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Methods Of Orbit Determination For The Micro Computer
by Dan Boulet 565 pages Level: Technical, college Techniques for calculating orbits of satellites, comets and planets |
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When Sir Isaac Newton published his "Three Laws Of Motion" in 1687, it
seemed that he had given the world a TOE - Theory Of Everything.
Newton's three laws seemed to govern all matter in the then known
universe - from the wandering stars (planets) to balls being tossed
off of towers in Pisa.
The limitations of Newton's three laws became quickly known when first electromagnetic effects were being explored and later when they were supplanted by Einstein's General Relativity, but they are STILL the basis of calculating planetary, satellite and other astronomical orbits. Since Newton's three laws can be easily understood by any reasonably bright high school student, what's the problem? Understanding Newton's laws as a theory is simple, applying them to real objects in the real Solar System is another matter. "Methods Of Orbit Determination For The Micro Computer" does not merely show how to insert numbers into an algorithm but explains in great detail how and why the algorithm works. Unlike many other books about astronomy calculations, "Methods" shows how the calculations are derived. The book starts off with chapters on time and various coordinate systems. It goes on to different techniques for extrapolating the position of an object from its previous position and velocity. But most of "Methods" is devoted to the "classical elements". These are values with picturesque names as "longitude of the ascending node" that are used to specify the orbit of an object such as a planet, comet or a satellite. For instance the two line elements that SkyWatch uses to track satellites is a superset of the classical elements. "Methods" explains how to determine the position and velocity of an orbiting object from its classical elements and also how to do the reverse: determine an object's elements from its position and velocity. Most of the chapters end with a series of BASIC programs (are people still using BASIC?) and their results to illustrate the major points covered within the chapter. "Methods" is not for a casual observer who want to make some quick calculations. It IS for someone who wants to gain a deeper understanding of practical celestial mechanics. It requires some simple calculus and vector geometry. While there are appendices to help bring the reader up to speed on these mathematical topics, a person who is not comfortable with mathematical calculations and manipulations is going to find this book hard going. I would not recommend it as an introduction to celestial mechanics either. In my opinion, it provides too many details without enough sign posts to guide the reader who is approaching the material for the first times. I would recommend "Methods Of Orbit Determination For The Micro Computer" as a reference book for someone with a good background of celestial mechanics who needs information on one or more of the many techniques described within it. |
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| Review by Ed Ehrlich | |
| Table Of Contents | |
