{"product_id":"space-trajectories-basic-and-advanced-topics-hardback-9781394293797","title":"Space Trajectories; Basic and Advanced Topics (Hardback) 9781394293797","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eSpace Trajectories\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eBasic and Advanced Topics\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eMax Cerf (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781394293797, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 31 October 2024\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e464 pages\u003cbr\u003e25.4 x 17.8 x 2.8 cm, 1.161 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e\u003cb\u003eAn authoritative reference that covers essential concepts of orbital mechanics and explains how they relate to advanced space trajectory applications\u003c\/b\u003e \u003c\/p\u003e\n\u003cp\u003e\u003ci\u003eSpace Trajectories\u003c\/i\u003e is the first book to offer a comprehensive exploration of orbital mechanics and trajectory optimization in a single volume. Beginning with a review of essential concepts, the book progresses to advanced space applications, highlighting methods used in today’s space missions.  \u003c\/p\u003e\n\u003cp\u003eThe contents are organized into three parts. The first part delves into free orbital motion, covering topics such as Keplerian motion, perturbed motion, the three-body problem, orbit determination, and collision risks in orbit. The second part focuses on controlled orbital motion, discussing impulsive transfer, orbital rendezvous, thrust level optimization, low-thrust transfer, and space debris cleaning. The third part examines ascent and reentry, including launch into orbit, launcher staging, analytical solutions in flat Earth, interplanetary missions, and atmospheric reentry.  \u003c\/p\u003e\n\u003cp\u003eEach chapter is written in a modular way, featuring conclusion summaries, key points, and suggestions for further investigation. Examples are included with detailed solutions methods that readers can apply to solve their own trajectory problems. \u003c\/p\u003e\n\u003cp\u003eWritten by an expert of the topic who has performed guidance of Ariane launchers for 30 years, \u003ci\u003eSpace Trajectories\u003c\/i\u003e includes information on: \u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eKeplerian motion, motion time law, universal formulation, equinoctial parameters, and Lagrange coefficients\u003c\/li\u003e \u003cli\u003eOsculating orbit, Gauss equations, gravitational and third body perturbations, Lissajous and Halo orbits, and invariant manifolds \u003c\/li\u003e \u003cli\u003eAstrometry measurements, Kalman filtering, orbit uncertainties, and collision probability\u003c\/li\u003e \u003cli\u003eTransfer in one, two, or three impulses, minimum-energy transfer, Lambert’s problem, high- and low-thrust transfer, and interplanetary path\u003c\/li\u003e \u003cli\u003eLaunch and reentry trajectories, propulsion systems, optimized thrust profiles, and launcher staging\u003c\/li\u003e\n\u003c\/ul\u003e \u003cp\u003e\u003ci\u003eSpace Trajectories\u003c\/i\u003e is an essential reference for students and researchers aiming to quickly understand the main issues in astrodynamics and the way to design trajectories, as well as space engineers seeking to consolidate their knowledge in the field of optimization and optimal control applied to aerospace and space missions.