DOCSLIB.ORG

Computational Methods for the Long-Term Propagation of Space Debris Orbits

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Computational Methods for the Long-Term Propagation of Space Debris Orbits Computational Methods for the Long-Term Propagation of Space Debris Orbits Robin Hofsteenge Master of Science Thesis Astrodynamics and Space Missions Faculty of Aerospace Engineering Computational Methods for the Long-Term Propagation of Space Debris Orbits MASTER OF SCIENCE THESIS For obtaining the degree of Master of Science in Aerospace Engineering at Delft University of Technology Robin Hofsteenge December 1, 2013 Faculty of Aerospace Engineering · Delft University of Technology Robin Hofsteenge, BSc Chair of Astrodynamics and Space Missions Faculty of Aerospace Engineering Delft University of Technology Kluyverweg 1, 2629 HS, Delft The Netherlands E-mail: [email protected] Cover figure: Part of a destroyed solar panel in orbit around the Earth. Final Version Document Version 1.1 December 1, 2013 This document was typeset using LATEX 2e. Preface The thesis project constitutes the final part of the Master of Science (MSc) program in Aerospace Engineering at Delft University of Technology. Specifically, this thesis project is about computational methods for the long-term propagation of space debris orbits. Prior to this project, a literature study was carried out. The present document continues on the findings of the literature study, but can be read as a stand-alone document. The report focuses on methods and concepts that have actually been implemented in the simulation code developed for the project. For a more complete treatment of the different perturbing forces acting on satellites or a more comprehensive overview of integration methods, the interested reader is encouraged to consult the report of the literature study (Hofsteenge, 2012). I would like to take this opportunity to express my gratitude toward my thesis supervisor, Ron Noomen, for his helpful guidance during the project. Our weekly meetings not only made sure I remained on the right track, but were also useful in keeping me inspired, despite any difficulties encountered. I would also like to thank my fellow MSc students on the ninth floor of the Faculty of Aerospace En- gineering for the pleasant working atmosphere. Finally, I would like to thank my parents for supporting me throughout my academic career. Robin Hofsteenge Delft, December 1, 2013 5 Abstract Space debris poses a significant problem for the space sector. This problem relates to potential collisions of debris objects with active satellites, which in many cases will lead to catastrophic damage. Due to the absence of natural decay mechanisms in the higher regions of space, debris objects in these regions have very long orbital lifetimes. In order to assess the hazards posed to active satellites, it is relevant to be able to predict how the orbits of these debris objects behave on long timescales. A simulation code in C++ has been created for this thesis project, capable of ef- ficient propagation of space debris trajectories over long periods of time (typically a century or more), while taking into account various relevant perturbing forces. The simulation code can be applied to simulate the orbits of debris objects with a wide range of area-to-mass ratios, from intact satellites to tiny flecks of paint. The results produced with the simulation code have been verified to be consistent with results presented in recent research papers on space debris. An extensive performance comparison has been made regarding the efficiency of different computational methods for carrying out accurate, long-term integra- tions of space debris orbits. Both traditional integration methods and symplectic integration methods were tested, the latter of which are interesting because of their energy conservation properties. All methods were also combined with different formulations of the equations of motion. Of the methods tested, the Dormand-Prince 8(7) integration method combined with Gauss’ form of Lagrange’s planetary equations in modified equinoctial el- ements was found to be the most efficient. The performance of the symplectic integration methods was markedly less for this application than for the integration of completely Hamiltonian systems, though it was certainly acceptable. The simulation code was also applied to predict the long-term orbital evolu- tion for debris objects in GEO and GNSS graveyard orbits. While proposed GEO graveyard orbits were found to be safe, graveyard orbits in the GNSS region were found to be susceptible to resonances induced by the luni-solar perturbations, and hence, require a careful selection of the initial orbital parameters. In all cases, debris objects with high area-to-mass ratios were determined to be dangerous to active satellites, regardless of the initial conditions of the graveyard orbit. 