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Investigation of Trajectory and Control Designs for a Solar Sail to the Moon

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Investigation of Trajectory and Control Designs for a Solar Sail to the Moon PhD Dissertations and Master's Theses 4-2021 Investigation of Trajectory and Control Designs for a Solar Sail to the Moon Michelle Nadeau [email protected] Follow this and additional works at: https://commons.erau.edu/edt Part of the Engineering Physics Commons Scholarly Commons Citation Nadeau, Michelle, "Investigation of Trajectory and Control Designs for a Solar Sail to the Moon" (2021). PhD Dissertations and Master's Theses. 583. https://commons.erau.edu/edt/583 This Thesis - Open Access is brought to you for free and open access by Scholarly Commons. It has been accepted for inclusion in PhD Dissertations and Master's Theses by an authorized administrator of Scholarly Commons. For more information, please contact [email protected]. INVESTIGATION OF TRAJECTORY AND CONTROL DESIGNS FOR A SOLAR SAIL TO THE MOON by Michelle Lara Nadeau A Thesis Submitted to the College of Arts and Sciences Department of Physical Sciences in Partial Fulfillment of the Requirements for the Degree of Master of Science in Engineering Physics Embry-Riddle Aeronautical University Daytona Beach, Florida April 2021 INVESTIGATION OF TRAJECTORY AND CONTROL DESIGNS FOR A SOLAR SAIL TO THE MOON by Michelle Lara Nadeau This thesis was prepared under the direction of the candidate’s Thesis Committee Chair, Dr. Sergey V. Drakunov, Professor, Daytona Beach Campus, and Thesis Committee Members, Dr. William MacKunis, Professor, Daytona Beach Campus, and Dr. Edwin J. Mierkiewicz, Professor, Daytona Beach Campus, and has been approved by the Thesis Committee. It was submitted to the Department of Physical Sciences in partial fulfillment of the requirements for the degree of Master of Science in Engineering Physics Thesis Review Committee: ____________________________________ Sergey V. Drakunov, Ph.D. Committee Chair Digitally signed by Edwin Mierkiewicz DN: cn=Edwin Mierkiewicz, o, ou, Edwin Mierkiewicz [email protected], c=US _________________________________ _______________________________Date: 2021.04.26 19:15:10 -05'00' William MacKunis, Ph.D. Edwin J. Mierkiewicz, Ph.D. Committee Member Committee Member _______________________________ ________________________________ John M. Hughes, Ph.D. Karen F. Gaines, Ph.D. Interim Chair, Dean, College of Arts and Sciences Department of Physical Sciences _______________________________ ___________ Christopher D. Grant, Ph.D. Date Associate Provost of Academic Support i Acknowledgements First, I would like to thank my thesis committee chair and research advisor, Dr. Drakunov, for his spectacular guidance this past year. Hearing about my internship on the Artemis program, it was he who came up with the project idea of designing the controls for a solar sail to deliver supplies the moon. I greatly appreciate his eager support to tie this project into my interests and all the time, energy, and expertise he dedicated to answering my questions and pointing me in the right direction. I would also like to thank my committee members, Dr. Mierkiewicz and Dr. MacKunis, for their valuable time and critique. An additional thanks goes to the folks in the Engineering Physics Propulsion Lab for letting me reference their related work herein and in my defense presentation. I look forward to our possible collaboration on a paper in the near future. Last but certainly not least – Many, many thanks to my partner, family, and friends who supported and encouraged me to be able to reach this point today. They probably did not expect such barbaric math to be on the slides, but they watched my thesis defense presentation anyway. I appreciate you all and cannot wait until the next time I see you in person again. iii Abstract Researcher: Michelle Lara Nadeau Title: Investigation of Trajectory and Control Designs for a Solar Sail to the Moon Institution: Embry-Riddle Aeronautical University Degree: Master of Science in Engineering Physics Year: 2021 NASA’s Artemis program and other government and commercial projects are working toward establishing a sustainable human presence on the moon. This thesis investigates the technical feasibility of a solar sail-based spacecraft (sailcraft) as a low-cost method of delivering cargo or science instruments to the moon and demonstrates how this sailcraft could be controlled to change its orbit. The concept is a low-cost, commercial launch vehicle-deployable, CubeSat- based sailcraft with a square sail, assumed attitude control, and a small payload traversing from low-Earth orbit toward the moon with zero propellant use. In this thesis, methods for sailcraft to increase altitude, the trajectory design process, and zero-propellant attitude control actuator options are explored. Three increasingly complex mathematical models were built in MATLAB around thrust vector control designs to get the concept sailcraft from Earth orbit toward the moon and transit simulations conducted. The third and most promising model developed a linear quadratic regulator controller to follow a logarithmic spiral reference trajectory and ensure the stability of the solution. As a result, a robust thrust vector control solution to minimize error from the reference trajectory was found and a solution method to assign the control gain matrix was developed. iv Table of Contents Page Thesis Review Committee .................................................................................................. ii Acknowledgements ............................................................................................................ iii Abstract .............................................................................................................................. iv List of Tables ................................................................................................................... viii List of Figures .................................................................................................................. viii Nomenclature .......................................................................................................................x Chapter I Introduction ..................................................................................................1 Problem Statement and Significance ...............................................1 Purpose Statement ............................................................................4 Research Questions ..........................................................................4 Applications .....................................................................................5 Delimitations ....................................................................................6 Limitations and Assumptions ..........................................................7 Definition of Terms........................................................................10 List of Acronyms ...........................................................................10 II Review of the Relevant Literature .............................................................12 Previous Work ...............................................................................12 Completed Solar Sail Missions ..........................................12 IKAROS .................................................................12 NanoSail-D2 ..........................................................14 LightSail I ..............................................................14 v LightSail II .............................................................14 Concept Papers...................................................................16 The Physics of Solar Sails..............................................................16 Solar Sail Structures ...........................................................16 Solar Radiation Pressure ....................................................17 Force Due to SRP...................................................20 Acceleration Due to SRP .......................................20 Comparing Sail Designs ........................................22 Characteristic Acceleration ........................22 Sail Loading ...............................................23 Lightness Number ......................................23 Cone and Clock Angles .........................................24 Eclipse Factor.....................................................................25 Orbital Mechanics ..........................................................................27 Define an Orbit ..................................................................27 Orbit Shapes ...........................................................27 Orbital Elements ....................................................30 Change an Orbit .................................................................31 Changing Orbital Altitude......................................33 Changing Orbital Plane Inclination .......................34 Reference Frames and Orbital Dynamics Models .............37 Earth-Centered Inertial Reference Frame ..............37 Heliocentric Ecliptic Inertial Reference Frame .....37 vi Radial-Tangential-Normal Reference Frame .........38 Rotating Reference Frames ....................................38 Restricted Two-Body Problems .............................40 Restricted Three-Body Problems ...........................41 Common Transfer Orbits for Solar Sails .......................................43 Maximization .....................................................................43 Spiral Trajectories ..............................................................45
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