Astronautics: The Physics of Space Flight

Preface to the Fourth Edition
Preface to the First Edition
Acknowledgements
Contents
Abbreviations
Symbols Used and Terminology
1 Rocket Fundamentals
	1.1 Rocket Propulsion
		1.1.1 Rocket Principle
		1.1.2 Total Thrust
	1.2 Jet Engine
		1.2.1 Nozzle Divergence
		1.2.2 Pressure Thrust
		1.2.3 Momentum Versus Pressure Thrust
	1.3 Rocket Performance
		1.3.1 Payload Considerations
		1.3.2 Rocket Efficiency
		1.3.3 Performance Parameters
	1.4 Problems
2 Rocket Flight
	2.1 Equation of Rocket Motion
	2.2 Rocket Equation
	2.3 Rocket in a Gravitational Field
	2.4 Delta-v Budget and Fuel Demand
	2.5 Relativistic Rocket
		2.5.1 Space Flight Dynamics
		2.5.2 Relativistic Rocket Equation
		2.5.3 Exhaust Considerations
		2.5.4 External Efficiency
		2.5.5 Space–Time Transformations
	2.6 Problem
3 Rocket Staging
	3.1 Serial Staging
		3.1.2 Rocket Equation
	3.2 Serial-Stage Optimization
		3.2.1 Road to Stage Optimization
		3.2.2 General Optimization
	3.3 Analytical Solutions
		3.3.1 Uniform Staging
		3.3.2 Uniform Exhaust Velocities
		3.3.3 Uneven Staging
	3.5 Other Types of Staging
	3.6 Problems
4 Thermal Propulsion
	4.1 Engine Thermodynamics
		4.1.1 Physics of Propellant Gases
		4.1.2 Flow Velocity
		4.1.3 Flow at the Throat
		4.1.4 Flow in the Nozzle
	4.2 Ideally Adapted Nozzle
		4.2.1 Ideal-Adaptation Criterion
		4.2.2 Ideal Nozzle Design
		4.2.3 Shock Attenuation and Pogo Oscillation
		4.2.4 Ideal Engine Performance
	4.3 Engine Thrust
		4.3.1 Engine Performance Parameters
		4.3.2 Thrust Performance
		4.3.3 Nozzle Efficiency
	4.4 Engine Design
		4.4.1 Combustion Chamber
		4.4.2 Nozzles
		4.4.3 Design Guidelines
	4.5 Problems
5 Electric Propulsion
	5.1 Overview
	5.2 Ion Thruster
		5.2.1 Ion Acceleration and Flow
		5.2.2 Ideal Engine Thrust
		5.2.3 Thruster Performance
	5.3 Electric Propulsion Optimization
	5.4 Problem
6 Atmospheric and Ascent Flight
	6.1 Earth’s Atmosphere
		6.1.1 Density Master Equation
		6.1.2 Atmospheric Structure
		6.1.3 Piecewise-Exponential Model
	6.2 Hypersonic Flow Theory
		6.2.1 Free Molecular Flow
		6.2.2 Newtonian Flow Theory
		6.2.3 Drag and Lift Coefficients
		6.2.4 Drag in Free Molecular Flow
		6.2.5 Aerodynamic Forces
	6.3 Equations of Motion
	6.4 Ascent Flight
		6.4.1 Ascent Phases
		6.4.2 Ascent-Optimization
		6.4.3 Gravity Turn
		6.4.4 Pitch Maneuver
		6.4.5 Constant-Pitch-Rate Maneuver
		6.4.6 Terminal State Control
		6.4.7 Optimal Ascent Trajectory
7 Orbits in the Two-Body System
	7.1 Fundamental Physics
		7.1.1 Gravitational Potential
		7.1.2 Gravitational Force
		7.1.3 Conservation Laws
		7.1.4 Newton’s Laws of Motion
		7.1.5 General Two-Body Problem
	7.2 General Principles of Motion
		7.2.1 Vector Derivatives
		7.2.2 Motion in a Central Force Field
