Comparação de modelos para o cálculo de pertubações orbitais devidas à maré terrestre

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Pertubações orbitais devidas a maré terrestre

Pós-graduação em Física - FEG

Determinação de órbitas com o GPS através de mínimos quadrados recursivo com rotações de Givens

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A new analysis of the GJ581 extrasolar planetary system

We have done a new analysis of the available observations of the GJ581 exoplanetary system. Today this system is controversial due to choices that can be done in the orbital determination. The main ones are the occurrence of aliases and the additional bodies-the planets f and g-announced in Vogt et al. (Astrophys J 723:954-965, 2010). Any dynamical study of exoplanets requires the good knowledge of the orbital elements and the investigations involving the planet g are particularly interesting, since this body would lie in the habitable zone (HZ) of the star GJ581. This region, for this system, is very attractive of the dynamical point of view due to several resonances of two and three bodies present there. In this work, we investigate the conditions under which the planet g may exist. We stress the fact that the planet g is intimately related with the orbital elements of the planet d; more precisely, we conclude that it is not possible to disconnect its existence from the determination of the eccentricity of the planet d. Concerning the planet f, we have found one solution with period a parts per thousand 450 days, but we are judicious about any affirmation concerning this body because its signal is in the threshold of detection and the high period is in a spectral region where the occurrence of aliases is very common. Besides, we outline some dynamical features of the HZ with the dynamical map and point out the role played by some resonances laying there.

Design and implementation of a novel multi-constellation FPGA-based dual frequency GNSS receiver for space applications

The PhD activity described in the document is part of the Microsatellite and Microsystem Laboratory of the II Faculty of Engineering, University of Bologna. The main objective is the design and development of a GNSS receiver for the orbit determination of microsatellites in low earth orbit. The development starts from the electronic design and goes up to the implementation of the navigation algorithms, covering all the aspects that are involved in this type of applications. The use of GPS receivers for orbit determination is a consolidated application used in many space missions, but the development of the new GNSS system within few years, such as the European Galileo, the Chinese COMPASS and the Russian modernized GLONASS, proposes new challenges and offers new opportunities to increase the orbit determination performances. The evaluation of improvements coming from the new systems together with the implementation of a receiver that is compatible with at least one of the new systems, are the main activities of the PhD. The activities can be divided in three section: receiver requirements definition and prototype implementation, design and analysis of the GNSS signal tracking algorithms, and design and analysis of the navigation algorithms. The receiver prototype is based on a Virtex FPGA by Xilinx, and includes a PowerPC processor. The architecture follows the software defined radio paradigm, so most of signal processing is performed in software while only what is strictly necessary is done in hardware. The tracking algorithms are implemented as a combination of Phase Locked Loop and Frequency Locked Loop for the carrier, and Delay Locked Loop with variable bandwidth for the code. The navigation algorithm is based on the extended Kalman filter and includes an accurate LEO orbit model.

Investigation on the Navigation Anomaly of Pioneer 10 and 11 probes

The present work consists of the investigation of the navigation of Pioneer 10 and 11 probes becoming known as the “Pioneer Anomaly”: the trajectories followed by the spacecrafts did not match the ones retrieved with standard navigation software. Mismatching appeared as a linear drift in the Doppler data received by the spacecrafts, which has been ascribed to a constant sunward acceleration of about 8.5×10-10 m/s2. The study presented hereafter tries to find a convincing explanation to this discrepancy. The research is based on the analysis of Doppler tracking data through the ODP (Orbit Determination Program), developed by NASA/JPL. The method can be summarized as: seek for any kind of physics affecting the dynamics of the spacecraft or the propagation of radiometric data, which may have not been properly taken into account previously, and check whether or not these might rule out the anomaly. A major effort has been put to build a thermal model of the spacecrafts for predicting the force due to anisotropic thermal radiation, since this is a model not natively included in the ODP. Tracking data encompassing more than twenty years of Pioneer 10 interplanetary cruise, plus twelve years of Pioneer 11 have been analyzed in light of the results of the thermal model. Different strategies of orbit determination have been implemented, including single arc, multi arc and stochastic filters, and their performance compared. Orbital solutions have been obtained without the needing of any acceleration other than the thermal recoil one indicating it as the responsible for the observed linear drift in the Doppler residuals. As a further support to this we checked that inclusion of additional constant acceleration as does not improve the quality of orbital solutions. All the tests performed lead to the conclusion that no anomalous acceleration is acting on Pioneers spacecrafts.