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Preface 1 Fundamentals of Orbital Motion 1.1 Introduction 1.2 The Laws of Motion 1.2.1 The Law of Inertia 1.2.2 The Law of Acceleration 1.2.3 The Law of Action and Reaction 1.3 The Law of Gravitation 1.4 Equations of Motion 1.4.1 The Equation of Inertial Motion 1.4.2 The Equation of Relative Motion 1.5 Working Units and Constants 1.5.1 the Heliocentric System 1.5.2 The Geocentric System 1.6 The Working Equation of Motion 1.7 Numerical Example 2 Time and Position 2.1 Introduction 2.2 The Fundamental References 2.3 The Empirical Frame of Reference 2.4 Time Scales 2.4.1 Universal time 2.4.2 Julian Date 2.4.3 Sidereal Time 2.4.4 Atomic Time 2.4.5 Dynamical Time 2.5 Coordinate Systems 2.5.1 Celestial Equatorial Systems 2.5.2 Terrestrial Equatorial Systems 2.5.3 Celestial Ecliptic Systems 2.6 Ecliptic-Equatorial Transformations 2.7 The Fundamental Vector Triangle 2.8 Reduction of Astronomical Coordinates 2.8.1 Planetary Aberration 2.8.2 The Instantaneous and Fixed Equator and Equinox 2.8.3 Astrometric Positions 2.8.4 Reductions for Aberration and Nutation 2.8.5 Reductions for Precession 2.8.6 Reductions for Geocentric Parallax 2.9 Computer Programs 2.9.1 Program LMST 2.9.2 Program XYZ 2.9.3 Program RAD 2.9.4 Program CQTRAN 2.9.5 Program ADAPP 2.9.6 Program ADCES 2.9.7 Program XYZCES 2.9.8 Program ADLAX 2.10 Numerical Examples 2.10.1 Computing Local Mean Sidereal Time 2.10.2 converting Spherical to Rectangular Coordinates 2.10.3 Converting Rectangular to Spherical Coordinates 2.10.4 Converting Equatorial to Ecliptic Coordinates 2.10.5 Reducing Apparent Place to Astrometric Place 2.10.6 Reducing RA and DEC from Jxxxx.x to J2000.0 2.10.7 Reducing Rectangular Coordinates from J2000.0 to Jxxxx.x 2.10.8 Reducing Geocentric Place to Topocentric 3 The Two-Body Problem 3.1 Introduction 3.2 The Two-Body Equation of Motion 3.3 The Orbital and Radial Rates 3.4 The Laws of Two-Body Motion 3.4.1 The conic Section Law 3.4.2 The Law of Areas 3.4.3 The Harmonic Law 3.4.4 The Vis-viva Law 3.5 Two-Body Motion by Numerical Integration 3.5.1 The f and g Series 3.5.2 Taylor Series 3.5.3 Runge-Kutta Five 3.5.4 Numerical Error 3.6 Computer Programs 3.6.1 Program FANDG 3.6.2 Program TAYLOR 3.6.3 Program RUNGE 3.7 Numerical Examples 3.7.1 Two-Body Motion by f and g Series 3.7.2 Two-Body Motion by Taylor Series 3.7.3 Two-Body Motion by Runge-Kutta Five 4 Orbit Geometry 4.1 Introduction 4.2 General Relationships 4.2.1 Angular Momentum and Angular Speed 4.2.2 Radial Speed and True Anomaly 4.2.3 True Anomaly and D 4.2.4 Eccentricity, Semiparameter, and D 4.3 Relationships between Geometry and Time 4.3.1 Elliptic Formulation 4.3.2 Hyperbolic Formulation 4.3.3 Parabolic Formulation 4.4 The Classical Elements from Position and Velocity 4.4.1 Three Fundamental Vectors 4.4.2 The conic Parameters 4.4.3 The Orientation Angles 4.4.4 The Mean Anomaly 4.4.5 The Time of Perifocal Passage 4.5 Position and Velocity from the Classical Elements 4.5.1 The Scalar Components of Elliptic Motion 4.5.2 The Scalar Components of Hyperbolic Motion 4.5.3 The Scalar Components of Parabolic Motion 4.5.4 The Unit Vector Components of Motion 4.6 Computer Programs 4.6.1 Program CLASSEL 4.6.2 Program POSVEL 4.7 Numerical Examples 4.7.1 Classical Elements for Mars 4.7.2 Classical Elements for Comet X 4.7.3 Classical Elements for Comet Y 4.7.4 Classical Elements for GEOS 4.7.5 Position and Velocity Elements for Pallas 4.7.6 Position and Velocity Elements for Recon 1 4.7.7 Position and Velocity Elements for Recon 2 4.7.8 Position and Velocity Elements for Recon 3 5 Ephemeris Generation 5.1 Introduction 5.2 The Differenced Kepler Equations 5.2.1 Elliptic Formulation 5.2.2 Hyperbolic Formulation 5.2.3 Parabolic Formulation 5.3 The Closed f and g Expressions 5.3.1 Elliptic Motion 5.3.2 Hyperbolic Motion 5.3.3 Parabolic Motion 5.4 The Universal Formulation 