		7.2.3 Vis-Viva Equation
		7.2.4 Effective Radial Motion
	7.3 Motion in a Gravitational Field
		7.3.1 Orbit Equation
		7.3.2 Position on the Orbit
		7.3.3 Orbital Velocity and Acceleration
		7.3.4 Orbital Energy
		7.3.5 Orbital Elements
		7.3.6 Nonsingular Elements
		7.3.7 Invariant Orbit Vectors
		7.3.8 Conversion Between Orbital Elements and State Vector
	7.4 Keplerian Orbits
		7.4.1 Circular Orbit
		7.4.2 Elliptic Orbit
		7.4.3 Hyperbolic Orbit
		7.4.4 Parabolic Orbit
		7.4.5 ε-Based Transformation
		7.4.6 h-Based Transformation
		7.4.7 State Vector Propagation
	7.5 Radial Trajectories
		7.5.1 Radial Elliptic Trajectory
		7.5.2 Radial Hyperbolic Trajectory
		7.5.3 Radial Parabolic Trajectory
		7.5.4 Free Fall
		7.5.5 Bounded Vertical Motion
	7.6 Life in Other Universes?
		7.6.1 Equation of Motion in n Dimensions
		7.6.2 4-Dimensional Universe
		7.6.3 Universes with ≥5 Dimensions
		7.6.4 Universes with ≤2 Dimensions
	7.7 Stellar Orbits
		7.7.1 Motion in General Gravitational Potentials
		7.7.2 Near-Circular Stellar Orbits in General Galaxies
		7.7.3 Stellar Orbits in Globular Cluster Galaxies
		7.7.4 Stellar Orbits in Disk-Shaped Galaxies
	7.8 Problems
8 Orbital Maneuvering
	8.1 Kick-Burn Maneuvers
		8.1.1 Principles
		8.1.2 Orbit Maintenance Maneuvers
		8.1.3 Kick-Burns in Circular Orbits
	8.2 Congruent Orbit Transfers
		8.2.1 Finite One-Impulse Maneuver
		8.2.2 Basics of Congruent Orbit Maneuvers
		8.2.3 Plane-Change Maneuvers
		8.2.4 Apsidal-Rotation Maneuver
	8.3 Orbit-Raising Transfers
		8.3.1 Orbit-Raising Principles
		8.3.2 The Tangential Burn
		8.3.3 Escape Transfers
		8.3.4 Hohmann Transfer
		8.3.5 Bi-Elliptic/Parabolic Transfer
		8.3.6 Tilted Orbit Transfer
		8.3.7 Ellipse-To-Ellipse Transfer
		8.3.8 Circle-To-Ellipse Transfer
		8.3.9 Super-Synchronous Transfer
		8.3.10 n-Impulse Transfers
		8.3.11 Continuous Thrust Transfer
	8.4 Lambert Transfer
		8.4.1 Orbital Boundary Value Problem
		8.4.2 Lambert Transfer Orbits
		8.4.3 Lambert’s Problem
		8.4.4 Minimum Effort Lambert Transfer
	8.5 Relative Orbits
		8.5.1 General Equation of Motion
		8.5.2 Circular Orbits
		8.5.3 Flyaround Trajectories
		8.5.4 Near-Circular Orbits
	8.6 Orbital Rendezvous
		8.6.1 Launch Phase
		8.6.2 Phasing
		8.6.3 Homing Phase
		8.6.4 Closing Phase
		8.6.5 Final Approach
		8.6.6 Shuttle–ISS Rendezvous
		8.6.7 Plume Impingement
	8.7 Problems
9 Interplanetary Flight
	9.1 Patched Conics
		9.1.1 Sphere of Influence (SOI)
		9.1.2 Patching Conics
	9.2 Departure Orbits
	9.3 Transfer Orbits
		9.3.1 Hohmann Transfers
		9.3.2 Near-Hohmann Transfers
	9.4 Arrival Orbit
	9.5 Flyby Maneuvers
		9.5.1 Overview
		9.5.2 Flyby Framework
		9.5.3 Planetocentric Flyby Analysis
		9.5.4 Heliocentric Flyby Analysis
		9.5.5 Transition of Orbital Elements
