Sailing with solar and planetary radiation pressure

Literature on solar sailing has thus far mostly considered solar radiation pressure (SRP) as the only contribution to sail force. However, considering a sail in a planetary mission scenario, a new contribution can be added. Since the planet itself emits radiation, this generates a radial planetary radiation pressure (PRP) that is also exerted on the sail. Hence, this work studies the combined effects of both SRP and PRP on a sail for two case studies, i.e. Earth and Venus. In proximity of the Earth, the effect of PRP can be significant under specific conditions. Around Venus, instead, PRP is by far the dominating contribution. These combined effects have been studied for single- and double-sided reflective coating and including eclipse. Results show potential increase in the net acceleration and a change in the optimal attitude to maximise the acceleration in a given direction. Moreover, an increasing semi-major axis manoeuvre is shown with and without PRP, to quantify the difference on a real-case scenario.     

Spacecraft formation and orbit control using differential attitude-dependent solar radiation pressure

This paper introduces a linear model for spacecraft formation dynamics subject to attitude-dependent solar radiation pressure (SRP) disturbance, with the SRP model accounting for both absorption and specular/diffuse reflection. Spacecraft attitude is represented in modified Rodriguez parameters (MRPs), which also parameterize the orientation of individual facets for a spacecraft with fixed geometry. Compared to earlier work, this model incorporates analytic approximation of the SRP-perturbed chief orbit behavior in a manner enabling its use in applications with infrequent guidance updates. Control examples are shown for single-plate representations of hypothetical spacecraft with generally realistic optical parameters. The results demonstrate the validity of the model and the feasibility of SRP-based formation and rendezvous control in orbits around small bodies and in high orbits around the Earth such as the GEO belt.     

DORIS processing at the European Space Operations Centre

This paper gives an overview of the DORIS related activities at the Navigation Support Office of the European Space Operations Centre. The DORIS activities were started in 2002 because of the launch of the Envisat satellite where ESOC is responsible for the validation of the Envisat Precise Orbits and a brief overview of the key Envisat activities at ESOC is given. Typical orbit comparison RMS values between the CNES POE (GDR-C) and the ESOC POD solution is 6.5, 18.8 and 23.1 mm in radial-, along- and cross-track direction. In the framework of the generation of the ITRF2008 ESOC participated in the reprocessing of all three space geodetic techniques; DORIS, SLR, and GPS. Here the main results of our DORIS reprocessing, in the framework of the International DORIS Service (IDS), are given. The WRMS of the weekly ESOC solution (esawd03) for the 2004–2009 period compared to the IDS-1 combined solution is of the order of 12 mm. Based on the long time series of homogeneously processed data a closer look is taken at the estimated solar radiation pressure parameters of the different satellites used in this DORIS analysis. The main aim being the stabilization of the Z-component of the geocentre estimates. We conclude that the ESOC participation to the IDS ITRF2008 contribution has been beneficial for both ESOC and the IDS. ESOC has profited significantly from the very open and direct communications and comparisons that took place within the IDS during the reprocessing campaign.     

Adjustable box-wing model for solar radiation pressure impacting GPS satellites

One of the major uncertainty sources affecting Global Positioning System (GPS) satellite orbits is the direct solar radiation pressure. In this paper a new model for the solar radiation pressure on GPS satellites is presented that is based on a box-wing satellite model, and assumes nominal attitude. The box-wing model is based on the physical interaction between solar radiation and satellite surfaces, and can be adjusted to fit the GPS tracking data.     

Shape optimization of a three-dimensional membrane-structured solar sail using an angular momentum unloading strategy

A shape of the satellite’s solar sail membrane is essential for unloading angular momentum in the three-axis stabilized attitude control system because the three-dimensional solar sail can receive solar radiation pressure from arbitrary directions. In this paper, the objective is the shape optimization of a three-dimensional membrane-structured solar sail using the angular momentum unloading strategy. We modelled and simulated the solar radiation pressure torque, for unloading angular momentum. Using the simulation system, since the unloading angular momentum rate is maximized, the shape of the three-dimensional solar sail was optimized using a Genetic algorithm and Sequential Quadratic Programming. The unloading velocity in the optimized shaped solar sail was greatly improved with respect to a conventional flat or pyramid solar sail.     