7 Contents Preface 5 Abstract 7 List of Symbols 13 List of Abbreviations 17 1 Introduction 19 2 Space Debris 21 2.1 History . 21 2.2 Dangers Related to Space Debris . 23 2.3 The Space Debris Environment . 23 2.4 Sources of Space Debris . 24 2.5 Characteristics of Debris Objects . 26 2.6 Guidelines Regarding Space Debris . 27 3 The GEO and GNSS Debris Environments 29 3.1 The GEO Debris Environment . 29 3.1.1 Debris Population in the GEO Region . 29 3.1.2 Existing Research . 32 3.2 The GNSS Debris Environment . 33 3.2.1 Debris Population in the GNSS Region . 33 3.2.2 Existing Research . 35 4 Force Model 37 4.1 Overview . 37 4.2 Central Gravitational Force . 40 4.3 Deviations in the Earth’s Gravity Field . 40 4.4 Gravitational Attraction of the Sun and the Moon . 45 4.5 Solar Radiation Pressure . 46 9 Contents 10 5 Orbit Formulation 53 5.1 Basic Laws of Astrodynamics . 53 5.2 Coordinate Systems . 54 5.2.1 Cartesian Coordinates . 54 5.2.2 Orbital Elements . 55 5.2.3 Modified Equinoctial Elements . 57 5.3 Modeling Perturbed Orbits . 58 5.3.1 Method of Cowell . 59 5.3.2 Method of Encke . 59 5.3.3 Method of Variation of Parameters . 60 5.4 Choice of Propagation Methods . 64 6 Traditional Integration Methods 67 6.1 Introduction . 68 6.2 Accuracy and Efficiency . 75 6.3 Fixed Step Size Methods . 76 6.3.1 Runge-Kutta 4 . 76 6.3.2 General Runge-Kutta Methods . 77 6.4 Adaptive Step Size Methods . 78 6.4.1 General Aspects . 78 6.4.2 Runge-Kutta-Fehlberg 5(6) . 80 6.4.3 Dormand-Prince 8(7) . 80 6.5 Choice of Integration Methods . 82 7 Symplectic Integration Methods 85 7.1 Exponential Operators . 85 7.2 Hamiltonian Mechanics . 87 7.3 Symplectic Mappings . 88 7.4 Symplectic Integrators . 89 7.4.1 General Formulation . 89 7.4.2 Hamiltonian Splitting . 89 7.4.3 Kinoshita’s Method . 90 7.4.4 SABA2n Methods . 91 7.5 Methods for Splitting the Hamiltonian . 93 7.5.1 T + V Splitting . 93 7.5.2 Wisdom-Holman Splitting . 94 8 Verification of the Simulation Code 95 8.1 Overview of the Simulation Code . 95 8.2 Two-Body Problem . 97 8.3 Positions of the Sun and the Moon . 98 8.4 Individual Perturbations . 100 8.4.1 J2-Term of the Earth’s Gravity Field . 101 8.4.2 Gravitational Attraction of the Sun . 104 Contents 11 8.4.3 Gravitational Attraction of the Moon . 105 8.4.4 Solar Radiation Pressure . 106 8.5 Long-Term Behavior . 110 9 Performance Comparison of Computational Methods 119 9.1 Overview . 120 9.2 Testing Methodology . 121 9.3 Two-Body Problem . 123 9.3.1 Round-Off Errors . 123 9.3.2 Error Growth . 126 9.3.3 Performance for a Circular Orbit . 129 9.3.4 Performance for a Highly Eccentric Orbit . 132 9.4 Perturbed Problem . 134 9.4.1 Important Remarks . 134 9.4.2 Choice of Reference . 138 9.4.3 Case I: Near-Circular GEO Graveyard Orbit – Low A/m . 140 9.4.4 Case II: Near-Circular GEO Graveyard Orbit – High A/m 145 9.4.5 Case III: Highly Eccentric GPS Graveyard Orbit – Low A/m ............................. 150 9.4.6 Case IV: Near-Circular GPS Graveyard Orbit – High A/m 155 9.5 Discussion . 160 10 Long-Term Debris Orbit Predictions 165 10.1 Introduction . 165 10.2 GEO Graveyard Orbits . 166 10.3 GNSS Graveyard Orbits . 170 10.3.1 Low Altitude Eccentric Orbits . 170 10.3.2 High Altitude Eccentric Orbits . 174 10.3.3 Near-Circular Orbits . 178 10.4 Discussion . 182 11 Conclusions and Recommendations 185 11.1 Conclusions . 185 11.2 Recommendations . 