	9.6 Problems
10 Planetary Entry
	10.1 Introduction
		10.1.1 Aerothermodynamical Challenges
		10.1.2 Entry Interface
		10.1.3 Deorbit Phase
	10.2 Equations of Motion
		10.2.1 Normalized Equations of Motion
		10.2.2 Reduced Equations of Motion
	10.3 Elementary Results
		10.3.1 Drag-Free Phase
		10.3.2 Ballistic Reentry
		10.3.3 Heat Flux
	10.4 Reentry with Lift
		10.4.1 Lift-Only Case
		10.4.2 General Results
		10.4.3 Near-Ballistic Reentry
	10.5 Reflection and Skip Reentry
		10.5.1 Reflection
		10.5.2 Skip Reentry
		10.5.3 Phugoid Mode
	10.6 Lifting Reentry
		10.6.1 Reentry Trajectory
		10.6.2 Critical Deceleration
		10.6.3 Heat Flux
	10.7 Space Shuttle Reentry
		10.7.1 Reentry Flight Design and Pre-Entry Phase
		10.7.2 Constant Heat Rate Phase (Thermal Control Phase)
		10.7.3 Equilibrium Glide Phase
		10.7.4 Constant-Drag Phase
		10.7.5 Transition Phase
		10.7.6 TAEM Phase
	10.8 Problems
11 Three-Body Systems
	11.1 The N-Body Problem
		11.1.1 Integrals of Motion
		11.1.2 Stability of an N-Body System
		11.1.3 N-Body Choreographies
	11.2 Synchronous 3-Body Orbits
		11.2.1 Collinear Configuration
		11.2.2 Equilateral Configuration
	11.3 Restricted Three-Body Problem
		11.3.1 Collinear Libration Points
		11.3.2 Equilateral Libration Points
	11.4 Circular Restricted Three-Body Problem
		11.4.1 Equation of Motion
		11.4.2 Symmetry Theorems
		11.4.3 Jacobi Integral and Effective Potential
		11.4.4 Stability at Libration Points
	11.5 CR3BP System Dynamics
		11.5.1 General System Dynamics
		11.5.2 Equation of Motion About Libration Points
		11.5.3 Motion About Collinear Libration Points
		11.5.4 Near-Rectilinear Halo Orbits and Butterfly Family of Orbits
		11.5.5 Transfers to Collinear Libration Points
		11.5.6 Weak Stability Boundary Transfers
		11.5.7 Motion About Equilateral Libration Points
		11.5.8 Distant Retrograde Orbits
	11.6 Hierarchical 3-Body Systems
		11.6.1 General H3BP System Description
		11.6.2 The RH3BP
		11.6.3 Circular Outer Orbit
		11.6.4 Eccentric Outer Orbit
	11.7 Problems
12 Orbit Perturbations
	12.1 Perturbation Methods
		12.1.1 The Osculating Orbit
		12.1.2 Numerical Perturbation Methods
		12.1.3 Analytical Perturbation Methods
	12.2 Gravitational Perturbations
		12.2.1 Geoid
		12.2.2 Gravitational Potential
		12.2.3 Lagrange’s Planetary Equations
		12.2.4 Numerical Perturbation Methods
	12.3 Gravitational Perturbation Effects
		12.3.1 Classification of Effects
		12.3.2 Removing Short-Periodic Effects
		12.3.3 Oblateness Perturbation
		12.3.4 Higher-Order Perturbations
		12.3.5 Sun-Synchronous Orbits
		12.3.6 Frozen Orbits
		12.3.7 Frozen Sun-Synchronous Orbits
	12.4 Resonant Orbits
		12.4.1 Resonance Conditions
		12.4.2 Resonance Dynamics
		12.4.3 Low Earth Orbits
		12.4.4 GPS Orbits
		12.4.5 Geostationary Orbit
