Orbital Motion 4th Edition by A. E. Roy – Ebook PDF Instant Download/Delivery: 0750310154, 9780750310154
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ISBN 10: 0750310154
ISBN 13: 9780750310154
Author: A. E. Roy
Long established as one of the premier references in the fields of astronomy, planetary science, and physics, the fourth edition of Orbital Motion continues to offer comprehensive coverage of the analytical methods of classical celestial mechanics while introducing the recent numerical experiments on the orbital evolution of gravitating masses and the astrodynamics of artificial satellites and interplanetary probes. Following detailed reviews of earlier editions by distinguished lecturers in the USA and Europe, the author has carefully revised and updated this edition. Each chapter provides a thorough introduction to prepare you for more complex concepts, reflecting a consistent perspective and cohesive organization that is used throughout the book. A noted expert in the field, the author not only discusses fundamental concepts, but also offers analyses of more complex topics, such as modern galactic studies and dynamical parallaxes. New to the Fourth Edition: * Numerous updates and reorganization of all chapters to encompass new methods * New results from recent work in areas such as satellite dynamics * New chapter on the Caledonian symmetrical n-body problem Extending its coverage to meet a growing need for this subject in satellite and aerospace engineering, Orbital Motion, Fourth Edition remains a top reference for postgraduate and advanced undergraduate students, professionals such as engineers, and serious amateur astronomers.
Orbital Motion 4th Table of contents:
Chapter 1 The Restless Universe
1.1 Introduction
1.2 The Solar System
1.2.1 Kepler’s laws
1.2.2 Bode’s law
1.2.3 Commensurabilities in mean motion
1.2.4 Comets, the Edgeworth–Kuiper Belt and meteors
1.2.5 Conclusions
1.3 Stellar Motions
1.3.1 Binary systems
1.3.2 Triple and higher systems of stars
1.3.3 Globular clusters
1.3.4 Galactic or open clusters
1.4 Clusters of Galaxies
1.5 Conclusion
Bibliography
Chapter 2 Coordinate and Time-Keeping Systems
2.1 Introduction
2.2 Position on the Earth’s Surface
2.3 The Horizontal System
2.4 The Equatorial System
2.5 The Ecliptic System
2.6 Elements of the Orbit in Space
2.7 Rectangular Coordinate Systems
2.8 Orbital Plane Coordinate Systems
2.9 Transformation of Systems
2.9.1 The fundamental formulae of spherical trigonometry
2.9.2 Examples in the transformation of systems
2.10 Galactic Coordinate System
2.11 Time Measurement
2.11.1 Sidereal time
2.11.2 Mean solar time
2.11.3 The Julian date
2.11.4 Ephemeris Time
Problems
Bibliography
Chapter 3 The Reduction of Observational Data
3.1 Introduction
3.2 Observational Techniques
3.3 Refraction
3.4 Precession and Nutation
3.5 Aberration
3.6 Proper Motion
3.7 Stellar Parallax
3.8 Geocentric Parallax
3.9 Review of Procedures
Problems
Bibliography
Chapter 4 The Two-Body Problem
4.1 Introduction
4.2 Newton’s Laws of Motion
4.3 Newton’s Law of Gravitation
4.4 The Solution to the Two-Body Problem
4.5 The Elliptic Orbit
4.5.1 Measurement of a planet’s mass
4.5.2 Velocity in an elliptic orbit
4.5.3 The angle between velocity and radius vectors
4.5.4 The mean, eccentric and true anomalies
4.5.5 The solution of Kepler’s equation
4.5.6 The equation of the centre
4.5.7 Position of a body in an elliptic orbit
4.6 The Parabolic Orbit
