Customer Reviews

Methods of Orbit Determination for the Microcomputer

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This is a very practical book on the calculation of orbits. Even though the derivations of many important relationships are described in some detail, the emphasis throughout is on applications. The reader need only accept the validity of the key equations and understand their symbology in order to use the computer programs that are included to explore the mathematical models.

The book begins 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. However, most of the book is devoted to the specification of the orbit of objects such as planets and comets as well as man-made structures.

The practical side of the book may seem a bit antiquated, but the programs included (they're in BASIC) can easily be converted to more modern languages such as Java or C++ since BASIC is an easy-to-read programming language.

I'd say the ideal audience is someone who already understands calculus and vector geometry as well as programming and has a fundamental understanding of the book's subject matter already. This really isn't an introduction to celestial mechanics. It tends to dig right into terminology that a novice to the subject might find confusing. It would make a good reference book for someone already familiar with the subject.

I include the table of contents because it is not included in the product description.

1. Fundamentals of Orbital Motion
1.1. Introduction
1.2. The Laws of Motion
1.3. The Law of Gravitation
1.4. Equations of Motion
1.5. Working Units and Constants
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
2.5. Coordinate Systems
2.6. Ecliptic-Equatorial Transformations
2.7. The Fundamental Vector Triangle
2.8. Reduction of Astronomical Coordinates
2.9. Computer Programs
2.10. Numerical Examples
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
3.5. Two-Body Motion by Numerical Integration
3.6. Computer Programs
3.7. Numerical Examples
4. Orbit Geometry
4.1. Introduction
4.2. General Relationships
4.3. Relationships between Geometry and Time
4.4. The Classical Elements from Position and Velocity
4.5. Position and Velocity from the Classical Elements
4.6. Computer Programs
4.7. Numerical Examples
5. Ephemeris Generation
5.1. Introduction
5.2. The Differenced Kepler Equations
5.3. The Closed f and g Expressions
5.4. The Universal Formulation
5.5. The Ephemeris
5.6. Computer Programs
5.7. Numerical Examples
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
6.7. Numerical Examples
7. Applied Numerical Methods
7.1. Introduction
7.2. Finding the Root of an Equation
7.3. Solving a System of Linear Equations
7.4. Polynomial Interpolation
7.5. Polynomial Regression
7.6. Multiple Linear Regression
7.7. Numerical Differentiation
7.8. Computer Programs
7.9. Numerical Examples
8. Preliminary Orbit Data
8.1. Introduction
8.2. Principal Constraints
8.3. The Topocentric Vector L
8.4. The Topocentric Vector R
8.5. Computer Programs
8.6. Numerical Examples
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
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
10.8. Program GAUSS
10.9. Numerical Examples
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
11.5. Program OLBERS
11.6. Numerical Example
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
12.6. Numerical Examples
Appendices
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 Constants Related to Units
C.2 Masses of the Planets