	12.5 Solar Radiation Pressure
		12.5.1 Effects of Solar Radiation
		12.5.2 Orbital Evolution
		12.5.3 Correction Maneuvers
	12.6 Celestial Perturbations
		12.6.1 Lunisolar Perturbations
		12.6.2 Relativistic Perturbations
	12.7 Drag
		12.7.1 Drag Perturbations
		12.7.2 Orbit Circularization
		12.7.4 Orbit Lifetime
	12.8 Problems
13 Reference Frames
	13.1 Spatial Frames
		13.1.1 Inertial Reference Frames
		13.1.2 Heliocentric Reference Frames
		13.1.3 Terrestrial Reference Frames
		13.1.4 Orbital Reference Frames
		13.1.5 Mission-Specific Topocentric Frames
		13.1.6 Vector Representations
	13.2 Time Frames
14 Orbit Geometry and Determination
	14.1 Orbit Geometry
		14.1.1 Solar Geometry
		14.1.2 Eclipse
		14.1.3 Access Area
		14.1.4 Earth Reference Ellipsoid
	14.2 Orbit Determination
		14.2.1 Orbit Tracking
		14.2.2 Generalized Orbit Determination Method
		14.2.3 GEO Orbit from Angles-Only Data
		14.2.4 Simple Orbit Estimation
		14.2.5 Modified Battin’s Method
		14.2.6 Advanced Orbit Determination
15 Spacecraft Attitude Dynamics
	15.1 Fundamentals of Rotation
		15.1.1 Elementary Physics
		15.1.2 Equations of Rotational Motion
		15.1.3 Coordinate Systems
		15.1.4 Rotation-to-Translation Equivalence
	15.2 Attitude Kinematics
		15.2.1 Stability
		15.2.2 Nutation
		15.2.3 General Torque-Free Motion
	15.3 Attitude Dynamics Under External Torque
		15.3.1 External Torques
		15.3.2 Road to Flat Spin
		15.3.3 Flat Spin Dynamics
	15.4 Gravity-Gradient Stabilization
		15.4.1 Gravity-Gradient Torque
		15.4.2 Gravity-Gradient Dynamics
	15.5 Space Elevator
		15.5.1 General Cable with Constant Cross-Section
		15.5.2 Untapered Space Elevator Cable
		15.5.3 Tapered Space Elevator Cable
16 Thermal Radiation Physics and Modeling
	16.1 Radiation Properties
		16.1.1 Radiometric Quantities
		16.1.2 Diffuse Radiators
		16.1.3 Black-Body Radiator
		16.1.4 Selective Surfaces
		16.1.5 Kirchhoff’s Law
	16.2 Radiation Exchange
		16.2.1 Transmitted and Absorbed Flux
		16.2.2 View Factor
		16.2.3 Point Radiators
		16.2.4 Radiation Exchange Between Two Bodies
		16.2.5 Spacecraft Thermal Balance
		16.2.6 α/ε Materials
	16.3 Thermal Modeling
		16.3.1 Thermal Requirements and Boundary Conditions
		16.3.2 Heat Equation
		16.3.3 Thermal Model Setup
		16.3.4 Geometric Mathematical Model (GMM)
		16.3.5 Thermal Mathematical Model (TMM)
		16.3.6 Applied Thermal Design and Analysis
		16.3.7 Case Studies
	16.4 Problems
Appendix A Planetary Parameters
A.1 Mean Orbit Radius
	Outline placeholder
		A.1.1 Titius-Bode Law
		A.1.2 Average Over True Anomaly
		A.1.3 Time Average
A.2 Mean Orbital Velocity
	Outline placeholder
		A.2.1 Average Over True Anomaly
		A.2.2 Time Average
Appendix B Approximate Analytical Solution for Uneven Staging
References
Index