4.7 The Hyperbolic Orbit
4.7.1 Velocity in a hyperbolic orbit
4.7.2 Position in the hyperbolic orbit
4.8 The Rectilinear Orbit
4.9 Barycentric Orbits
4.10 Classification of Orbits with Respect to the Energy Constant
4.11 The Orbit in Space
4.12 f and g Series
4.13 The Use of Recurrence Relations
4.14 Universal Variables
Problems
Bibliography
Chapter 5 The Many-Body Problem
5.1 Introduction
5.2 The Equations of Motion in the Many-Body Problem
5.3 The Ten Known Integrals and Their Meanings
5.4 The Force Function
5.5 The Virial Theorem
5.6 Sundman’s Inequality
5.7 The Mirror Theorem
5.8 Reassessment of the Many-Body Problem
5.9 Lagrange’s Solutions of the Three-Body Problem
5.10 General Remarks on the Lagrange Solutions
5.11 The Circular Restricted Three-Body Problem
5.11.1 Jacobi’s integral
5.11.2 Tisserand’s criterion
5.11.3 Surfaces of zero velocity
5.11.4 The stability of the libration points
5.11.5 Periodic orbits
5.11.6 The search for symmetric periodic orbits
5.11.7 Examples of some families of periodic orbits
5.11.8 Stability of periodic orbits
5.11.9 The surface of section
5.11.10 The stability matrix
5.12 The General Three-Body Problem
5.12.1 The caseC<0
5.12.2 The case forC=0
5.12.3 Jacobian coordinates
5.13 Jacobian Coordinates for the Many-Body Problem
5.13.1 The equations of motion of the simple n-body Hos
5.13.2 The equations of motion of the general n-body HDS
5.13.3 An unambiguous nomenclature for a general HDs
5.14 The Hierarchical Three-Body Stability Criterion
Problems
Bibliography
Chapter 6 The Caledonian Symmetric N-Body Problem
6.1 Introduction
6.2 The Equations of Motions
6.3 Sundman’s Inequality
6.4 Boundaries of Real and Imaginary Motion in the Caledonian Symmetrical N-Body Problem
6.5 The Caledonian Symmetric Model forn=1
6.6 The Caledonian Symmetric Model forn=2
6.6.1 The Szebehely Ladder and Szebehely’s Constant 2
6.6.2 Regions of real motion in theρ1,ρ2,ρ12 space
6.6.3 Climbing the rungs of Szebehely’s Ladder
6.6.4 The case whenE0<0
6.6.5 Unequal massesμ1≠μ2in then=2 case
6.6.6 Szebehely’s Constant
6.6.7 Loks and Sergysels’ study of the general four-body problem
6.7 The Caledonian Symmetric Problem forn=3
6.8 The Caledonian Symmetric N-Body Problem for Odd N
Bibliography
Chapter 7 General Perturbations
7.1 The Nature of the Problem
7.2 The Equations of Relative Motion
7.3 The Disturbing Function
7.4 The Sphere of Influence
7.5 The Potential of a Body of Arbitrary Shape
7.6 Potential at a Point Within a Sphere
7.7 The Method of the Variation of Parameters
7.7.1 Modification of the mean longitude at the epoch
7.7.2 The solution of Lagrange’s planetary equations
7.7.3 Short- and long-period inequalities
7.7.4 The resolution of the disturbing force
7.8 Lagrange’s Equations of Motion
7.9 Hamilton’s Canonic Equations
7.10 Derivation of Lagrange’s Planetary Equations from Hamilton’s Canonic Equations
Problems
Bibliography
Chapter 8 Special Perturbations
8.1 Introduction
8.2 Factors in Special Perturbation Problems
8.2.1 The type of orbit
8.2.2 The operational requirements
8.2.3 The formulation of the equations of motion
8.2.4 The numerical integration procedure
8.2.5 The available computing facilities
8.3 Cowell’s Method
8.4 Encke’s Method
8.5 The Use of Perturbational Equations
8.5.1 Derivation of the perturbation equations (caseh≠0)
8.5.2 The relations between the perturbation variables, the rectangular co-ordinates and velocity components, and the usual conic-section elements.