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eAbout the Author xv\u003c\/p\u003e \u003cp\u003eForeword xvii\u003c\/p\u003e \u003cp\u003eAcknowledgments xix\u003c\/p\u003e \u003cp\u003eIntroduction xxi\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I Free Orbital Motion 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Two-Body Problem 3\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction 3\u003c\/p\u003e \u003cp\u003e1.2 Keplerian Motion 3\u003c\/p\u003e \u003cp\u003e1.2.1 Dynamic Model 4\u003c\/p\u003e \u003cp\u003e1.2.2 Prime Integrals 5\u003c\/p\u003e \u003cp\u003e1.2.3 Orbit Shape 7\u003c\/p\u003e \u003cp\u003e1.3 Motion Time Law 12\u003c\/p\u003e \u003cp\u003e1.3.1 Elliptical Orbit 12\u003c\/p\u003e \u003cp\u003e1.3.2 Hyperbolic Orbit 14\u003c\/p\u003e \u003cp\u003e1.3.3 Parabolic Orbit 15\u003c\/p\u003e \u003cp\u003e1.3.4 Lagrange Coefficients 16\u003c\/p\u003e \u003cp\u003e1.3.5 Universal Variable 18\u003c\/p\u003e \u003cp\u003e1.4 Orbital Parameters 23\u003c\/p\u003e \u003cp\u003e1.4.1 Classical Orbital Parameters 23\u003c\/p\u003e \u003cp\u003e1.4.2 Relation to Position and Velocity 23\u003c\/p\u003e \u003cp\u003e1.4.3 Equinoctial Orbital Parameters 25\u003c\/p\u003e \u003cp\u003e1.4.4 Earth Orbits 25\u003c\/p\u003e \u003cp\u003e1.5 Conclusion 31\u003c\/p\u003e \u003cp\u003e1.5.1 The Key Points 31\u003c\/p\u003e \u003cp\u003e1.5.2 To Go Further 31\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Perturbed Motion 33\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 33\u003c\/p\u003e \u003cp\u003e2.2 Unperturbed Motion 34\u003c\/p\u003e \u003cp\u003e2.2.1 Keplerian Model 34\u003c\/p\u003e \u003cp\u003e2.2.2 Orbital Parameters 34\u003c\/p\u003e \u003cp\u003e2.2.3 Useful Frames 36\u003c\/p\u003e \u003cp\u003e2.3 Perturbed Motion 36\u003c\/p\u003e \u003cp\u003e2.3.1 Osculating Orbit 37\u003c\/p\u003e \u003cp\u003e2.3.2 Derivation Formula 37\u003c\/p\u003e \u003cp\u003e2.3.3 Gauss Equations 38\u003c\/p\u003e \u003cp\u003e2.3.4 Lagrange Equations 41\u003c\/p\u003e \u003cp\u003e2.3.5 Equinoctial Parameters 43\u003c\/p\u003e \u003cp\u003e2.3.6 Integration Methods 44\u003c\/p\u003e \u003cp\u003e2.4 Gravitational Perturbations 48\u003c\/p\u003e \u003cp\u003e2.4.1 Gravitational Potential 49\u003c\/p\u003e \u003cp\u003e2.4.2 Spherical Body 49\u003c\/p\u003e \u003cp\u003e2.4.3 Nonspherical Body 51\u003c\/p\u003e \u003cp\u003e2.4.4 First Zonal Term 54\u003c\/p\u003e \u003cp\u003e2.5 Other Perturbations 58\u003c\/p\u003e \u003cp\u003e2.5.1 Third-Body Attraction 58\u003c\/p\u003e \u003cp\u003e2.5.2 Atmospheric Friction 64\u003c\/p\u003e \u003cp\u003e2.5.3 Radiation Pressure 65\u003c\/p\u003e \u003cp\u003e2.6 Conclusion 65\u003c\/p\u003e \u003cp\u003e2.6.1 The Key Points 65\u003c\/p\u003e \u003cp\u003e2.6.2 To Go Further 66\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Three-Body Problem 67\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 67\u003c\/p\u003e \u003cp\u003e3.2 Circular-Restricted Three-Body Problem 68\u003c\/p\u003e \u003cp\u003e3.2.1 Motion Equations 68\u003c\/p\u003e \u003cp\u003e3.2.2 Accessible Region 