An Integrated Transmission-Media Noise Calibration Software For Deep-Space Radio Science Experiments

The thesis describes the implementation of a calibration, format-translation and data conditioning software for radiometric tracking data of deep-space spacecraft. All of the available propagation-media noise rejection techniques available as features in the code are covered in their mathematical formulations, performance and software implementations. Some techniques are retrieved from literature and current state of the art, while other algorithms have been conceived ex novo. All of the three typical deep-space refractive environments (solar plasma, ionosphere, troposphere) are dealt with by employing specific subroutines. Specific attention has been reserved to the GNSS-based tropospheric path delay calibration subroutine, since it is the most bulky module of the software suite, in terms of both the sheer number of lines of code, and development time. The software is currently in its final stage of development and once completed will serve as a pre-processing stage for orbit determination codes. Calibration of transmission-media noise sources in radiometric observables proved to be an essential operation to be performed of radiometric data in order to meet the more and more demanding error budget requirements of modern deep-space missions. A completely autonomous and all-around propagation-media calibration software is a novelty in orbit determination, although standalone codes are currently employed by ESA and NASA. The described S/W is planned to be compatible with the current standards for tropospheric noise calibration used by both these agencies like the AMC, TSAC and ESA IFMS weather data, and it natively works with the Tracking Data Message file format (TDM) adopted by CCSDS as standard aimed to promote and simplify inter-agency collaboration.

Design of a GNSS receiver for the ESEO mission

This thesis was carried out inside the ESA's ESEO mission and focus in the design of one of the secondary payloads carried on board the spacecraft: a GNSS receiver for orbit determination. The purpose of this project is to test the technology of the orbit determination in real time applications by using commercial components. The architecture of the receiver includes a custom part, the navigation computer, and a commercial part, the front-end, from Novatel, with COCOM limitation removed, and a GNSS antenna. This choice is motivated by the goal of demonstrating the correct operations in orbit, enabling a widespread use of this technology while lowering the cost and time of the device’s assembly. The commercial front-end performs GNSS signal acquisition, tracking and data demodulation and provides raw GNSS data to the custom computer. This computer processes this raw observables, that will be both transferred to the On-Board Computer and then transmitted to Earth and provided as input to the recursive estimation filter on-board, in order to obtain an accurate positioning of the spacecraft, using the dynamic model. The main purpose of this thesis, is the detailed design and development of the mentioned GNSS receiver up to the ESEO project Critical Design Review, including requirements definition, hardware design and breadboard preliminary test phase design.

An Instrument Design for Space-Based Optical Observation of Space Debris

Currently, observations of space debris are primarily performed with ground-based sensors. These sensors have a detection limit at some centimetres diameter for objects in Low Earth Orbit (LEO) and at about two decimetres diameter for objects in Geostationary Orbit (GEO). The few space-based debris observations stem mainly from in-situ measurements and from the analysis of returned spacecraft surfaces. Both provide information about mostly sub-millimetre-sized debris particles. As a consequence the population of centimetre- and millimetre-sized debris objects remains poorly understood. The development, validation and improvement of debris reference models drive the need for measurements covering the whole diameter range. In 2003 the European Space Agency (ESA) initiated a study entitled “Space-Based Optical Observation of Space Debris”. The first tasks of the study were to define user requirements and to develop an observation strategy for a space-based instrument capable of observing uncatalogued millimetre-sized debris objects. Only passive optical observations were considered, focussing on mission concepts for the LEO, and GEO regions respectively. Starting from the requirements and the observation strategy, an instrument system architecture and an associated operations concept have been elaborated. The instrument system architecture covers the telescope, camera and onboard processing electronics. The proposed telescope is a folded Schmidt design, characterised by a 20 cm aperture and a large field of view of 6°. The camera design is based on the use of either a frame-transfer charge coupled device (CCD), or on a cooled hybrid sensor with fast read-out. A four megapixel sensor is foreseen. For the onboard processing, a scalable architecture has been selected. Performance simulations have been executed for the system as designed, focussing on the orbit determination of observed debris particles, and on the analysis of the object detection algorithms. In this paper we present some of the main results of the study. A short overview of the user requirements and observation strategy is given. The architectural design of the instrument is discussed, and the main tradeoffs are outlined. An insight into the results of the performance simulations is provided.

Earth gravity field recovery using GPS, GLONASS, and SLR satellites

The time variable Earth’s gravity field provides the information about mass transport within the system Earth, i.e., the relationship of mass transport between atmosphere, oceans, and land hydrology. We recover the low-degree parameters of the time variable gravity field using microwave observations from GPS and GLONASS satellites and from SLR data to five geodetic satellites, namely LAGEOS-1/2, Starlette, Stella, and AJISAI. GPS satellites are particularly sensitive to specific coefficients of the Earth's gravity field, because of the deep 2:1 orbital resonance with Earth rotation (two revolutions of the GPS satellites per sidereal day). The resonant coefficients cause, among other, a “secular” drift (actually periodic variations of very long periods) of the semi-major axes of up to 5.3 m/day of GPS satellites. We processed 10 years of GPS and GLONASS data using the standard orbit models from the Center of Orbit Determination in Europe (CODE) with a simultaneous estimation of the Earth gravity field coefficients and other parameters, e.g., satellite orbit parameters, station coordinates, Earth rotation parameters, troposphere delays, etc. The weekly GNSS gravity solutions up to degree and order 4/4 are compared to the weekly SLR gravity field solutions. The SLR-derived geopotential coefficients are compared to monthly GRACE and CHAMP results.