5.4.1 The Coefficients C, S, and U 5.4.2 The Equations of Motion 5.5 The Ephemeris 5.6 Computer Programs 5.6.1 Program SEARCH 5.6.2 Program RADEC 5.7 Numerical Examples 5.7.1 Ephemeris for GEOS 5.7.2 Ephemeris for Pallas 5.7.3 Ephemeris for Comet X 5.7.4 Right Ascension and Declination of Comet X 6 Special Perturbations 6.1 Introduction 6.2 Direct and Indirect Attractions 6.3 The Method of Cowell 6.4 The Method of Encke 6.5 A Perturbed Ephemeris 6.6 Computer Programs 6.6.1 Program ATTRACT 6.6.2 Program COWELL 6.6.3 Program ENCKE 6.7 Numerical Examples 6.7.1 Solar and Planetary Attractions 6.7.2 The Motion of Mars 6.7.3 The Motion of Uranus 7 Applied Numerical Methods 7.1 Introduction 7.2 Finding the Root of an Equation 7.2.1 The Bisection Method 7.2.2 The Newton-Raphson Method 7.3 Solving a System of Linear Equations 7.3.1 Naive Gauss Elimination 7.3.2 Partial Pivoting 7.4 Polynomial Interpolation 7.5 Polynomial Regression 7.6 Multiple Linear Regression 7.7 Numerical Differentiation 7.7.1 The Interpolating Polynomial 7.7.2 The Regression Polynomial 7.8 Computer Programs 7.8.1 Program PTERP 7.8.2 Program PGRESS 7.8.3 Program MGRESS 7.9 Numerical Examples 7.9.1 Polynomial Interpolation and Differentiation 7.9.2 Polynomial Regression and Differentiation 7.9.3 Multiple Linear Regression 8 Preliminary Orbit Data 8.1 Introduction 8.2 Principal Constraints 8.3 The Topocentric Vector L 8.4 The Topocentric Vector R 8.4.1 Vector R for Geocentric Orbits 8.4.2 Vector R for Heliocentric Orbits 8.5 Computer Programs 8.5.1 Program ADGRESS 8.5.2 Program GEO 8.5.3 Program HELO 8.6 Numerical Examples 8.6.1 Regression of Angular Data for Satellite GEOS 8.6.2 Regression of Angular Data for Comet Rebek-Jewel 8.6.3 Topocentric Vector to the Geocenter 8.6.4 Topocentric Vector to the Heliocenter 9 The Method of Laplace 9.1 Introduction 9.2 Solution by Successive Differentiation 9.3 The Scalar Equations for the Range and Rate 9.4 The Scalar Equation for the Radial Distance 9.5 The Scalar Equation of Lagrange 9.6 The Vector Orbital Elements 9.7 Program LAPLACE 9.8 Numerical Examples 9.8.1 The Orbit of Satellite GEOS 9.8.2 The Orbit of Comet Rebek-Jewel 10 The Method of Gauss 10.1 Introduction 10.2 Solution by f and g Expressions 10.3 The Scalar Equations for the Ranges 10.4 The First Approximation 10.5 The Scalar Equations Relating p and r at Epoch 10.6 The Scalar Equation of Lagrange 10.7 The Vector Orbital Elements 10.7.1 Initial Position Vector 10.7.2 Initial Velocity Vector 10.7.3 Refinement of the Elements 10.8 Program GAUSS 10.9 Numerical Examples 10.9.1 The Orbit of Pallas 10.9.2 The Orbit of Comet Rebek-Jewel 11 The Method of Olbers 11.1 Introduction 11.2 Solution by Euler's Equation 11.3 The Scalar Equations for the Range 11.4 The Vector Orbital Elements 11.4.1 The Radius Vectors 11.4.2 The Velocity Vector 11.5 Program OLBERS 11.6 Numerical Example 11.6.1 The Orbit of Comet Z 11.6.2 The Orbit of Comet Rebek-Jewel 12 Orbit Improvement 12.1 Introduction 12.2 The Differential Equations of Condition 12.3 Numerical Evaluation of the Partial Derivatives 12.4 Comparing Observation with Theory 12.5 Computer Programs 12.5.1 Program IMPROVE 12.5.2 Program CORRECT 12.6 Numerical Examples 12.6.1 Improved Orbit for GEOS 12.6.2 Improved Orbit for Rebek-Jewel 12.6.3 Improved Orbit for Pallas A Vectors A.1 Basic Vector Operations A.2 The Dot and Cross Products B Elementary Calculus B.1 Differentiation B.2 Integration C Astronomical Constants C.1 Constant Related to Units C.2 Masses of the Planets Index |
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