69\u003c\/p\u003e \u003cp\u003e3.2.3 Lagrange Points 71\u003c\/p\u003e \u003cp\u003e3.3 Periodic Orbits 74\u003c\/p\u003e \u003cp\u003e3.3.1 Linearized Solution 74\u003c\/p\u003e \u003cp\u003e3.3.2 Periodic Solution 80\u003c\/p\u003e \u003cp\u003e3.3.3 Halo Orbits 83\u003c\/p\u003e \u003cp\u003e3.4 Transfers 86\u003c\/p\u003e \u003cp\u003e3.4.1 Linearization in the Orbit Vicinity 86\u003c\/p\u003e \u003cp\u003e3.4.2 Invariant Manifolds 88\u003c\/p\u003e \u003cp\u003e3.4.3 Transfer Strategies 89\u003c\/p\u003e \u003cp\u003e3.5 Conclusion 93\u003c\/p\u003e \u003cp\u003e3.5.1 The Key Points 93\u003c\/p\u003e \u003cp\u003e3.5.2 To Go Further 93\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Orbit Determination 95\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 95\u003c\/p\u003e \u003cp\u003e4.2 Measurements 96\u003c\/p\u003e \u003cp\u003e4.2.1 Observation System 96\u003c\/p\u003e \u003cp\u003e4.2.2 Measurements 100\u003c\/p\u003e \u003cp\u003e4.2.3 Directions of Stars 102\u003c\/p\u003e \u003cp\u003e4.3 Preliminary Orbit Estimation 104\u003c\/p\u003e \u003cp\u003e4.3.1 Position Measurements 104\u003c\/p\u003e \u003cp\u003e4.3.2 Direction Measurements 107\u003c\/p\u003e \u003cp\u003e4.4 Continuous Orbit Estimation 110\u003c\/p\u003e \u003cp\u003e4.4.1 Least Squares 111\u003c\/p\u003e \u003cp\u003e4.4.2 Differential Correction 113\u003c\/p\u003e \u003cp\u003e4.4.3 Kalman Filtering 116\u003c\/p\u003e \u003cp\u003e4.5 Conclusion 119\u003c\/p\u003e \u003cp\u003e4.5.1 The Key Points 119\u003c\/p\u003e \u003cp\u003e4.5.2 To Go Further 119\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Collision Risks 121\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 121\u003c\/p\u003e \u003cp\u003e5.2 Orbit Uncertainties 122\u003c\/p\u003e \u003cp\u003e5.2.1 Orbital Motion 122\u003c\/p\u003e \u003cp\u003e5.2.2 Ellipsoid of Uncertainty 124\u003c\/p\u003e \u003cp\u003e5.2.3 Gaussian Model 126\u003c\/p\u003e \u003cp\u003e5.3 Conjunction 129\u003c\/p\u003e \u003cp\u003e5.3.1 Numerical Simulation 129\u003c\/p\u003e \u003cp\u003e5.3.2 Orbit-to-Orbit Distance 129\u003c\/p\u003e \u003cp\u003e5.3.3 Trajectory-to-Orbit Distance 133\u003c\/p\u003e \u003cp\u003e5.3.4 Combined Covariance 134\u003c\/p\u003e \u003cp\u003e5.4 Risk of Collision 136\u003c\/p\u003e \u003cp\u003e5.4.1 Short Conjunction 137\u003c\/p\u003e \u003cp\u003e5.4.2 Probability of Collision 138\u003c\/p\u003e \u003cp\u003e5.4.3 Analytical Formula 140\u003c\/p\u003e \u003cp\u003e5.4.4 Maximum Probability 141\u003c\/p\u003e \u003cp\u003e5.4.5 Long Conjunction 143\u003c\/p\u003e \u003cp\u003e5.5 Conclusion 145\u003c\/p\u003e \u003cp\u003e5.5.1 The Key Points 145\u003c\/p\u003e \u003cp\u003e5.5.2 To Go Further 145\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II Controlled Orbital Motion 147\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Impulsive Transfer 149\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 149\u003c\/p\u003e \u003cp\u003e6.2 Orbit Target 150\u003c\/p\u003e \u003cp\u003e6.2.1 Problem Formulation 150\u003c\/p\u003e \u003cp\u003e6.2.2 Transfer in One Impulse 151\u003c\/p\u003e \u003cp\u003e6.2.3 Transfer in Two or Three Impulses 155\u003c\/p\u003e \u003cp\u003e6.3 Point Target 160\u003c\/p\u003e \u003cp\u003e6.3.1 Problem Formulation 