188 A JGM-3 Gravitational Coefficients 189 B Routines for the Positions of the Sun and the Moon 191 C Important Equations in Astrodynamics 195 Bibliography 197 List of Symbols A Area [m2] a Acceleration vector of orbiting object [m/s2] a Semi-major axis [m] CR Radiation pressure coefficient [-] Cn;m Gravity field coefficient [-] c Speed of light, c = 2:998792458 · 108 [m/s] D Difference between the mean longitudes of the Sun and the Moon [◦] d Degrees of freedom of system E Eccentric anomaly [◦] En Energy of photon [J] er Unit position vector of the object [-] e Unit vector pointing from the object to the Sun [-] eSun Unit vector pointing to the Sun [-] e Eccentricity [-] e Local truncation error F Mean angular distance of the Moon from the ascending node [◦] f Force function f Collection of all perturbing accelerations that cannot be expressed as a potential [m/s2] 2 ft Total acceleration [m/s ] 2 fN Transverse component of perturbing acceleration [m/s ] 2 fS Radial component of perturbing acceleration [m/s ] 2 fW Normal component of perturbing acceleration [m/s ] G Universal gravitational constant, G = 6:67384 · 10−11 [m2/kg s2] g0 Jacobian matrix H Angular momentum [m2/s] Ha Altitude of apogee [m] Hp Altitude of perigee [m] DHgeo Difference in altitude with the geostationary altitude [m] 13 Contents 14 H Hamiltonian [m2/s2] h Integration step size [s] i Inclination [◦] J Symplectic identity [-] Jn (=−Cn0) Zonal gravity field coefficient [-] Ki Slope function ki Slope
Load more

Recommended publications
  • Orbit Determination Using Modern Filters/Smoothers and Continuous Thrust Modeling
    Orbit Determination Using Modern Filters/Smoothers and Continuous Thrust Modeling by Zachary James Folcik B.S. Computer Science Michigan Technological University, 2000 SUBMITTED TO THE DEPARTMENT OF AERONAUTICS AND ASTRONAUTICS IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN AERONAUTICS AND ASTRONAUTICS AT THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY JUNE 2008 © 2008 Massachusetts Institute of Technology. All rights reserved. Signature of Author:_______________________________________________________ Department of Aeronautics and Astronautics May 23, 2008 Certified by:_____________________________________________________________ Dr. Paul J. Cefola Lecturer, Department of Aeronautics and Astronautics Thesis Supervisor Certified by:_____________________________________________________________ Professor Jonathan P. How Professor, Department of Aeronautics and Astronautics Thesis Advisor Accepted by:_____________________________________________________________ Professor David L. Darmofal Associate Department Head Chair, Committee on Graduate Students 1 [This page intentionally left blank.] 2 Orbit Determination Using Modern Filters/Smoothers and Continuous Thrust Modeling by Zachary James Folcik Submitted to the Department of Aeronautics and Astronautics on May 23, 2008 in Partial Fulfillment of the Requirements for the Degree of Master of Science in Aeronautics and Astronautics ABSTRACT The development of electric propulsion technology for spacecraft has led to reduced costs and longer lifespans for certain
    [Show full text]
  • Assessment of Earth Gravity Field Models in the Medium to High Frequency Spectrum Based on GRACE and GOCE Dynamic Orbit Analysis
    Article Assessment of Earth Gravity Field Models in the Medium to High Frequency Spectrum Based on GRACE and GOCE Dynamic Orbit Analysis Thomas D. Papanikolaou 1,2,* and Dimitrios Tsoulis 3 1 Geoscience Australia, Cnr Jerrabomberra Ave and Hindmarsh Drive, Symonston, ACT 2609, Australia 2 Cooperative Research Centre for Spatial Information, Docklands, VIC 3008, Australia 3 Department of Geodesy and Surveying, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece; [email protected] * Correspondence: [email protected] Received: 22 October 2018; Accepted: 23 November 2018; Published: 27 November 2018 Abstract: An analysis of current static and time-variable gravity field models is presented focusing on the medium to high frequencies of the geopotential as expressed by the spherical harmonic coefficients. A validation scheme of the gravity field models is implemented based on dynamic orbit determination that is applied in a degree-wise cumulative sense of the individual spherical harmonics. The approach is applied to real data of the Gravity Field and Steady-State Ocean Circulation (GOCE) and Gravity Recovery and Climate Experiment (GRACE) satellite missions, as well as to GRACE inter-satellite K-band ranging (KBR) data. Since the proposed scheme aims at capturing gravitational discrepancies, we consider a few deterministic empirical parameters in order to avoid absorbing part of the gravity signal that may be included in the monitored orbit residuals. The present contribution aims at a band-limited analysis for identifying characteristic degree ranges and thresholds of the various GRACE- and GOCE-based gravity field models. The degree range 100–180 is investigated based on the degree-wise cumulative approach.
