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Thesis Submitted to Florida Institute of Technology in Partial Fulfllment of the Requirements for the Degree Of Dynamics of Spacecraft Orbital Refueling by Casey Clark Bachelor of Aerospace Engineering Mechanical & Aerospace Engineering College of Engineering 2016 A thesis submitted to Florida Institute of Technology in partial fulfllment of the requirements for the degree of Master of Science in Aerospace Engineering Melbourne, Florida July, 2018 ⃝c Copyright 2018 Casey Clark All Rights Reserved The author grants permission to make single copies. We the undersigned committee hereby approve the attached thesis Dynamics of Spacecraft Orbital Refueling by Casey Clark Dr. Tiauw Go, Sc.D. Associate Professor. Mechanical & Aerospace Engineering Committee Chair Dr. Jay Kovats, Ph.D. Associate Professor Mathematics Outside Committee Member Dr. Markus Wilde, Ph.D. Assistant Professor Mechanical & Aerospace Engineering Committee Member Dr. Hamid Hefazi, Ph.D. Professor and Department Head Mechanical & Aerospace Engineering ABSTRACT Title: Dynamics of Spacecraft Orbital Refueling Author: Casey Clark Major Advisor: Dr. Tiauw Go, Sc.D. A quantitative collation of relevant parameters for successfully completed exper- imental on-orbit fuid transfers and anticipated orbital refueling future missions is performed. The dynamics of connected satellites sustaining fuel transfer are derived by treating the connected spacecraft as a rigid body and including an in- ternal mass fow rate. An orbital refueling results in a time-varying local center of mass related to the connected spacecraft. This is accounted for by incorporating a constant mass fow rate in the inertia tensor. Simulations of the equations of motion are performed using the values of the parameters of authentic missions in an endeavor to provide conclusions regarding the efect of an internal mass transfer on the attitude of refueling spacecraft. The efect of a nonzero internal mass fow rate is qualitatively investigated and a parametric analysis is performed in order to validate the conclusion. A damping efect occurs as a result of the internal mass transfer; implying that the control efort required to stabilize spacecraft sustaining fuel transfer could be less than what is necessary in the absence of an internal mass fow rate. iii Table of Contents Abstract iii List of Figures vi List of Tables ix Abbreviations x Acknowledgments xv Dedication xvi 1 Introduction 1 1.1 Motivation . 2 1.2 Research Objective . 2 1.3 Outline . 3 1.4 On-Orbit Refueling Missions and Patents . 3 1.4.1 ETS-VII . 4 1.4.2 Orbital Express . 5 1.4.3 Robotic Refueling Mission . 7 1.4.4 Restore-L . 9 1.4.5 Recent Patents . 11 iv 2 Dynamics of Connected Spacecraft Sustaining Fuel Transfer 12 2.1 Point Mass Model . 13 2.1.1 Center of Mass Location . 14 2.1.2 Time Derivative of the Inertia Tensor . 16 2.1.3 Newton-Euler Formulation . 18 2.1.4 Euler Transformation19 ..................... 20 2.2 Spacecraft Model . 23 2.2.1 Center of Mass Location . 24 2.2.2 Modifcation of the Inertia Tensor . 25 2.2.3 Modifcation of Newton-Euler Formulation . 27 2.3 Orbital Disturbances . 28 2.3.1 Atmospheric Drag . 28 2.3.2 Solar Radiation Pressure . 32 2.3.3 Thrust Plume Impingement . 33 2.3.4 Gravity Gradient28 ....................... 34 3 Simulations 36 3.1 Astro and NextSat . 38 3.2 TRMM . 42 3.3 Centaur II . 49 4 Conclusion 56 Bibliography 58 Appendices 62 v List of Figures 1.1 Hikoboshi and Orihime12 ........................ 4 1.2 ASTRO and NextSat11 ......................... 6 1.3 RRM Servicer Module1 ......................... 7 1.4 Visual Inspection Poseable Invertebrate Robot33 ........... 8 1.5 Restore-L Servicer29 .......................... 10 2.1 Model of Connected Spacecraft Undergoing Fuel Transfer . 13 2.2 Point Mass Model of Connected Spacecraft in the Space Set . 13 2.3 Point Mass Model in the Body Set Centered at the COM . 14 2.4 Space and Body Set . 14 2.5 Rotation from One Cartesian Coordinate System to Another . 20 2.6 Sequencing of Euler Rotations . 21 2.7 Rigidly Connected Spacecraft in the Body Set . 23 2.8 Projected Area Experiencing Drag . 29 2.9 Adversely Orientated Connected Spacecraft . 30 23 2.10 Coefcient of Drag CD vs. Altitude for Diferent Projected Areas 30 2.11 Nominal Density and Scaling Height based on Altitude24 . 31 2.12 Solar Radiation Pressure Force on Surface Area25 . 32 2.13 Thrust Plume Impingement25 ..................... 33 3.1 Hard Docking scenario of Cubic Spacecraft (b = 0) . 37 vi 3.2 Astro and NextSat - System Response . 39 3.3 Astro and NextSat - Diference between System Responses . 40 3.4 Torque Experienced by Astro and Next Sat . 41 3.5 TRMM - Orientation and Angular Velocity for 100% Fuel Transfer . 43 3.6 TRMM - Orientation and Angular Velocity - Diference between Simulations for 100% Fuel Transfer . 