160\u003c\/p\u003e \u003cp\u003e6.3.2 Minimum-Energy Transfer 161\u003c\/p\u003e \u003cp\u003e6.3.3 Minimum-Eccentricity Transfer 162\u003c\/p\u003e \u003cp\u003e6.3.4 Noncollinear Transfer 163\u003c\/p\u003e \u003cp\u003e6.3.5 Collinear Transfer 168\u003c\/p\u003e \u003cp\u003e6.4 Point and Time Target 171\u003c\/p\u003e \u003cp\u003e6.4.1 Lambert’s Problem 171\u003c\/p\u003e \u003cp\u003e6.4.2 Lambert’s Theorem 171\u003c\/p\u003e \u003cp\u003e6.4.3 Transfer Time Equation 175\u003c\/p\u003e \u003cp\u003e6.4.4 Universal Variable 181\u003c\/p\u003e \u003cp\u003e6.4.5 Solution Methods 183\u003c\/p\u003e \u003cp\u003e6.5 Conclusion 184\u003c\/p\u003e \u003cp\u003e6.5.1 The Key Points 184\u003c\/p\u003e \u003cp\u003e6.5.2 To Go Further 184\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Orbital Rendezvous 187\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 187\u003c\/p\u003e \u003cp\u003e7.2 Phasing and Transfer 188\u003c\/p\u003e \u003cp\u003e7.2.1 Orbital Model 188\u003c\/p\u003e \u003cp\u003e7.2.2 Phasing 189\u003c\/p\u003e \u003cp\u003e7.2.3 Transfer 190\u003c\/p\u003e \u003cp\u003e7.2.4 Visibility 197\u003c\/p\u003e \u003cp\u003e7.3 Target in Circular Orbit 198\u003c\/p\u003e \u003cp\u003e7.3.1 Hill–Clohessy–Wiltshire Equations 198\u003c\/p\u003e \u003cp\u003e7.3.2 Free Motion 200\u003c\/p\u003e \u003cp\u003e7.3.3 Maneuvers 204\u003c\/p\u003e \u003cp\u003e7.3.4 Approach Scenario 206\u003c\/p\u003e \u003cp\u003e7.4 Control Laws 206\u003c\/p\u003e \u003cp\u003e7.4.1 Optimum Control 206\u003c\/p\u003e \u003cp\u003e7.4.2 Specific Controls 210\u003c\/p\u003e \u003cp\u003e7.5 Conclusion 214\u003c\/p\u003e \u003cp\u003e7.5.1 The Key Points 214\u003c\/p\u003e \u003cp\u003e7.5.2 To Go Further 214\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Optimal Thrust Level 215\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 215\u003c\/p\u003e \u003cp\u003e8.2 Problem Formulation 216\u003c\/p\u003e \u003cp\u003e8.2.1 Optimal Control Problem 216\u003c\/p\u003e \u003cp\u003e8.2.2 Conditions for Optimality 217\u003c\/p\u003e \u003cp\u003e8.2.3 Property of the Velocity Costate 218\u003c\/p\u003e \u003cp\u003e8.3 Analytical Solution 221\u003c\/p\u003e \u003cp\u003e8.3.1 Direction of Thrust 221\u003c\/p\u003e \u003cp\u003e8.3.2 Costate Vector 225\u003c\/p\u003e \u003cp\u003e8.3.3 Injection Point and Direction 226\u003c\/p\u003e \u003cp\u003e8.3.4 Reduced Problem 228\u003c\/p\u003e \u003cp\u003e8.3.5 Performance Estimate 229\u003c\/p\u003e \u003cp\u003e8.4 Application 230\u003c\/p\u003e \u003cp\u003e8.4.1 Optimized Thrust Profile 230\u003c\/p\u003e \u003cp\u003e8.4.2 Fixed Thrust Level 232\u003c\/p\u003e \u003cp\u003e8.5 Conclusion 236\u003c\/p\u003e \u003cp\u003e8.5.1 The Key Points 236\u003c\/p\u003e \u003cp\u003e8.5.2 To Go Further 237\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Low-Thrust Transfer 239\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 239\u003c\/p\u003e \u003cp\u003e9.2 Problem Formulation 240\u003c\/p\u003e \u003cp\u003e9.2.1 Dynamics 240\u003c\/p\u003e \u003cp\u003e9.2.2 Optimal Control Problem 242\u003c\/p\u003e \u003cp\u003e9.2.3 Local Control Laws 245\u003c\/p\u003e \u003cp\u003e9.2.4 Edelbaum’s Solution 249\u003c\/p\u003e \u003cp\u003e9.3 Transfers to the Geostationary Orbit 