Fundamentals of astrodynamics and applications 4th Edition (2013)

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7.4.2 Range-only Processing 452
7.5 Three Position Vectors and Time 454
7.5.1 Gibbs Method 454
7.5.2 Herrick-Gibbs 461
7.6 Two Position Vectors and Time—Lambert’s Problem 467
7.6.1 Lambert—Minimum Energy 470
7.6.2 Lambert—Gauss’s Solution 475
7.6.3 Lambert—Thorne’s Solution 480
7.6.4 Lambert—Universal Variables 489
7.6.5 Lambert Solution—Battin Method 493
7.7 Application: Targeting Problem 498
Chapter 8 Special Perturbation Techniques 517
8.1 Historical Background 517
8.2 Introduction to Perturbations 518
8.3 Encke’s Formulation 523
8.4 Cowell’s Formulation 525
8.5 Numerical Integration Methods 526
8.5.1 Implementing an Integrator and Determining Step Size 535
8.6 Disturbing Forces 538
8.6.1 Gravity Field of a Central Body 538
8.6.2 Atmospheric Drag 551
8.6.3 Third-Body Perturbations 574
8.6.4 Solar-Radiation Pressure 578
8.6.5 Other Perturbations 584
8.7 Forming Numerical Solutions 591
8.7.1 Application: Simplified Acceleration Model 593
8.7.2 Application: Complex Acceleration Model 596
8.8 Practical Considerations 599
8.8.1 Verifying and Validating the Propagator 599
8.8.2 Physical Data and Sources 601
Chapter 9 General Perturbation Techniques 609
9.1 Historical Background 609
9.2 Introduction 613
9.2.1 The Method of Perturbations 617
9.3 Variation of Parameters 619
9.3.1 Lagrangian VOP (Conservative Effects) 621
9.3.2 Gaussian VOP (Nonconservative and Conservative Effects) 628
9.4 Hamilton’s Formulation 637
9.5 Disturbing-Potential Formulations 641
9.5.1 Gravity Potential in Terms of the Satellite’s Orbital Elements 641
9.5.2 Third-Body Potential in Terms of the Satellite’s Orbital Elements 643
9.5.3 Tidal-Motion Potential in Terms of the Satellite’s Orbital Elements 645
9.6 Linearized Perturbations and Effects 646
9.6.1 Central-Body Analysis 647
9.6.2 Drag Analysis 671
9.6.3 Third-Body Analysis 679
9.6.4 Solar-Radiation Analysis 685
9.7 Forming Analytical Solutions 689