8.5.3 Numerical integration procedure
8.5.4 Rectilinear or almost rectilinear orbits
8.6 Regularization Methods
8.7 Numerical Integration Methods
8.7.1 Recurrence relations
8.7.2 Runge-Kutta four
8.7.3 Multistep methods
8.7.4 Numerical methods
Problems
Bibliography
Chapter 9 The Stability and Evolution of the Solar System
9.1 Introduction
9.2 Chaos and Resonance
9.3 Planetary Ephemerides
9.4 The Asteroids
9.5 Rings, Shepherds, Tadpoles, Horseshoes and Co-Orbitals
9.5.1 Ring systems
9.5.2 Small satellites of Jupiter and Saturn
9.5.3 Spirig and Waldvogel’s analysis
9.5.4 Satellite-ring interactions
9.6 Near-Commensurable Satellite Orbits
9.7 Large-Scale Numerical Integrations
9.7.1 The outer planets for 120000 years
9.7.2 Element plots for 1000000 years
9.7.3 Does Pluto’s perihelion librate or circulate?
9.7.3 The outer planets for108 years-and longer!
9.7.5 The analytical approach against the numerical approach
9.7.6 The whole planetary system
9.8 Empirical Stability Criteria
9.9 Conclusions
Bibliography
Chapter 10 Lunar Theory
10.1 Introduction
10.2 The Earth-Moon System
10.3 The Saros
10.4 Measurement of the Moon’s Distance, Mass and Size
10.5 The Moon’s Rotation
10.6 Selenographic Coordinates
10.7 The Moon’s Figure
10.8 The Main Lunar Problem
10.9 The Sun’s Orbit in the Main Lunar Problem
10.10 The Orbit of the Moon
10.11 Lunar Theories
10.12 The Secular Acceleration of the Moon
Bibliography
Chapter 11 Artificial Satellites
11.1 Introduction
11.2 The Earth as a Planet
11.2.1 The Earth’s shape
11.2.2 Clairaut’s formula
11.2.3 The Earth’s interior
11.2.4 The Earth’s magnetic field
11.2.5 The Earth’s atmosphere
11.2.6 Solar-terrestrial relationships
11.3 Forces Acting on an Artificial Earth Satellite
11.4 The Orbit of a Satellite About an Oblate Planet
11.4.1 The short-period perturbations of the first order
11.4.2 The secular perturbations of the first order
11.4.3 Long-period perturbations from the third harmonic
11.4.4 Secular perturbations of the second-order and long-period perturbations
11.5 The Use of Hamilton-Jacobi Theory in the Artificial Satellite Problem
11.6 The Effect of Atmospheric Drag on an Artificial Satellite
11.7 Tesseral and Sectorial Harmonics in the Earth’s Gravitational Field
Problems
Bibliography
Chapter 12 Rocket Dynamics and Transfer Orbits
12.1 Introduction
12.2 Motion of a Rocket
12.2.1 Motion of a rocket in a gravitational field
12.2.2 Motion of a rocket in an atmosphere
12.2.3 Step rockets
12.2.4 Alternative forms of rocket
12.3 Transfer Between Orbits in a Single Central Force Field
12.3.1 Transfer between circular, coplanar orbits
12.3.2 Parabolic and hyperbolic transfer orbits
12.3.3 Changes in the orbital elements due to a small impulse
12.3.4 Changes in the orbital elements due to a large impulse
12.3.5 Variation of fuel consumption with transfer time
12.3.6 Sensitivity of transfer orbits to small errors in position and velocity at cut-off
12.3.7 Transfer between particles orbiting in a central force field
12.4 Transfer Orbits in Two or More Force Fields
2.4.1 The hyperbolic escape from the first body
12.4.2 Entry into orbit about the second body
12.4.3 The hyperbolic capture
12.4.4 Accuracy of previous analysis and the effect of error
12.4.5 The fly-past as a velocity amplifier
Problems
Bibliography
Chapter 13 Interplanetary and Lunar Trajectories
13.1 Introduction
13.2 Trajectories in Earth-Moon Space
13.3 Feasibility and Precision Study Methods
13.4 The Use of Jacobi’s Integral
13.5 The Use of the Lagrangian Solutions
13.6 The Use of Two-Body Solutions
13.7 Artificial Lunar Satellites
13.7.1 Relative sizes of lunar satellite perturbations due to different causes
13.7.2 Jacobi’s integral for a close lunar satellite
13.8 Interplanetary Trajectories
13.9 The Solar System as a Central Force Field
13.10 Minimum-Energy Interplanetary Transfer Orbits
13.11 The Use of Parking Orbits in Interplanetary Missions
13.12 The Effect of Errors in Interplanetary Orbits
Problems
Bibliography
Chapter 14 Orbit Determination and Interplanetary Navigation
14.1 Introduction
14.2 The Theory of Orbit Determination
14.3 Laplace’s Method
14.4 Gauss’s Method
14.5 Olbers’s Method for Parabolic Orbits
14.6 Orbit Determination with Additional Observational Data
14.7 The Improvement of Orbits
14.8 Interplanetary Navigation
14.8.1 Stabilized platforms and accelerometers
14.8.2 Navigation by on-board optical equipment
14.8.3 Observational methods and probable accuracies
Bibliography
Chapter 15 Binary and Other Few-Body Systems
15.1 Introduction
15.2 Visual Binaries
15.3 The Mass-Luminosity Relation
15.4 Dynamical Parallaxes
15.3 Eclipsing Binaries
15.6 Spectroscopic Binaries
15.7 Combination of Deduced Data
15.8 Binary Orbital Elements
15.9 The Period of a Binary
15.10 Apsidal Motion
15.11 Forces Acting on a Binary System
15.12 Triple Systems
15.3 The Inadequacy of Newton’s Law of Gravitation
15.14 The Figures of Stars in Binary Systems
15.15 The Roche Limits
15.16 Circumstellar Matter
15.17 The Origin of Binary Systems
Problems
Bibliography
Chapter 16 Many-Body Stellar Systems
16.1 Introduction
16.2 The Sphere of Influence
16.3 The Binary Encounter
16.4 The Cumulative Effect of Small Encounters
16.5 Some Fundamental Concepts
16.6 The Fundamental Theorems of Stellar Dynamics
16.6.1 Jeans’s theorem
16.7 Some Special Cases for a Stellar System in a Steady State
16.8 Galactic Rotation
16.8.1 Oort’s constants
16.8.2 The period of rotation and angular velocity of the galaxy
16.8.3 The mass of the Galaxy
16.8.4 The mode of rotation of the Galaxy
16.8.5 The gravitational potential of the Galaxy
16.8.6 Galactic stellar orbits
16.8.7 The high-velocity stars
16.9 Spherical Stellar Systems
16.9.1 Application of the virial theorem to a spherical system
16.9.2 Stellar orbits in a spherical system
16.9.3 The distribution of orbits within a spherical system
16.10 Modern Galactic Studies
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