251\u003c\/p\u003e \u003cp\u003e9.3.1 Dynamic Model 251\u003c\/p\u003e \u003cp\u003e9.3.2 Optimal Control Problem 253\u003c\/p\u003e \u003cp\u003e9.3.3 Solution Method 255\u003c\/p\u003e \u003cp\u003e9.3.4 Application Cases 258\u003c\/p\u003e \u003cp\u003e9.4 Transfers Between Circular Orbits 262\u003c\/p\u003e \u003cp\u003e9.4.1 Dynamic Model 262\u003c\/p\u003e \u003cp\u003e9.4.2 Optimal Control Problem 263\u003c\/p\u003e \u003cp\u003e9.4.3 Form of Optimal Trajectories 265\u003c\/p\u003e \u003cp\u003e9.4.4 Solution Method 268\u003c\/p\u003e \u003cp\u003e9.4.5 Application Case 270\u003c\/p\u003e \u003cp\u003e9.5 Conclusion 273\u003c\/p\u003e \u003cp\u003e9.5.1 The Key Points 273\u003c\/p\u003e \u003cp\u003e9.5.2 To Go Further 273\u003c\/p\u003e \u003cp\u003e9.5.3 Authorizations 274\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Space Debris Cleaning 275\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 275\u003c\/p\u003e \u003cp\u003e10.2 Problem Formulation 276\u003c\/p\u003e \u003cp\u003e10.2.1 Debris Orbits 276\u003c\/p\u003e \u003cp\u003e10.2.2 Cleaning Program 277\u003c\/p\u003e \u003cp\u003e10.2.3 Optimization Problem 279\u003c\/p\u003e \u003cp\u003e10.3 Transfer Problem 280\u003c\/p\u003e \u003cp\u003e10.3.1 Generic Transfer Strategy 280\u003c\/p\u003e \u003cp\u003e10.3.2 High-Thrust Propulsion 281\u003c\/p\u003e \u003cp\u003e10.3.3 Low-Thrust Propulsion 282\u003c\/p\u003e \u003cp\u003e10.3.4 Reduced Formulation 284\u003c\/p\u003e \u003cp\u003e10.4 Solution Method 285\u003c\/p\u003e \u003cp\u003e10.4.1 Simulated Annealing 285\u003c\/p\u003e \u003cp\u003e10.4.2 Cost Function 287\u003c\/p\u003e \u003cp\u003e10.4.3 Solution Process 290\u003c\/p\u003e \u003cp\u003e10.5 Application Case 290\u003c\/p\u003e \u003cp\u003e10.5.1 High-Thrust Case 292\u003c\/p\u003e \u003cp\u003e10.5.2 Low-Thrust Case 294\u003c\/p\u003e \u003cp\u003e10.5.3 Comparison of High and Low-Thrust Solutions 296\u003c\/p\u003e \u003cp\u003e10.6 Conclusion 297\u003c\/p\u003e \u003cp\u003e10.6.1 The Key Points 297\u003c\/p\u003e \u003cp\u003e10.6.2 To Go Further 297\u003c\/p\u003e \u003cp\u003e10.6.3 Authorizations 297\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart III Launch and Reentry 299\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Launch into Orbit 301\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 301\u003c\/p\u003e \u003cp\u003e11.2 Launcher Dynamics 302\u003c\/p\u003e \u003cp\u003e11.2.1 Force Models 302\u003c\/p\u003e \u003cp\u003e11.2.2 Motion Equations 304\u003c\/p\u003e \u003cp\u003e11.3 Launcher Configuration 307\u003c\/p\u003e \u003cp\u003e11.3.1 Propulsive ΔV 307\u003c\/p\u003e \u003cp\u003e11.3.2 Staging 308\u003c\/p\u003e \u003cp\u003e11.3.3 Preliminary Design 310\u003c\/p\u003e \u003cp\u003e11.3.4 Versatility 311\u003c\/p\u003e \u003cp\u003e11.4 Trajectory Optimization 312\u003c\/p\u003e \u003cp\u003e11.4.1 Constraints 312\u003c\/p\u003e \u003cp\u003e11.4.2 Risk Mitigation 315\u003c\/p\u003e \u003cp\u003e11.4.3 Optimal Control Problem 316\u003c\/p\u003e \u003cp\u003e11.4.4 Numerical Methods 318\u003c\/p\u003e \u003cp\u003e11.4.5 Trajectory Segmentation 320\u003c\/p\u003e \u003cp\u003e11.5 Guidance 322\u003c\/p\u003e \u003cp\u003e11.5.1 Implicit Guidance 323\u003c\/p\u003e \u003cp\u003e11.5.2 Explicit