    [Show full text]
  • The Evolution of Earth Gravitational Models Used in Astrodynamics
    JEROME R. VETTER THE EVOLUTION OF EARTH GRAVITATIONAL MODELS USED IN ASTRODYNAMICS Earth gravitational models derived from the earliest ground-based tracking systems used for Sputnik and the Transit Navy Navigation Satellite System have evolved to models that use data from the Joint United States-French Ocean Topography Experiment Satellite (Topex/Poseidon) and the Global Positioning System of satellites. This article summarizes the history of the tracking and instrumentation systems used, discusses the limitations and constraints of these systems, and reviews past and current techniques for estimating gravity and processing large batches of diverse data types. Current models continue to be improved; the latest model improvements and plans for future systems are discussed. Contemporary gravitational models used within the astrodynamics community are described, and their performance is compared numerically. The use of these models for solid Earth geophysics, space geophysics, oceanography, geology, and related Earth science disciplines becomes particularly attractive as the statistical confidence of the models improves and as the models are validated over certain spatial resolutions of the geodetic spectrum. INTRODUCTION Before the development of satellite technology, the Earth orbit. Of these, five were still orbiting the Earth techniques used to observe the Earth's gravitational field when the satellites of the Transit Navy Navigational Sat­ were restricted to terrestrial gravimetry. Measurements of ellite System (NNSS) were launched starting in 1960. The gravity were adequate only over sparse areas of the Sputniks were all launched into near-critical orbit incli­ world. Moreover, because gravity profiles over the nations of about 65°. (The critical inclination is defined oceans were inadequate, the gravity field could not be as that inclination, 1= 63 °26', where gravitational pertur­ meaningfully estimated.
    [Show full text]
  • Draft American National Standard Astrodynamics
    BSR/AIAA S-131-200X Draft American National Standard Astrodynamics – Propagation Specifications, Test Cases, and Recommended Practices Warning This document is not an approved AIAA Standard. It is distributed for review and comment. It is subject to change without notice. Recipients of this draft are invited to submit, with their comments, notification of any relevant patent rights of which they are aware and to provide supporting documentation. Sponsored by American Institute of Aeronautics and Astronautics Approved XX Month 200X American National Standards Institute Abstract This document provides the broad astrodynamics and space operations community with technical standards and lays out recommended approaches to ensure compatibility between organizations. Applicable existing standards and accepted documents are leveraged to make a complete—yet coherent—document. These standards are intended to be used as guidance and recommended practices for astrodynamics applications in Earth orbit where interoperability and consistency of results is a priority. For those users who are purely engaged in research activities, these standards can provide an accepted baseline for innovation. BSR/AIAA S-131-200X LIBRARY OF CONGRESS CATALOGING DATA WILL BE ADDED HERE BY AIAA STAFF Published by American Institute of Aeronautics and Astronautics 1801 Alexander Bell Drive, Reston, VA 20191 Copyright © 200X American Institute of Aeronautics and Astronautics All rights reserved No part of this publication may be reproduced in any form, in an electronic retrieval
    [Show full text]
  • The Joint Gravity Model 3
    Journal of Geophysical Research Accepted for publication, 1996 The Joint Gravity Model 3 B. D. Tapley, M. M. Watkins,1 J. C. Ries, G. W. Davis,2 R. J. Eanes, S. R. Poole, H. J. Rim, B. E. Schutz, and C. K. Shum Center for Space Research, University of Texas at Austin R. S. Nerem,3 F. J. Lerch, and J. A. Marshall Space Geodesy Branch, NASA Goddard Space Flight Center, Greenbelt, Maryland S. M. Klosko, N. K. Pavlis, and R. G. Williamson Hughes STX Corporation, Lanham, Maryland Abstract. An improved Earth geopotential model, complete to spherical harmonic degree and order 70, has been determined by combining the Joint Gravity Model 1 (JGM 1) geopotential coef®cients, and their associated error covariance, with new information from SLR, DORIS, and