New flare model using recent measurements of the solar ultraviolet irradiance

The solar photon output from the Sun, which was once thought to be constant, varies considerably over time scales from seconds during solar flares to years due to the solar cycle. This is especially true in the wavelengths shorter than 190 nm. These variations cause significant deviations in the Earth and space environment on similar time scales, which then affects many things including satellite drag, radio communications, atmospheric densities and composition of particular atoms, molecules, and ions of Earth and other planets, as well as the accuracy in the Global Positioning System (GPS). The Flare Irradiance Spectral Model (FISM) is an empirical model that estimates the solar irradiance at wavelengths from 0.1 to 190 nm at 1 nm resolution with a time cadence of 60 s. This is a high enough temporal resolution to model variations due to solar flares, for which few accurate measurements at these wavelengths exist. This model also captures variations on the longer time scales of solar rotation (days) and solar cycle (years). Daily average proxies used are the 0–4 nm irradiance, the Mg II c/w, F10.7, as well as the 1 nm bins centered at 30.5 nm, 121.5 (Lyman Alpha), and 36.5 nm. The GOES 0.1–0.8 nm irradiance is used as the flare proxy. The FISM algorithms are given, and results and comparisons are shown that demonstrate the FISM estimations agree within the stated uncertainties to the various measurements of the solar Vacuum Ultraviolet (VUV) irradiance.     

Comparison of ANN and MLR models for estimating solar radiation in Turkey using NOAA/AVHRR data

In this paper, the estimation capacities of MLR and ANN are investigated to estimate monthly-average daily SR over Turkey. The satellite data are used for 73 different locations over Turkey. Land surface temperature, altitude, latitude, longitude and month are offered as the input variables for modeling ANN and MLR to get SR. Estimations of SR are evaluated with the meteorological values by using the statistical bases. The obtained results indicated that the ANN model could achieve a satisfactory performance when compared to the MLR model. Moreover, it is understood that more accurate results in estimation of SR are obtained in the use of satellite data, rather than the use of meteorological station data. Finally, the built ANN model is used to estimate the yearly average of daily SR over Turkey. As a result, satellite-based SR map for Turkey is generated.     

Observation bio-effect of SW-global solar radiation in Ilorin in the tropics

The annual variation of global (total) solar radiation measured over four (4) years (1995–1998) at Ilorin (8°32′N, 4°34′E) was studied and the bio-effects of the variation is herein reported. The weekly averages of the solar radiation flux were obtained and plotted. The profile of the weekly averages of the insolation shows two notable “wells” corresponding to the harmattan dry season and the rainy season. It was deduced that the duration of the seasons was directly proportional to the sizes of the “wells”, while the depths of the “wells” correspond to the severity of the causes of the “wells”. The fall and rise rates of the depth of the edges of the wells are inversely proportional to the ecological effects of the variation of the radiation. The rates of decrease and increase of the radiation flux affect the depths of the “wells” and were found to be rapid and shallow for the “Harmattan Well”, and gentle and deep for the “Rain Well”. The width (duration), rate of change and depth of the “Harmattan Well” bring about stress for both animals and plants.     

Solar sail near the Sun: Point-like and extended models of radiation source

Some modifications of solar sail radiation pressure forces on a plate and on a sphere for use in the numerical simulation of ‘local-optimal’ (or ‘instantaneously optimal’) trajectories of a spacecraft with a solar sail are suggested. The force model development is chronologically reviewed, including its connection with solar sail surface reflective and thermal properties. The sail surface is considered as partly absorbing, partly reflective (specular and diffuse), partly transparent. Thermal balance is specified because the spacecraft moves from circular Earth orbit to near-Sun regions and thermal limitations on the sail film are taken into account. A spherical sail-balloon can be used in near-Sun regions for scientific research beginning with the solar-synchronous orbit and moving outward from the Sun. The Sun is considered not only as a point-like source of radiation but also as an extended source of radiation which is assumed to be consequently as a point-like source of radiation, a uniformly bright flat solar disc and uniformly bright solar sphere.     

Experimental investigation of transient thermal behavior of an airship under different solar radiation and airflow conditions

Knowledge of the thermal behavior of airships is crucial to the development of airship technology. An experiment apparatus is constructed to investigate the thermal response characteristics of airships, and the transient temperature distributions of both hull and inner gas are obtained under the irradiation of a solar simulator and various airflow conditions. In the course of the research, the transient temperature change of the experimental airship is measured for four airflow speeds of 0 m/s (natural convection), 3.26 m/s, 5.5 m/s and 7.0 m/s, and two incident solar radiation values of 842.4 W/m² and 972.0 W/m². The results show that solar irradiation has significant influence on the airship hull and inner gas temperatures even if the airship stays in a ground airflow environment where the heat transfer is dominated by radiation and convection. The airflow around the airship is conducive to reduce the hull temperature and temperature nonuniformity. Transient thermal response of airships rapidly varies with time under solar radiation conditions and the hull temperature remains approximately constant in ∼5–10 min. Finally, a transient thermal model of airship is developed and the model is validated through comparison with the experimental data.     