Guidance 324\u003c\/p\u003e \u003cp\u003e11.5.3 Flight Control 326\u003c\/p\u003e \u003cp\u003e11.6 Conclusion 327\u003c\/p\u003e \u003cp\u003e11.6.1 The Key Points 327\u003c\/p\u003e \u003cp\u003e11.6.2 To Go Further 327\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Launcher Staging 329\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 329\u003c\/p\u003e \u003cp\u003e12.2 Staging Problem 330\u003c\/p\u003e \u003cp\u003e12.2.1 Launcher Modeling 330\u003c\/p\u003e \u003cp\u003e12.2.2 Trajectory Modeling 332\u003c\/p\u003e \u003cp\u003e12.2.3 Global Problem 334\u003c\/p\u003e \u003cp\u003e12.3 Impulsive Method 335\u003c\/p\u003e \u003cp\u003e12.3.1 Propulsive Velocity Increment 335\u003c\/p\u003e \u003cp\u003e12.3.2 Staging Problem 336\u003c\/p\u003e \u003cp\u003e12.3.3 Staging Loops 337\u003c\/p\u003e \u003cp\u003e12.4 Coupled Method 339\u003c\/p\u003e \u003cp\u003e12.4.1 Control Law 339\u003c\/p\u003e \u003cp\u003e12.4.2 Iterations and Margins 340\u003c\/p\u003e \u003cp\u003e12.4.3 Versatile Configuration 341\u003c\/p\u003e \u003cp\u003e12.4.4 Application Case 1: Number of Boosters 342\u003c\/p\u003e \u003cp\u003e12.4.5 Application Case 2: Upper Stage Loading 345\u003c\/p\u003e \u003cp\u003e12.5 Propellant Reserve 348\u003c\/p\u003e \u003cp\u003e12.5.1 Performance and Reserve 348\u003c\/p\u003e \u003cp\u003e12.5.2 Iterative Method 349\u003c\/p\u003e \u003cp\u003e12.5.3 Embedded Method 350\u003c\/p\u003e \u003cp\u003e12.5.4 Application Case 351\u003c\/p\u003e \u003cp\u003e12.6 Conclusion 354\u003c\/p\u003e \u003cp\u003e12.6.1 The Key Points 354\u003c\/p\u003e \u003cp\u003e12.6.2 To Go Further 354\u003c\/p\u003e \u003cp\u003e12.6.3 Authorizations 354\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Flat Earth Solutions 355\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Introduction 355\u003c\/p\u003e \u003cp\u003e13.2 Ballistic Launch at Constant Acceleration 355\u003c\/p\u003e \u003cp\u003e13.2.1 Modeling 356\u003c\/p\u003e \u003cp\u003e13.2.2 Optimal Solution 357\u003c\/p\u003e \u003cp\u003e13.2.3 Application Case 358\u003c\/p\u003e \u003cp\u003e13.3 Injection into Orbit at Constant Acceleration 359\u003c\/p\u003e \u003cp\u003e13.3.1 Modeling 359\u003c\/p\u003e \u003cp\u003e13.3.2 Optimal Solution 359\u003c\/p\u003e \u003cp\u003e13.3.3 Application Case 361\u003c\/p\u003e \u003cp\u003e13.4 Vertical Launch at Variable Thrust 363\u003c\/p\u003e \u003cp\u003e13.4.1 Modeling 363\u003c\/p\u003e \u003cp\u003e13.4.2 Optimal Solution 364\u003c\/p\u003e \u003cp\u003e13.4.3 Application Case 366\u003c\/p\u003e \u003cp\u003e13.5 Injection into Orbit at Variable Thrust 367\u003c\/p\u003e \u003cp\u003e13.5.1 Modeling 367\u003c\/p\u003e \u003cp\u003e13.5.2 Optimal Solution 368\u003c\/p\u003e \u003cp\u003e13.5.3 Switching Function 370\u003c\/p\u003e \u003cp\u003e13.5.4 Numerical Solution 372\u003c\/p\u003e \u003cp\u003e13.6 Transition to the Round Earth 374\u003c\/p\u003e \u003cp\u003e13.6.1 Change of Coordinates 374\u003c\/p\u003e \u003cp\u003e13.6.2 Continuation Method 376\u003c\/p\u003e \u003cp\u003e13.6.3 Application Case 378\u003c\/p\u003e \u003cp\u003e13.7 Conclusion 381\u003c\/p\u003e \u003cp\u003e13.7.1 The Key Points 381\u003c\/p\u003e \u003cp\u003e13.7.2 To Go Further 381\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Interplanetary