GPS tracking of TOPEX/Poseidon, laser tracking of LAGEOS 1, LAGEOS 2, and Stella, and additional DORIS tracking of SPOT 2. The resulting ®eld, JGM 3, which has been adopted for the TOPEX/Poseidon altimeter data rerelease, yields improved orbit accuracies as demonstrated by better ®ts to withheld tracking data and substantially reduced geographically correlated orbit error. Methods for analyzing the performance of the gravity ®eld using high-precision tracking station positioning were applied. Geodetic results, including station coordinates and Earth orientation parameters, are signi®cantly improved with the JGM 3 model. Sea surface topography solutions from TOPEX/Poseidon altimetry indicate that the ocean geoid has been improved. Subset solutions performed by withholding either the GPS data or the SLR/DORIS data were computed to demonstrate the effect of these particular data sets on the gravity model used for TOPEX/Poseidon orbit determination.
    [Show full text]
  • Statistical Orbit Determination
    Preface The modem field of orbit determination (OD) originated with Kepler's inter­ pretations of the observations made by Tycho Brahe of the planetary motions. Based on the work of Kepler, Newton was able to establish the mathematical foundation of celestial mechanics. During the ensuing centuries, the efforts to im­ prove the understanding of the motion of celestial bodies and artificial satellites in the modem era have been a major stimulus in areas of mathematics, astronomy, computational methodology and physics. Based on Newton's foundations, early efforts to determine the orbit were focused on a deterministic approach in which a few observations, distributed across the sky during a single arc, were used to find the position and velocity vector of a celestial body at some epoch. This uniquely categorized the orbit. Such problems are deterministic in the sense that they use the same number of independent observations as there are unknowns. With the advent of daily observing programs and the realization that the or­ bits evolve continuously, the foundation of modem precision orbit determination evolved from the attempts to use a large number of observations to determine the orbit. Such problems are over-determined in that they utilize far more observa­ tions than the number required by the deterministic approach. The development of the digital computer in the decade of the 1960s allowed numerical approaches to supplement the essentially analytical basis for describing the satellite motion and allowed a far more rigorous representation of the force models that affect the motion. This book is based on four decades of classroom instmction and graduate- level research.
    [Show full text]
  • The Celestial Mechanics Approach: Theoretical Foundations
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by RERO DOC Digital Library J Geod (2010) 84:605–624 DOI 10.1007/s00190-010-0401-7 ORIGINAL ARTICLE The celestial mechanics approach: theoretical foundations Gerhard Beutler · Adrian Jäggi · Leoš Mervart · Ulrich Meyer Received: 31 October 2009 / Accepted: 29 July 2010 / Published online: 24 August 2010 © Springer-Verlag 2010 Abstract Gravity field determination using the measure- of the CMA, in particular to the GRACE mission, may be ments of Global Positioning receivers onboard low Earth found in Beutler et al. (2010) and Jäggi et al. (2010b). orbiters and inter-satellite measurements in a constellation of The determination of the Earth’s global gravity field using satellites is a generalized orbit determination problem involv- the data of space missions is nowadays either based on ing all satellites of the constellation. The celestial mechanics approach (CMA) is comprehensive in the sense that it encom- 1. the observations of spaceborne Global Positioning (GPS) passes many different methods currently in use, in particular receivers onboard low Earth orbiters (LEOs) (see so-called short-arc methods, reduced-dynamic methods, and Reigber et al. 2004), pure dynamic methods. The method is very flexible because 2. or precise inter-satellite distance monitoring of a close the actual solution type may be selected just prior to the com- satellite constellation using microwave links (combined bination of the satellite-, arc- and technique-specific normal with the measurements of the GPS receivers on all space- equation systems. It is thus possible to generate ensembles crafts involved) (see Tapley et al.
