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An Investigation Into Satellite Drag Modeling Performance

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AN INVESTIGATION INTO SATELLITE DRAG MODELING PERFORMANCE BY Stephen Russell Mance Submitted to the graduate degree program in Aerospace Engineering and the Graduate Faculty of the University of Kansas in partial fulfillment of the requirements for the degree of Master‟s of Science. Chairperson: Dr. Craig McLaughlin Committee Members: Dr. David Downing Dr. Shahriar Keshmiri Date Defended:________________ The Thesis Committee for Stephen Russell Mance certifies that this is the approved version of the following thesis: AN INVESTIGATION INTO SATELLITE DRAG MODELING PERFORMANCE Committee: Chairperson: Dr. Craig McLaughlin Dr. David Downing Dr. Shahriar Keshmiri Date Approved:________________ ii ABSTRACT The errors in current atmospheric drag modeling are the primary source of error for orbit determination for objects in low Earth orbit (LEO) at lower altitudes in periods of high solar activity. This is a direct result of significant advancements in conservative force modeling in the form of high accuracy geopotential models. When these new geopotential models are applied to orbit determination packages, the majority of the error source shifts to non-conservative forces such as solar radiation pressure, Earth albedo, Earth infrared (IR), and atmospheric drag. During periods of high solar activity, the density of the atmosphere is highly variable due to interactions with the Sun and the upper atmosphere. These variations are very difficult for empirical density models to estimate and cause significant errors in deriving precise orbits. For this reason, increasing the accuracy and fidelity of atmospheric density models is crucial in order to further increase the accuracy of orbit determination during these times. If equipped, on-board accelerometers can provide measurements of the non- conservative accelerations that a spacecraft encounters along its orbit. A very accurate approximation of the force on a spacecraft due to atmospheric drag can be found by accounting for all other non-conservative forces and considering the remainder to be drag. Accuracy is reduced when using that force to find the density of the atmosphere due to the nature of the drag equation. The drag coefficient (CD) is used to balance the acceleration due to drag and the density of the atmosphere. Determining the value of iii the drag coefficient is arduous for most applications. To make the process easier, the projected area (A) and mass (m) terms in the drag equation are often lumped together with CD to form what is called the ballistic coefficient, CDA/m. This is actually the inverse of the traditional definition of the ballistic coefficient. By using this term, the uncertainties in the projected area and mass can be lumped in with the drag coefficient. Approximating the ballistic coefficient using two line element sets (TLE) was one objective of this research. TLEs are based on radar and optical observations and are thus are not nearly as accurate as other tracking methods, but are advantageous because of the multitude of satellites cataloged over the last several decades. The method of ballistic coefficient estimation presented here can be used quickly and without significant resources since TLEs are widely available. The results of this study indicate the ballistic coefficients generated for spacecraft in orbits less than 500 km in the 2001-2004 time period were within 8.2% of ballistic coefficients derived from analytical methods when using the analytical ballistic coefficients as truth. For satellites around 800 km or above, the ballistic coefficients generated were over 100% from those derived using analytical methods. Creating corrections to existing density models has become a popular way of capturing these variations. Several techniques have been devised to generate these corrections in the past few decades. This thesis utilizes corrections to the NRLMSISE-00 empirical model of the atmosphere generated using the dynamic calibration of the atmosphere (DCA) technique. These corrections, along with the iv NRLMSISE-00 empirical model, are implemented into GEODYN, NASA‟s precision orbit determination and parameter estimation program, to create three GEODYN versions; an unmodified GEODYN with the MSIS-86 atmospheric model, a version using the NRLMSISE-00 model, and a version using the DCA corrections. Any improvements using these new density routines will provide a direct benefit to orbit estimation which, in turn, improves science data. In this thesis, the GEOSAT Follow-On (GFO), Starlette, Stella, and Geo- Forschungs-Zentrum-1 (GFZ-1) satellites were processed with the three versions of GEODYN in the waning of the most recent solar maximum. The results show that the NRLMSISE-00 empirical model can capture slightly more variations in the atmosphere than the previous MSIS-86 model, especially in high solar activity conditions. The DCA corrections produced results similar to the NRLMSISE-00 model, but after an investigation into the drag coefficient estimated through GEODYN, a more detailed investigation is necessary to determine the validity of these results. This is likely due to the altitude or time period of the satellites chosen for processing being outside the range of the DCA corrections to the NRLMSISE-00 routine. v ACKNOWLEDGEMENTS First and foremost I would like to thank my adviser, Dr. Craig McLaughlin for the opportunity to conduct research under his advising. He provided many important didactic discussions in which I gained an enormous amount of understanding through his pedagogy. I would also like to thank Dr. Shahriar Keshmiri and Dr. David Downing for serving on my committee and providing valuable insight and feedback. The researchers at NASA GSFC and SGT Inc. provided an invaluable experience by allowing me to visit and receive in-depth training on the GEODYN software package. While I was there, Frank Lemoine provided me with many insightful discussions and through his patience and guidance I was able to accomplish a great deal. Steve Klosko, Dave Rowlands, Doug Chinn, and Nikita Zelensky also provided many useful suggestions and instruction. I would like to thank Kansas NASA EPSCoR for providing the funding which made much of this research possible through a Partnership Development Grant and also DOD EPSCoR. I also acknowledge Matthew Wilkins and Chris Sabol for their contribution of the test cases which verified the NRLMSISE-00 model and for their generous suggestions. A portion of this research was provided by the Air Force Research Laboratory‟s Space Scholar program. I would also like to acknowledge several AFRL researchers including Chin Lin for providing a research topic, Sam Cable for vi providing HASDM data, and Eric Sutton and Frank Marcos for many valuable discussions. Lastly, I would like to thank all of those close to me. My family and friends have been extremely supportive of my efforts and I would not be in the place I am today without them. vii TABLE OF CONTENTS ABSTRACT ................................................................................................................ iii ACKNOWLEDGEMENTS ...................................................................................... vi TABLE OF CONTENTS ........................................................................................ viii NOMENCLATURE .................................................................................................. xii LIST OF FIGURES ................................................................................................. xvi LIST OF TABLES .................................................................................................. xxii 1 INTRODUCTION ............................................................................................... 1 1.1 Objectives ......................................................................................... 1 1.2 Motivation ........................................................................................ 1 1.3 Precision Orbit Determination Challenges ................................... 3 1.3.1 Geopotential Forces ........................................................................... 4 1.3.2 Atmospheric Drag ............................................................................. 6 1.3.2.1 Diurnal variations .............................................................................. 8 1.3.2.2 27-day solar-rotation cycle ................................................................ 9 1.3.2.3 11-year solar cycle ............................................................................ 9 1.3.2.4 Semi-annual/seasonal variations ..................................................... 10 1.3.2.5 Cyclical variations ........................................................................... 10 1.3.2.6 Rotating atmosphere ........................................................................ 10 1.3.2.7 Winds .............................................................................................. 11 1.3.2.8 Magnetic-storm variations ............................................................... 11 1.3.2.9 Irregular short-periodic variations ................................................... 11 1.3.2.10 Tides ................................................................................................ 12 1.3.3 Third-Body Perturbations ................................................................ 12 1.3.4 Radiation Pressure Forces ............................................................... 13 1.3.5 Magnetic Field ................................................................................
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