44 3.7 TRMM - Torque due to Atmospheric Drag and Gravity Gradient for 100% Fuel Transfer . 45 3.8 TRMM - Orientation and Angular Velocity for 55% Fuel Transfer . 46 3.9 TRMM - Orientation and Angular Velocity - Displacement between Simulations for 55% Fuel Transfer . 47 3.10 TRMM - Torque due to Atmospheric Drag and Gravity Gradient for 55% Fuel Transfer . 48 3.11 Spacecraft 2 with a Cylindrical Body . 49 kg 3.12 Centaur II - System Response form _ = 0:5 . 50 s kg 3.13 Centaur II - Diference between System Responses form _ = 0:5 s ...................................... 51 kg 3.14 Centaur II - Torque form _ = 0:5 . 52 s kg 3.15 Centaur II - System Response form _ = 10 . 53 s kg 3.16 Centaur II - Diference between System Responses form _ = 10 s ...................................... 54 kg 3.17 Centaur II - Torque form _ = 10 . 55 s 1 TRMM - Orientation and Angular Velocity for 85% Fuel Transfer . 62 vii 2 TRMM - Orientation and Angular Velocity - Displacement between Simulations for 85% Fuel Transfer . 63 3 TRMM - Torque due to Atmospheric Drag and Gravity Gradient for 85% Fuel Transfer . 64 4 TRMM - Orientation and Angular Velocity for 70% Fuel Transfer . 65 5 TRMM - Orientation and Angular Velocity - Displacement between Simulations for 70% Fuel Transfer . 65 6 TRMM - Torque due to Atmospheric Drag and Gravity Gradient for 70% Fuel Transfer . 66 kg 7 Centaur II - Orientation and Angular velocity withm _ = 1 . 67 s 8 Centaur II - Orientation and Angular velocity - Displacement be- kg tween Simulations form _ = 1 without Mass Transfer . 68 s 9 Centaur II - Torque due to Atmospheric Drag and Gravity Gradient kg form _ = 1 .............................. 69 s kg 10 Centaur II - Orientation and Angular velocity withm _ = 2:5 . 70 s 11 Centaur II - Orientation and Angular velocity - Displacement be- kg tween Simulations form _ = 2:5 without Mass Transfer . 71 s 12 Centaur II - Torque due to Atmospheric Drag and Gravity Gradient kg form _ = 2:5 ............................. 72 s viii List of Tables 3.1 Astro and NextSat Simulation Parameters . 38 3.2 TRMM Simulation Parameters . 42 3.3 Centaur II Simulation Parameters . 49 ix List of Symbols, Nomenclature or Abbreviations (OE) Orbital Express (ETS-VII) Engineering Test Satellite Seven (DARPA) Defense Advanced Research Projects Agency (ASTRO) Autonomous Space Transport Robotic Operations vehicle (NextSat) Next Generation Serviceable Satellite (TRL) Technology Readiness Level (NASDA) National Space Development Agency of Japan (ESA) European Space Agency (CRL) Communication Laboratory (DLR) Deutsches Zentrum f¨urLuftund Raumfahrt (ETL) Electrotechnical Laboratory (NAL) National Aerospace Laboratory (6-DOF) Six-Degree of Freedom (ORU) Orbital Replacement Unit (RRM) Robotic Refueling Mission (Dextre) Special Purpose Dexterous Manipulator robot x (CSA) Candian Space Agency (VIPIR) Visiual Inspection Poseable Invertebrate Robot (CORD) Cryogen Orbital Resupply Domonstration (LEO) Low Earth Orbit (SSCO) Satellite Servicing Capabilites Ofce (GSFC) Goddard Space Flight Center (COM) Center of Mass xi S(x; y; z) nThe space set reference inertial reference frame m1 nMass of spacecraft or point 1 m2 nMass of spacecraft or point 2 F nTotal body force vector ρ nDistance vector from the time-varying COM to the line of action of the line of action of the force S r1(0) nInitial position vector from the origin of the space set to the COM of pacecraft or point 1 S r2(0) nInitial position vector from the origin of the space set to the COM of spacecraft or point 2 S rCM (0) nInitial position vector from the origin of the space set to the local COM of the connected spacecraft or points S Θ nOrientation of the time-varying COM in the space set S ! nAngular velocity of the time-varying COM in the space set M nTotal mass of connected spacecraft or points m10 nInitial mass of spacecraft or point 1 m20 nInitial mass of spacecraft or point 2 m_ 1 nMass fow rate out of spacecraft or point 1 m_ 2 nMass fow rate into spacecraft or point 2 m_ nPositive and constant mass fow rate from spacecraft or point 1 to spacecraft or point 2 B(x0; y0; z0) nThe principal body set axes fxed at the time-varying COM S r_CM (0) nInitial, constant time rate of change of the distance vector from the origin of the space set to the time-varying local COM of the connect -ed spacecraft or points S rCM (t) nTime-varying vector from the origin of the space set to the time -varying local COM of the connected spacecraft or points D nThe constant position vector in the space set representing the difer -ence between the distances of spacecraft or points from the local COM D nConstant distance along the x' axis representing the difer- ence between the distances of spacecraft or points from the local COM T nTotal time of mass transfer 0 x1(t) nTime-varying distance from the COM of spacecraft or point 1 along
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