    [Show full text]
  • Non-Averaged Regularized Formulations As an Alternative to Semi-Analytical Orbit Propagation Methods
    Celestial Mechanics and Dynamical Astronomy manuscript No. (will be inserted by the editor) Non-averaged regularized formulations as an alternative to semi-analytical orbit propagation methods Davide Amato ¨ Claudio Bombardelli ¨ Giulio Ba`u ¨ Vincent Morand ¨ Aaron J. Rosengren Received: date / Accepted: date Abstract This paper is concerned with the comparison of semi-analytical and non-averaged propagation methods for Earth satellite orbits. We analyse the total integration error for semi-analytical methods and propose a novel decomposition into dynamical, model truncation, short-periodic, and numerical error com- ponents. The first three are attributable to distinct approximations required by the method of averaging, which fundamentally limit the attainable accuracy. In contrast, numerical error, the only component present in non-averaged methods, can be significantly mitigated by employing adaptive numerical algorithms and regularized formulations of the equations of motion. We present a collection of non-averaged methods based on the integration of existing regularized formulations of the equations of motion through an adaptive solver. We implemented the collection in the orbit propagation code THALASSA, which we make publicly available, and we compared the non-averaged methods to the semi-analytical method implemented in the orbit prop- agation tool STELA through numerical tests involving long-term propagations (on the order of decades) of LEO, GTO, and high-altitude HEO orbits. For the test cases considered, regularized non-averaged methods were found to be up to two times slower than semi-analytical for the LEO orbit, to have comparable speed for the GTO, and to be ten times as fast for the HEO (for the same accuracy).
    [Show full text]
  • Why Atens Enjoy Enhanced Accessibility for Human Space Flight
    (Preprint) AAS 11-449 WHY ATENS ENJOY ENHANCED ACCESSIBILITY FOR HUMAN SPACE FLIGHT Daniel R. Adamo* and Brent W. Barbee† Near-Earth objects can be grouped into multiple orbit classifications, among them being the Aten group, whose members have orbits crossing Earth's with semi-major axes less than 1 astronomical unit. Atens comprise well under 10% of known near-Earth objects. This is in dramatic contrast to results from recent human space flight near-Earth object accessibility studies, where the most favorable known destinations are typically almost 50% Atens. Geocentric dynamics explain this enhanced Aten accessibility and lead to an understanding of where the most accessible near-Earth objects reside. Without a com- prehensive space-based survey, however, highly accessible Atens will remain largely un- known. INTRODUCTION In the context of human space flight (HSF), the concept of near-Earth object (NEO) accessibility is highly subjective (Reference 1). Whether or not a particular NEO is accessible critically depends on mass, performance, and reliability of interplanetary HSF systems yet to be designed. Such systems would cer- tainly include propulsion and crew life support with adequate shielding from both solar flares and galactic cosmic radiation. Equally critical architecture options are relevant to NEO accessibility. These options are also far from being determined and include the number of launches supporting an HSF mission, together with whether consumables are to be pre-emplaced at the destination. Until the unknowns of HSF to NEOs come into clearer focus, the notion of relative accessibility is of great utility. Imagine a group of NEOs, each with nearly equal HSF merit determined from their individual characteristics relating to crew safety, scientific return, resource utilization, and planetary defense.
    [Show full text]
  • Highly-Reduced Dynamic Orbits and Their Use for Global Gravity Field
    HIGHLY-REDUCED DYNAMIC ORBITS AND THEIR USE View metadata, citation and similarFOR papers GLOBAL at core.ac.uk GRAVITY FIELD RECOVERY: brought to you by CORE A SIMULATION STUDY FOR GOCE provided by RERO DOC Digital Library A. JÄGGI1, H. BOCK1, R. PAIL2 AND H. GOIGINGER2 1 University of Bern, Astronomical Institute, Sidlerstrasse 5, 3012 Bern, Switzerland ([email protected], [email protected]) 2 TU Graz, Institute of Navigation and Satellite Geodesy, Steyrergasse 30, 8010 Graz, Austria ([email protected], [email protected]) Received: November 2, 2007; Revised: February 4, 2008; Accepted: March 17, 2008 ABSTRACT The so-called highly reduced-dynamic (HRD) orbit determination strategy and its use for the determination of the Earth’s gravitational field are analyzed. We discuss the functional model for the generation of HRD orbits, which are a compromise of the two extreme cases of dynamic and purely geometrically determined kinematic orbits. For gravity field recovery the energy integral approach is applied, which is based on the law of energy conservation in a closed system. The potential of HRD orbits for gravity field determination is studied in the frame of a simulated test environment based on a realistic GOCE orbit configuration. The results are analyzed, assessed, and compared with the respective reference solutions based on a kinematic orbit scenario. The main advantage of HRD orbits is the fact that they contain orbit velocity information, thus avoiding numerical differentiation on the orbit positions. The error characteristics are usually much smoother, and the computation of gravity field solutions is more efficient, because less densely sampled orbit information is sufficient.
