution for precise orbit determination, orbit predictions, and estimation of geodetic parameters.

Solar Radiation Pressure and Gravitational Waves Effects on Sun-Synchronous Orbits

For certain values of semi-major axis and eccentricity, orbit plane precession caused by Earth oblate is synchronous with the mean orbital motion of the apparent Sun (a sun-synchronism). Many forces cause slow changes in the inclination and ascending node of sun-synchronous orbits. In this work, we investigate the analytical perturbations due to the direct solar radiation pressure and gravitational waves effects. A full analytical solution is obtained using technique of canonical Lie-transformation up to the order three in (the oblateness of the Earth). The solar radiation pressure and gravitational waves perturbations cause second order effects on all the elements of the elliptic orbit (the eccentricity, inclination, ascending node, argument of perigee, and semi-major axis) consequently these perturbations will cause disturbance in the sun-synchronism. Also we found that the perturbation or the behavior of gravitational waves almost the same as the perturbation or the behavior of solar radiation pressure and their coupling will incorporate the sun-synchronism through the secular rate of the ascending node precession.

Photon Pressure Force on Space Debris TOPEX/Poseidon Measured by Satellite Laser Ranging

AbstractThe (TOPography EXperiment) TOPEX/Poseidon (T/P) altimetry mission operated for 13 years before the satellite was decommissioned in January 2006, becoming a large space debris object at an altitude of 1,340 km. Since the end of the mission, the interaction of T/P with the space environment has driven the satellite's spin dynamics. Satellite laser ranging (SLR) measurements collected from June 2014 to October 2016 allow for the satellite spin axis orientation to be determined with an accuracy of 1.7°. The spin axis coincides with the platform yaw axis (formerly pointing in the nadir direction) about which the body rotates in a counterclockwise direction. The combined photometric and SLR data collected over the 11 year time span indicates that T/P has continuously gained rotational energy at an average rate of 2.87 J/d and spins with a period of 10.73 s as of 19 October 2016. The satellite attitude model shows a variation of the cross‐sectional area in the Sun direction between 8.2 m2 and 34 m2. The direct solar radiation pressure is the main factor responsible for the spin‐up of the body, and the exerted photon force varies from 65 μN to 228 μN around the mean value of 138.6 μN. Including realistic surface force modeling in orbit propagation algorithms will improve the prediction accuracy, giving better conjunction warnings for scenarios like the recent close approach reported by the ILRS Space Debris Study Group—an approximate 400 m flyby between T/P and Jason‐2 on 20 June 2017.

CODE’s new solar radiation pressure model for GNSS orbit determination

The Empirical CODE Orbit Model (ECOM) of the Center for Orbit Determination in Europe (CODE), which was developed in the early 1990s, is widely used in the International GNSS Service (IGS) community. For a rather long time, spurious spectral lines are known to exist in geophysical parameters, in particular in the Earth Rotation Parameters (ERPs) and in the estimated geocenter coordinates, which could recently be attributed to the ECOM. These effects grew creepingly with the increasing influence of the GLONASS system in recent years in the CODE analysis, which is based on a rigorous combination of GPS and GLONASS since May 2003. In a first step we show that the problems associated with the ECOM are to the largest extent caused by the GLONASS, which was reaching full deployment by the end of 2011. GPS-only, GLONASS-only, and combined GPS/GLONASS solutions using the observations in the years 2009–2011 of a global network of 92 combined GPS/GLONASS receivers were analyzed for this purpose. In a second step we review direct solar radiation pressure (SRP) models for GNSS satellites. We demonstrate that only even-order short-period harmonic perturbations acting along the direction Sun-satellite occur for GPS and GLONASS satellites, and only odd-order perturbations acting along the direction perpendicular to both, the vector Sun-satellite and the spacecraft’s solar panel axis. Based on this insight we assess in the third step the performance of four candidate orbit models for the future ECOM. The geocenter coordinates, the ERP differences w. r. t. the IERS 08 C04 series of ERPs, the misclosures for the midnight epochs of the daily orbital arcs, and scale parameters of Helmert transformations for station coordinates serve as quality criteria. The old and updated ECOM are validated in addition with satellite laser ranging (SLR) observations and by comparing the orbits to those of the IGS and other analysis centers. Based on all tests, we present a new extended ECOM which substantially reduces the spurious signals in the geocenter coordinate $$z$$ (by about a factor of 2–6), reduces the orbit misclosures at the day boundaries by about 10 %, slightly improves the consistency of the estimated ERPs with those of the IERS 08 C04 Earth rotation series, and substantially reduces the systematics in the SLR validation of the GNSS orbits.

Navigation solution for a geostationary satellite based on its dynamic equations and occasional GNSS measurements

The paper offers solution to the problem of geostationary spacecraft navigation by navigation satellite signal measurements using nonlinear dynamic equations, which include perturbing factors such as non-sphericity of the gravitational field of the Earth, gravitational attraction of the Moon and the Sun, and direct solar radiation pressure. This solution uses the iterative Kalman filter based on UD-decomposition and is focused on the onboard implementation with limited computing resources. The estimates of current coordinates and velocity components obtained with the Kalman filter are taken into account when integrating nonlinear equations of a spacecraft motion up to the next solution time moment. With undetermined solar radiation pressure coefficient, the proposed solution proved efficient in terms of accuracy requirements for the spaceborne satellite navigation receiver. The tests were conducted using a GPS signal simulator and a receiver.