Trajectory 383\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Introduction 383\u003c\/p\u003e \u003cp\u003e14.2 Trajectory Modeling 384\u003c\/p\u003e \u003cp\u003e14.2.1 Patched Conics 384\u003c\/p\u003e \u003cp\u003e14.2.2 Sphere of Influence 385\u003c\/p\u003e \u003cp\u003e14.2.3 Heliocentric Phase 387\u003c\/p\u003e \u003cp\u003e14.2.4 Planetocentric Phase 390\u003c\/p\u003e \u003cp\u003e14.3 Escape Conditions 392\u003c\/p\u003e \u003cp\u003e14.3.1 Keplerian Motion 392\u003c\/p\u003e \u003cp\u003e14.3.2 Hyperbolic Orbit 393\u003c\/p\u003e \u003cp\u003e14.3.3 Escape Velocity 395\u003c\/p\u003e \u003cp\u003e14.3.4 Fly-by Maneuver 397\u003c\/p\u003e \u003cp\u003e14.4 Mission Scenario 399\u003c\/p\u003e \u003cp\u003e14.4.1 Launch Strategy 399\u003c\/p\u003e \u003cp\u003e14.4.2 Tisserand Criterion 401\u003c\/p\u003e \u003cp\u003e14.4.3 Scenario Optimization 405\u003c\/p\u003e \u003cp\u003e14.4.4 Correction Maneuvers 406\u003c\/p\u003e \u003cp\u003e14.5 Conclusion 409\u003c\/p\u003e \u003cp\u003e14.5.1 The Key Points 409\u003c\/p\u003e \u003cp\u003e14.5.2 To Go Further 410\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Atmospheric Reentry 411\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Introduction 411\u003c\/p\u003e \u003cp\u003e15.2 Motion Equations 411\u003c\/p\u003e \u003cp\u003e15.2.1 Reentry Missions and Vehicles 411\u003c\/p\u003e \u003cp\u003e15.2.2 Rotating Geocentric Frame 413\u003c\/p\u003e \u003cp\u003e15.2.3 Spherical Coordinates 414\u003c\/p\u003e \u003cp\u003e15.2.4 Forces Applied 416\u003c\/p\u003e \u003cp\u003e15.2.5 Differential Equations of Motion 419\u003c\/p\u003e \u003cp\u003e15.2.6 Trajectory Optimization 420\u003c\/p\u003e \u003cp\u003e15.3 Orbital Phase 421\u003c\/p\u003e \u003cp\u003e15.3.1 Deorbitation 422\u003c\/p\u003e \u003cp\u003e15.3.2 Ballistic Range 424\u003c\/p\u003e \u003cp\u003e15.3.3 Return Maneuver 425\u003c\/p\u003e \u003cp\u003e15.4 Atmospheric Phase 427\u003c\/p\u003e \u003cp\u003e15.4.1 Simplified Equations 427\u003c\/p\u003e \u003cp\u003e15.4.2 Reentry Corridor 428\u003c\/p\u003e \u003cp\u003e15.4.3 Flight Corridor 430\u003c\/p\u003e \u003cp\u003e15.4.4 Accessible Area 432\u003c\/p\u003e \u003cp\u003e15.4.5 Steep Reentry 435\u003c\/p\u003e \u003cp\u003e15.5 Conclusion 436\u003c\/p\u003e \u003cp\u003e15.5.1 The Key Points 436\u003c\/p\u003e \u003cp\u003e15.5.2 To Go Further 436\u003c\/p\u003e \u003cp\u003eShort Bibliography 437\u003c\/p\u003e \u003cp\u003eWeb links 438\u003c\/p\u003e \u003cp\u003eIndex 439\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mechanical engineering \u0026amp; materials [\u003ca title=\"See our other books on Mechanical engineering \u0026amp; materials\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mechanical%20engineering%20\u0026amp;%20materials%20%5BTG%5D%22\"\u003eTG\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley","offers":[{"title":"Brand New","offer_id":52511052792088,"sku":"9781394293797","price":88.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781394293797.jpg?v=1786580214","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/space-trajectories-basic-and-advanced-topics-hardback-9781394293797","provider":"Freshly Printed Books","version":"1.0","type":"link"}