Influence of curved thin-film device on deformation of a solar sail

A spinning solar sail IKAROS’s membrane is estimated to unexpectedly deform into an inverted pyramid shape due to thin-film devices with curvature, such as thin-film solar cells and steering devices on the membrane. It is important to investigate the deformation caused by the curved thin-film devices and predict the sail shape because the out-of-plane deformation greatly affects solar radiation pressure (SRP) and SRP torque. The purpose of this paper is to clarify the relationship between the global shape and orientation and position of curved thin-film devices and to evaluate SRP torque on the global shape using finite element analysis. The global shape is evaluated based on the out-of-plane displacement and the SRP torque. When the curved thin-film devices make the membrane shrink in the circumferential, diagonal, and radial direction, the sail deforms into a pyramid shape, an inverted pyramid one, and a saddle one, respectively. The saddle shape is more desirable for solar sails than the inverted pyramid shape and the pyramid one from the viewpoint of shape stability to SRP and control of SRP torque in the normal direction of the sail (windmill torque). The position of the thin-film device tends to increase the absolute value of windmill torque when it is biased circumferentially from the petal central axis. The suggested design principles for the arrangement of thin-film devices is that the curved thin-film devices should be directed so that the sail shrinks in the radial direction in order to deform the sail into a saddle shape with high shape stability, and the position of the thin-film devices should be biased in the circumferential direction paying attention to the absolute value of windmill torque to determine the direction of windmill torque.     

Surface shape control of integrated paraboloid space reflector consisting of sub-reflectors exploiting modulated solar pressure

Reflectors are very critical space elements and can be used not only as solar collectors/reflectors, telecommunication radio antennas and telescopes but also for dual-usage such as solar sails and solar concentrators to probe and sublimate materials from asteroids when actively controlling the surface shape. In this paper, the surface shape of a slack reflector with negligible elastic deformations will be controlled to be a paraboloid by actively modulating the solar radiation pressure (SRP) force using reflectivity control devices (RCDs) across the reflector. Nonlinear static equilibrium equations for an arbitrary infinitesimal within the reflector along the radial, circumferential and transverse directions are established considering the external modulated SRP force and internal tensions respectively. The coupled radial stress differential governing equation and reflectivity algebraic equation are obtained for the paraboloid reflector by the help of the formulation of an inverse problem based on equilibrium equations previously established. Some analytical and numerical analysis for reflectors with ideal and non-perfect SRP force models are performed respectively. The conclusions concerning about how to control the reflector’s surface shape successfully using allowed reflectivity, resulting in reasonable stress range, moreover, how to get the feasible solutions influenced by the reflector’s size parameters, are all based on the presented analytical and numerical analysis.     

Cosmic radiation exposure of aircraft occupants on simulated high-latitude flights during solar proton events from 1 January 1986 through 1 January 2008

From 1 January 1986 through 1 January 2008, GOES satellites recorded 170 solar proton events. For 169 of these events, we estimated effective and equivalent dose rates and doses of galactic cosmic radiation (GCR) and solar cosmic radiation (SCR), received by aircraft occupants on simulated high-latitude flights. Dose rate and dose estimates that follow are for altitudes 30, 40, 50, and 60 kft, in that order.     

Performance analysis of an attitude control system for solar sails using sliding masses

This paper deals with the attitude control performance analysis of a square solar sail. Two sliding masses are moved inside and along mast lanyards for the control around the pitch and yaw axes. An optimal linear controller with a feedback and a feedforward part is used to control the attitude of the sail. Numerical simulations have been carried out to investigate the system’s ability of performing precise and near-time-optimal reorientation maneuvers as well as the controller’s sensitivity with respect to the sail parameters, as the center of pressure to the center of mass offset or the sail’s size. Our simulation results are finally shown and discussed.     