On the effects of each term of the geopotential perturbation along the time I: Quasi-circular orbits

This paper provides a useful new method to determine minimum and maximum range of values for the degree and order of the geopotential coefficients required for simulations of orbits of satellites around the Earth. The method consists in a time integration of the perturbing acceleration coming from each harmonic of the geopotential during a time interval T. More precisely, this integral represents the total velocity contribution of a specific harmonic during the period T. Therefore, for a pre-fixed minimum contribution, for instance 1×10-8m/s during the period of time T, any harmonic whose contribution is below this value can, safely, be neglected. This fact includes some constraints in the degree and order of the terms which are present in the geopotential formula, saving computational efforts compared to the integration of the full model. The advantage of this method is the consideration of other perturbations in the dynamics (we consider the perturbations of the Sun, the Moon, and the direct solar radiation pressure with eclipses), since these forces affect the value of the perturbation of the geopotential, because these perturbations depend on the trajectory of the spacecraft, that is dependent on the dynamical model used. In this paper, we work with quasi-circular orbits and we present several simulations showing the bounds for the maximum degree and order (M) that should be used in the geopotential for different situations, e. g., for a satellite near 500km of altitude (like the GRACE satellites at the beginning of their mission) we found 35⩽M⩽198 for T=1day. We analyzed the individual contribution of the second order harmonic (J2) and we use its behavior as a parameter to determine the lower limit of the number of terms of the geopotential model. In order to test the accuracy of our truncated model, we calculate the mean squared error between this truncated model and the “full” model, using the CBERS (China-Brazil Earth Resources Satellite) satellite in this test.

Analytical Third Order Solution for Coupling Effects of Earth Oblateness and Direct Solar Radiation Pressure on the Motion of Artificial Satellites

Coupling effects of Earth oblateness and direct solar radiation pressure on the motion of an artificial satellite are evaluated. Secular and periodic terms are retained up to order three and two respectively, where the coefficient of the second zonal harmonic of the geopotential is considered of first order. The solution revealed the existence of secular terms at order three that arises from the couplings between terms, of lower orders, resulting from the solar radiation pressure.

Semi-analytical study of the rotational motion stability of artificial satellites using quaternions

This study at aims performing the stability analysis of the rotational motion to artificial satellites using quaternions to describe the satellite attitude (orientation on the space). In the system of rotational motion equations, which is composed by four kinematic equations of the quaternions and by the three Euler equations in terms of the rotational spin components. The influence of the gravity gradient and the direct solar radiation pressure torques have been considered. Equilibrium points were obtained through numerical simulations using the softwares Matlab and Octave, which are then analyzed by the Routh-Hurwitz Stability Criterion.

The impact of Earth’s shadow on the long-term evolution of space debris

Direct solar radiation pressure and Earth’s shadow crossings are known to be responsible for short-term variations of space debris orbital elements, the higher the area-to-mass ratio the larger the perturbation. Nevertheless, existing studies have always been performed on periods of time shorter than 150 years. Considering longer time scales of the order of a 1000 years, this paper focuses on the long-term periodic evolution of space debris trajectories caused by successive Earth’s shadow crossings. Other perturbations as the geopotential and third-body gravitational attractions obviously play a role and compete with the one which is described in this paper. Symplectic numerical propagations and new (semi-)analytical models are developed to identify a frequency associated to shadow entry and exit eccentric anomalies. It is shown that Earth’s shadow is responsible for large deviations from the initial orbital elements, even on shorter period of times, and that this effect increases along with the area-to-mass ratio.

Dynamical evolution of high area-to-mass ratio objects in Molniya orbits

For special demands, some notable orbit types have been developed by human, including the Molniya orbits, which have a relatively high eccentricity up to about 0.7, and a period of 12h. Considering that space debris with high area-to-mass ratio (A/M) has been discovered, such objects may also exist in Molniya orbits due to spacecraft and upper stages fragmentation events. However, there are not sufficient studies of the complex dynamical phenomena of such orbits. These studies can enrich the knowledge about the long-term evolution of these orbits, be helpful to propose uncatalogued objects observation and identification, and also set the protected region as well as active debris removal. In this paper, the characteristics of 2:1 resonance of Molniya satellite orbits are studied. A large set of numerical simulations, including all the relevant perturbations, is carried out to further investigate the main characteristics, and special attention is payed to the dynamical evolution of objects with high A/M, particularly affected by the direct solar radiation pressure. The long-term dynamical evolution of orbital elements, as well as the dependency of lifetime on the A/M value, is discussed.

Second order constraints in the theory of invariant relative orbits including relativistic and direct solar radiation pressure effects

Working with the mean orbit elements, the secular drift of the longitude of the ascending node and the sum of the argument of perigee and mean anomaly are set equal between two neighboring orbits. By having both orbits drift at equal angular rates on the average, they will not separate over time due to the influence of the perturbative effects of the asphericity of the Earth. The relativistic corrections and the direct solar radiation pressure to the equations of motion, as is considered in this work. The problem is stated. The expressions for the time rate of change of the longitude of the ascending node and the sum of the argument of perigee and mean anomaly in terms of the augmented Delaunay canonical elements are obtained. The expressions for the second order conditions that guarantee that the drift rates of two neighboring orbits are equal on the average are derived. Keywords: Invariant relative orbits, Spacecraft flying formations, Relativistic corrections, Direct solar radiation pressure.