Short-arc tracklet association for geostationary objects

Measurement association and initial orbit determination is a fundamental task when building up a database of space objects. This paper proposes an efficient and robust method to determine the orbit using the available information of two tracklets, i.e. their line-of-sights and their derivatives. The approach works with a boundary-value formulation to represent hypothesized orbital states and uses an optimization scheme to find the best fitting orbits. The method is assessed and compared to an initial-value formulation using a measurement set taken by the Zimmerwald Small Aperture Robotic Telescope of the Astronomical Institute at the University of Bern. False associations of closely spaced objects on similar orbits cannot be completely eliminated due to the short duration of the measurement arcs. However, the presented approach uses the available information optimally and the overall association performance and robustness is very promising. The boundary-value optimization takes only around 2% of computational time when compared to optimization approaches using an initial-value formulation. The full potential of the method in terms of run-time is additionally illustrated by comparing it to other published association methods.

Association of optical tracklets from a geosynchronous belt survey via the direct Bayesian admissible region approach

The direct Bayesian admissible region approach is an a priori state free measurement association and initial orbit determination technique for optical tracks. In this paper, we test a hybrid approach that appends a least squares estimator to the direct Bayesian method on measurements taken at the Zimmerwald Observatory of the Astronomical Institute at the University of Bern. Over half of the association pairs agreed with conventional geometric track correlation and least squares techniques. The remaining pairs cast light on the fundamental limits of conducting tracklet association based solely on dynamical and geometrical information.

Capability of a space-based space surveillance system to detect and track objects in GEO, MEO and LEO orbits

In this paper we present the results from the coverage and the orbit determination accuracy simulations performed within the recently completed ESA study “Assessment Study for Space Based Space Surveillance (SBSS) Demonstration System” (Airbus Defence and Space consortium). This study consisted in investigating the capability of a space based optical sensor (SBSS) orbiting in low Earth orbit (LEO) to detect and track objects in GEO (geosynchronous orbit), MEO (medium Earth orbit) and LEO and to determinate and improve initial orbits from such observations. Space based systems may achieve better observation conditions than ground based sensors in terms of astrometric accuracy, detection coverage, and timeliness. The primary observation mode of the proposed SBSS demonstrator is GEO surveillance, i.e. the systematic search and detection of unknown and known objects. GEO orbits are specific and unique orbits from dynamical point of view. A space-based sensor may scan the whole GEO ring within one sidereal day if the orbit and pointing directions are chosen properly. For an efficient survey, our goal was to develop a leak-proof GEO fence strategy. Collaterally, we show that also MEO, LEO and other (GTO,Molniya, etc.) objects would be possible to observe by the system and for a considerable number of LEO objects to down to size of 1 cm we can obtain meaningful statistical data for improvement and validation of space debris environment models

Comparison of GOCE-GPS gravity fields derived by different approaches

Several techniques have been proposed to exploit GNSS-derived kinematic orbit information for the determination of long-wavelength gravity field features. These methods include the (i) celestial mechanics approach, (ii) short-arc approach, (iii) point-wise acceleration approach, (iv) averaged acceleration approach, and (v) energy balance approach. Although there is a general consensus that—except for energy balance—these methods theoretically provide equivalent results, real data gravity field solutions from kinematic orbit analysis have never been evaluated against each other within a consistent data processing environment. This contribution strives to close this gap. Target consistency criteria for our study are the input data sets, period of investigation, spherical harmonic resolution, a priori gravity field information, etc. We compare GOCE gravity field estimates based on the aforementioned approaches as computed at the Graz University of Technology, the University of Bern, the University of Stuttgart/Austrian Academy of Sciences, and by RHEA Systems for the European Space Agency. The involved research groups complied with most of the consistency criterions. Deviations only occur where technical unfeasibility exists. Performance measures include formal errors, differences with respect to a state-of-the-art GRACE gravity field, (cumulative) geoid height differences, and SLR residuals from precise orbit determination of geodetic satellites. We found that for the approaches (i) to (iv), the cumulative geoid height differences at spherical harmonic degree 100 differ by only ≈10 % ; in the absence of the polar data gap, SLR residuals agree by ≈96 % . From our investigations, we conclude that real data analysis results are in agreement with the theoretical considerations concerning the (relative) performance of the different approaches.

Processing 20 years of SLR observations to GNSS satellites

We process 20 years of SLR observations to GPS and GLONASS satellites using the reprocessed 3-day and 1-day microwave orbits provided by the Center for Orbit Determination in Europe (CODE) for the period 1994-2013. We study the dependency of the SLR residuals on the type, size, and a number of corner cubes in satellite laser reflector arrays (LRA). We show that the mean SLR residuals and the RMS of residuals depend on the coating of LRA and the block or type of GNSS satellites. The SLR mean residuals are also a function of the equipment used at SLR stations including detector types and detecting modes.