Offers a concise, practical, and student-friendly introduction to orbital mechanics for aerospace and astronautical engineering courses
Orbital mechanics is one of the foundational disciplines of aerospace engineering, providing the theoretical and practical tools needed to understand, model, and navigate the trajectories of spacecraft both in Earth orbit and on interplanetary missions. Introduction to Orbital Mechanics: A Concise and Practical Approach presents essential principles in a concise, progressive manner.
Ideally suited to the academic structure of both 10-week quarters and 14-week semesters, this textbook begins with a historical perspective on the development of orbital mechanics before introducing the essential physical principles of orbital motion. Students are guided through the basic two-body problem for position and velocity in the plane of an orbit, followed by orbital motion in three-dimensions. Those core topics are then extended to orbital maneuvers, interplanetary transfers, and planetary encounters. More advanced topics including orbital perturbations and ground tracks, orbital decay, methods for orbit determination, spacecraft rendezvous, and three-body motion are then presented. References supporting the mathematical derivations for the advanced topics are provided. Finally, the fundamentals of rocket propulsion and launch dynamics are covered, rounding out a comprehensive yet concise overview of orbital mechanics. Worked examples and end-of-chapter problems reinforce concepts, ensuring students progressively build understanding while maintaining focus on the core topics most relevant to modern spaceflight. This textbook:
- Focuses on clarity and accessibility, avoiding unnecessary mathematical complexity in advanced topics
- Covers orbital motion in both the orbital plane and in three dimensions
- Contains in-depth discussion of orbital maneuvers, interplanetary trajectories, and planetary encounters
- Discusses satellite ground tracks, perturbations, and orbit decay
- Surveys methods for orbit determination from observations
- Covers orbital rendezvous and spacecraft motion in the Earth-Moon system
- Considers practical issues related to spacecraft propulsion and launch dynamics
Introduction to Orbital Mechanics: A Concise and Practical Approach is perfect for upper-level undergraduates studying orbital mechanics and rocket propulsion within aerospace or astronautical engineering programs. The text is also suitable for related courses in physics and astronomy and serves as a valuable reference for early-career engineers entering the aerospace industry.
Table of Contents:
About the Author xi
Preface xiii
Acknowledgments xvii
1 Introduction 1
1.1 Astronomy and the Development of Orbital Mechanics 1
1.2 The Development of the Orbital Mechanics of Spacecraft 7
1.3 A First Estimate of Planetary Periods 10
1.4 Examples of Non-Western Astronomy 12
1.4.1 Babylonian 12
1.4.2 Chinese 13
1.4.3 Mayan 15
1.5 Problem 16
2 Orbits and Trajectories 17
2.1 Gravitational Forces, the 2-Body Model and Newton’s Laws of Motion 17
2.2 Further Justification, and Limitations, of the 2-Body Model 19
2.3 The Governing Equation for 2-Body Orbital Motion 21
2.4 Conservation Laws of Angular Momentum and Energy 23
2.4.1 Conservation of Specific Angular Momentum 24
2.4.2 Conservation of Specific Mechanical Energy 25
2.5 The Orbit Equation 27
2.6 The Geometry of 2-Body Orbits and Trajectories 28
2.6.1 Elliptical Orbits 29
2.6.2 Parabolic Trajectories 32
2.6.3 Relationships Between the Energy and Angular Momentum and the Eccentricity and Velocities of an Orbit 32
2.6.4 Hyperbolic Trajectories 35
2.6.5 Degenerate Cases 40
2.7 Problems 41
3 Elapsed Time and Position on Orbits and Trajectories 45
3.1 Circular Orbits 45
3.2 Elliptical Orbits 46
3.2.1 Geometric Method - Elliptical Orbits 46
3.2.2 Analytical Method - Elliptical Orbits 50
3.2.3 Orbits with Periapsis Passage 52
3.2.4 Inverse Problem 53
3.3 Parabolic Trajectories 55
3.4 Hyperbolic Trajectories 55
3.4.1 Geometric Method - Hyperbolic Trajectories 56
3.4.2 Analytical Method - Hyperbolic Trajectories 57
3.5 Problems 59
4 Orbits in Three Dimensions 65
4.1 Three-Dimensional Orbital Elements 65
4.2 Reference Frames 69
4.2.1 Heliocentric Reference Frame 69
4.2.2 Geocentric Reference Frame 71
4.2.3 Perifocal Reference Frame 72
4.2.4 Topocentric Reference Frame 73
4.3 Coordinate Frame Transformations 73
4.3.1 Transformations Between Perifocal, Geocentric, and Topocentric Coordinates 76
4.4 Problems 80
5 Orbital Maneuvers 83
5.1 Impulsive Maneuvers 83
5.2 The Hohmann Transfer 84
5.3 Limiting Geometries for Transfer Between Two Orbits 86
5.4 Bi-Elliptic Hohmann Transfer 87
5.5 Phasing Maneuver 90
5.6 General Transfer 91
5.7 Chase Maneuver 94
5.8 Apse Line Rotation 95
5.9 Plane Changes 97
5.10 Combined Maneuvers 99
5.11 Problems 99
6 Interplanetary Trajectories and Maneuvers 103
6.1 Planetary Phasing 103
6.2 Patched-Conic Approximation 105
6.3 Sphere of Influence 106
6.4 Earth-Departure Trajectories 108
6.5 Planetary Hohmann Transfers 109
6.6 General Planetary Approach 112
6.7 Planetary Encounters 115
6.8 Problems 120
7 Earth Satellites and Ground Tracks 123
7.1 Satellite Ground Tracks 123
7.2 Earth Rotation Effects 124
7.3 Geosynchronous/Geostationary Orbits 128
7.4 Orbital Perturbations – Gravitational Effects 130
7.5 Orbital Perturbations – Atmospheric Drag Effects 136
7.6 Problems 139
8 Methods for Orbit Determination 141
8.1 Simultaneous Velocity and Radius Vectors Known 141
8.2 Three Position Vectors Known (Gibbs’/Gauss’ Method) 141
8.3 Lambert’s Problem (Two Vector Positions Plus Times Known) 145
8.4 Topocentric-Based Systems 148
8.4.1 Range, Azimuth, and Elevation (and Their Rates) Known 148
8.4.2 Azimuths and Elevations Known at Multiple Times 150
8.5 Problems 152
9 Relative Motion and the Restricted 3-Body Problem 155
9.1 Relative Motion 155
9.2 Restricted 3-Body Problem and Earth-Moon Trajectories 161
9.3 Restricted 3-Body Problem – Whole-Field Solution 164
9.4 Problems 169
10 Rocket Fundamentals and Space Propulsion 171
10.1 Principles of Rocket Thrust 171
10.2 Rocket Performance 174
10.3 Staging 177
10.4 Sounding Rockets 181
10.5 Electric Spacecraft Propulsion 183
10.6 Low-Thrust Maneuvers for Orbit Raising 190
10.7 Problems 191
Appendix 1 Solar System Properties 195
Index 197
About the Author :
James C. Hermanson, PhD, is Professor in the William E. Boeing Department of Aeronautics & Astronautics at the University of Washington, Seattle. He has held faculty positions at Worcester Polytechnic Institute and the University of Connecticut, as well as positions in industry at Boeing Aerospace Company and United Technologies Corporation. His research spans propulsion, combustion, gas dynamics, heat transfer and multiphase flow, cryogenics, and microgravity science, with projects funded by NASA, the National Science Foundation, the Office of Naval Research, the State of Washington, and private industry.