Improving the orbits of GPS block IIA satellites during eclipse seasons

During Sun-Earth eclipse seasons, GPS-IIA satellites perform noon, shadow and post-shadow yaw maneuvers. If the yaw maneuvers are not properly taken into account in the orbit determination process, two problems appear: (1) the observations residuals increase since the modeled position of the satellite’s navigation antenna differs from the true position, and (2) the non-conservative forces like solar radiation pressure or Earth radiation pressure are mismodeled due to the wrong orientation of the satellite’s surfaces in space.     

Symplectic integration of space debris motion considering several Earth’s shadowing models

In this work, we present a symplectic integration scheme to numerically compute space debris motion. Such an integrator is particularly suitable to obtain reliable trajectories of objects lying on high orbits, especially geostationary ones. Indeed, it has already been demonstrated that such objects could stay there for hundreds of years. Our model takes into account the Earth’s gravitational potential, luni-solar and planetary gravitational perturbations and direct solar radiation pressure. Based on the analysis of the energy conservation and on a comparison with a high order non-symplectic integrator, we show that our algorithm allows us to use large time steps and keep accurate results. We also propose an innovative method to model Earth’s shadow crossings by means of a smooth shadow function. In the particular framework of symplectic integration, such a function needs to be included analytically in the equations of motion in order to prevent numerical drifts of the energy. For the sake of completeness, both cylindrical shadows and penumbra transitions models are considered. We show that both models are not equivalent and that big discrepancies actually appear between associated orbits, especially for high area-to-mass ratios.     

Reanalysis of radiation belt electron phase space density using various boundary conditions and loss models

Data assimilation is becoming an increasingly important tool for understanding the near Earth hazardous radiation environments. Reanalysis of the radiation belts can be used to identify the electron acceleration mechanism and distinguish local acceleration from radial diffusion. However, for any practical applications we need to determine how reliable is reanalysis, and how significant is the dependence of the results on the assumptions of the code and choice of boundary conditions. We present the sensitivity of reanalysis of the radiation belt electron phase space density (PSD) to the assumed location of the outer boundary, using the VERB code and a Kalman filter. We analyze the sensitivity of reanalysis to changes in the electron-loss throughout the domain, and the sensitivity to the assumed boundary condition and its effect on the innovation vector. All the simulations presented in this study for all assumed loss models and boundary conditions, show that peaks in the phase space density of relativistic electrons build up between 4.5 and 6 R_E during relativistic electron flux enhancements in the outer radiation belt. This clearly shows that peaks build up in the heart of the electron radiation belt independent of the assumptions in the model, and that local acceleration is operating there. The work here is also an important step toward performing reanalysis using observations from current and future missions.     

An estimation of tropospheric corrections using GPS and synoptic data: Improving Urmia Lake water level time series from Jason-2 and SARAL/AltiKa satellite altimetry

Tropospheric correction is one of the most important corrections in satellite altimetry measurements. Tropospheric wet and dry path delays have strong dependence on temperature, pressure and humidity. Tropospheric layer has particularly high variability over coastal regions due to humidity, wind and temperature gradients. Depending on the extent of water body and wind conditions over an inland water, Wet Tropospheric Correction (WTC) is within the ranges from a few centimeters to tens of centimeters. Therefore, an extra care is needed to estimate tropospheric corrections on the altimetric measurements over inland waters. This study assesses the role of tropospheric correction on the altimetric measurements over the Urmia Lake in Iran. For this purpose, four types of tropospheric corrections have been used: (i) microwave radiometer (MWR) observations, (ii) tropospheric corrections computed from meteorological models, (iii) GPS observations and (iv) synoptic station data. They have been applied to Jason-2 track no. 133 and SARAL/AltiKa track no. 741 and 356 corresponding to 117–153 and the 23–34 cycles, respectively. In addition, the corresponding measurements of PISTACH and PEACHI, include new retracking method and an innovative wet tropospheric correction, have also been used. Our results show that GPS observation leads to the most accurate tropospheric correction. The results obtained from the PISTACH and PEACHI projects confirm those obtained with the standard SGDR, i.e., the role of GPS in improving the tropospheric corrections. It is inferred that the MWR data from Jason-2 mission is appropriate for the tropospheric corrections, however the SARAL/AltiKa one is not proper because Jason-2 possesses an enhanced WTC near the coast. Furthermore, virtual stations are defined for assessment of the results in terms of time series of Water Level Height (WLH). The results show that GPS tropospheric corrections lead to the most accurate WLH estimation for the selected virtual stations, which improves the accuracy of the obtained WLH time series by about 5%.