    [Show full text]
  • Improvements in Autonomous GPS Navigation of Low Earth Orbit Satellites
    Ph.D. Thesis Doctoral Program in Aerospace Science & Technology Improvements in autonomous GPS navigation of Low Earth Orbit satellites Pere Ramos-Bosch Advisors: Dr. Manuel Hern´andezPajares [1] Dr. J.Miguel Juan Zornoza [1] Dr. Oliver Montenbruck [2] [1] Research group of Astronomy and Geomatics (gAGE) Depts. of Applied Mathematics IV and Applied Physics Universitat Polit`ecnicade Catalunya (UPC), Spain [2] German Space Operations Center (DLR), Germany September 10, 2008 ii Acknowledgements I would like to thank my advisors, Dr. Manuel Hern´andezPajares, Dr. Miguel Juan Zornoza and Dr. Oliver Montenbruck for their enthusiastic support and useful discussions in the whole development of this thesis. Without their unconditional aid that work would had not been possible. I would like to thank the funding support for both the thesis and a stage at the German Space Operations Center (Deutsches Zentrum f¨urLuft- und Raumfahrt - DLR) from the “Departament d’Universitats, Recerca i Societat de la Informaci´ode la Generalitat de Catalunya” and from the European Social Fund. This work started in the frame of the Neural Networks for Radion- avigation project funded by ESA (grant number ITT4584). I would like to thank the project team for their support, and to the Institute of Navigation for their Student Sponsorship to present the initial version of this work at ION GNSS 2006, held in Fort Worth, USA, in September 2006. Special thanks to Bruce Haines of JPL for kindly providing attitude data for JASON satellite. I would also like to thank all the people in the group of Astronomy and GEomatics (gAGE), it has been a real pleasure to share with you all kind of discussions.
    [Show full text]
  • Pseudo-Stochastic Orbit Modeling Techniques for Low-Earth Orbiters
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by RERO DOC Digital Library J Geod (2006) 80: 47–60 DOI 10.1007/s00190-006-0029-9 ORIGINAL ARTICLE A. Jäggi · U. Hugentobler · G. Beutler Pseudo-stochastic orbit modeling techniques for low-Earth orbiters Received: 1 March 2005 / Accepted: 24 January 2006 / Published online: 30 March 2006 © Springer-Verlag 2006 Abstract The Earth’s non-spherical mass distribution and Keywords Low-Earth orbiter (LEO) · Precise orbit atmospheric drag cause the strongest perturbations on very determination (POD) · Pseudo-stochastic orbit modeling · low-Earth orbiting satellites (LEOs). Models of gravitational GPS and non-gravitational accelerations are utilized in dynamic precise orbit determination (POD) with GPS data, but it is 1 Introduction also possible to derive LEO positions based on GPS pre- cise point positioning without dynamical information. We Gravitational forces related to the Earth’s oblateness and the use the reduced-dynamic technique for LEO POD, which non-gravitational forces due to residual atmospheric densities combines the geometric strength of the GPS observations are responsible for the strongest perturbations acting on sat- with the force models, and investigate the performance of ellites in very low-Earth orbits. These forces produce large different pseudo-stochastic orbit parametrizations, such as periodic variations in the orbit and a decay in the orbital instantaneous velocity changes (pulses), piecewise constant height. Radial orbit differences caused by atmospheric drag accelerations, and continuous piecewise linear accelerations. after one day may reach 150 m for an initial height of 500 km The estimation of such empirical orbit parameters in a stan- (Beutler 2004) during normal solar activity.
    [Show full text]