Table Of ContentMASTER'S THESIS
Orbital Accuracy Analysis for a
Geosynchronous Synthetic Aperture
Radar Imaging Satellite
enol Özkan
Master of Science
Space Engineering - Space Master
Luleå University of Technology
Department of Computer Science, Electrical and Space Engineering
CRANFIELD UNIVERSITY
SCHOOL OF ENGINEERING
MSc THESIS
Academic Year 2010-2011
¨
S¸enol Ozkan
Orbital Accuracy Analysis for a Geosynchronous Synthetic
Aperture Radar Imaging Satellite
Supervisors: Dr. Stephen E. Hobbs
Dr. Peter Roberts
July 2011
This thesis is submitted in partial (75%) fulfillment of the requirements for the
Degree of MSc in Astronautics and Space Engineering.
(cid:13)c Cranfield University, 2011. All rights reserved. No part of this publication may
be reproduced without the written permission of the copyright holder.
i
Abstract
In geosynchronous region, operating a synthetic aperture radar can be advantageous
compared to low Earth orbiting radars. Difficulties arise due to the long integra-
tion duration requirement of this configuration. Image recovery from the signals
recorded during long integration durations depends on the quality of the phase his-
tory knowledge. Knowing the phase history accurately requires modelling the phase
shifts that might influence the image recovery process. In this project, the orbital
perturbation sources that can cause phase shifts have been analysed and modelled.
An orbit propagator software was developed in order to observe the effects of the
perturbations on the orbit, and a discussion was made about the uncertainties as-
sociated with the developed software. It was seen that the models developed in this
study are accurate enough to have a GEOSAR mission with 8 hours of integration
duration. However, it must be noted that a solar pressure model study was not
included in this work, and later it should be carried out in order to cover all of the
perturbation sources.
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iii
Acknowledgements
I would like to thank my supervisors Dr. Stephen Hobbs and Dr. Peter Roberts for
their guidance throughout the project.
I also want to thank my dear friend B. Y. Kaya for his support.
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CONTENTS v
Contents
Contents v
List of Figures ix
List of Tables xi
Abbreviations xiii
1 Introduction 1
1.1 Aim of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Structure of the Document . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Literature Review 3
2.1 GEO Environment and GEOSAR . . . . . . . . . . . . . . . . . . . . 3
2.1.1 Geosynchronous Orbit . . . . . . . . . . . . . . . . . . . . . . 3
2.1.2 Synthetic Aperture Radar . . . . . . . . . . . . . . . . . . . . 4
2.1.3 SAR Requirements in GEO . . . . . . . . . . . . . . . . . . . 5
2.2 Coordinate Systems and Time Systems . . . . . . . . . . . . . . . . . 7
2.2.1 Coordinate Systems . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.2 Time Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Perturbation Sources in GEO . . . . . . . . . . . . . . . . . . . . . . 9
vi CONTENTS
2.3.1 Non-spherical Gravitational Potential . . . . . . . . . . . . . . 10
2.3.2 Lunisolar and Third Body Perturbations . . . . . . . . . . . . 13
2.3.3 Solar Pressure Perturbation & Albedo . . . . . . . . . . . . . 14
2.3.4 Tidal Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.5 Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.6 Micrometeoroids . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3.7 Atmospheric Drag . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4 Perturbation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4.1 Cowell’s Method . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4.2 Encke’s Method . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4.3 Variation of Parameters . . . . . . . . . . . . . . . . . . . . . 24
2.5 Integration Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3 Software Development 26
3.1 Software and Toolkits Used . . . . . . . . . . . . . . . . . . . . . . . 26
3.1.1 NAIF SPICE Toolkit . . . . . . . . . . . . . . . . . . . . . . . 27
3.1.2 Text Progress Bar . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2 Orbit Propagator Structure . . . . . . . . . . . . . . . . . . . . . . . 28
3.3 Coding of Perturbation Method . . . . . . . . . . . . . . . . . . . . . 29
3.4 Integration Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.4.1 MatLAB ODE Solvers . . . . . . . . . . . . . . . . . . . . . . 30
3.4.2 Achieving the Required Accuracy . . . . . . . . . . . . . . . . 31
3.4.3 Perturbation Method and Integration Method . . . . . . . . . 32
3.5 Non-spherical Earth Perturbations . . . . . . . . . . . . . . . . . . . 35
3.5.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
CONTENTS vii
3.5.2 Validations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.5.3 Uncertainty in the Model . . . . . . . . . . . . . . . . . . . . . 38
3.6 Lunisolar and Third Body Perturbations . . . . . . . . . . . . . . . . 40
3.6.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.6.2 Validations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.6.3 Uncertainty in the Model . . . . . . . . . . . . . . . . . . . . . 42
3.7 Tidal Perturbations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.7.1 Issues with the Model . . . . . . . . . . . . . . . . . . . . . . 44
3.7.2 Suggestions for Solutions of the Issues . . . . . . . . . . . . . 44
3.7.3 Uncertainty in the Model . . . . . . . . . . . . . . . . . . . . . 45
3.8 Relativistic Perturbations . . . . . . . . . . . . . . . . . . . . . . . . 45
3.9 STK Report Parsing Utility . . . . . . . . . . . . . . . . . . . . . . . 46
4 Results 47
4.1 Non-spherical Earth Model Effects . . . . . . . . . . . . . . . . . . . 49
4.1.1 Acceleration Magnitudes . . . . . . . . . . . . . . . . . . . . . 49
4.1.2 Perturbations . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.2 Lunisolar and Third Body Effects . . . . . . . . . . . . . . . . . . . . 53
4.2.1 Acceleration Magnitudes . . . . . . . . . . . . . . . . . . . . . 53
4.2.2 Perturbations . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.3 Tidal Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.4 Relativistic Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5 Discussion 59
5.1 Discussion of the Perturbations . . . . . . . . . . . . . . . . . . . . . 59
Description:Academic Year 2010-2011. Senol¨ c Cranfield University, 2011. All rights perturbation sources that can cause phase shifts have been analysed and modelled. A.1 Solid Earth tide corrections for k. Ф0Х The final chapter presents the findings of the thesis and gives suggestions for future work.
