An Introduction To The Mathematics And Methods Of Astrodynamics

Teaching text developed by U.S. Air Force Academy and designed as a first course emphasizes the universal variable formulation. Develops the basic two-body and n-body equations of motion; orbit determination; classical orbital elements, coordinate transformations; differential correction; more. Includes specialized applications to lunar and interplanetary flight, example problems, exercises. 1971 edition.

In this 'information age' satellites are playing an increasingly important role in everything from communication and navigation to the military and weather. The command and control of satellites is based on the work of Johannes Kepler (1571-1630) and the science that evolved from his fundamental theories. The physics involved in the command and control of satellites is usually categorized as orbital mechanics. Orbital mechanics is based on the desire to predict the path of a satellite in it's orbit around the earth. One of the first requirements is to develop a co-ordinate system that is easy to use and measure and defines the motion of body or satellite in its orbit. After this is accomplished the propagation of the orbital path needs to be calculated. There are numerous ways to do this. A seminal work in this procedure is "Fundamentals of Astrodynamics" by Bate, Mueller & White and "Methods of Orbit Determination" by Escobal. The next problem to address are the numerous perturbation effects. The most prominent of these effects are due to the fact that the earth is not a perfect sphere (it is oblate), the moons orbit produces a periodically disruptive effect on the orbiting body; atmospheric drag, solar radiation pressure and the precession of the earth about its axis also alter the theoretical orbit. Relativistic effects play a role in the station-keeping of the satellite as do all the above perturbations. The next step in the command and control of the satellite involves the dynamics of space flight and the mechanics of maneuvering a body in orbit by means of thrust vectors, calculating delta-v requirements. This book outlines the unclassified methods of calculating and controlling the orbits of satellites.

Newton's laws of motion and his universal law of gravitation described mathematically the motion of two bodies undergoing mutual gravitational attraction. However, it is impossible to solve analytically the equation of motion for three gravitationally interacting bodies. This book discusses some techniques used to obtain numerical solutions of the equations of motion for planets and satellites, which are of fundamental importance to solar-system dynamicists and to those involved in planning the orbits of artificial satellites. The first part introduces the classical two-body problem and solves it by rigorously developing the six integrals of the motion, starting from Newton's three laws of motion and his law of gravitation and then using vector algebra to develop the integrals. The various forms of the solution flow naturally from the integrals. In the second part, several modern perturbation techniques are developed and applied to cases of practical importance. For example, the perturbed two-body problem for an oblate planet or for a nonsymmetric rotating planet is considered, as is the effect of drag on a satellite. The two-body problem is regularized, and the nonlinear differential equation is thereby transformed to a linear one by further embedding several of the integrals. Finally, a brief sketch of numerical methods is given, as the perturbation equations must be solved by numerical rather than by analytical methods.

In recent years, an unprecedented interest in novel and revolutionary space missions has risen out of the advanced NASA and ESA programs. Astrophysicists, astronomers, space systems engineers, mathematicians and scientists have been cooperating to implement novel and ground-breaking space missions. Recent progress in mathematical dynamics has enabled development of specialised spacecraft orbits and propulsion systems. Recently, the concept of flying spacecraft in formation has gained a lot of interest within the community. These progresses constitute the background to a significant renaissance of research dealing with astrodynamics and its applications. Modern Astrodynamics is designed as a stepping stone for the exposition of modern astrodynamics to students, researchers, engineers and scientists. This volume will present the main constituents of the astrodynamical science in an elaborate, comprehensive and rigorous manner. Although the volume will contain a few distinct chapters, it will render a coherent portrayal of astrodynamics. Encompasses the main constituents of the astrodynamical sciences in an elaborate, comprehensive and rigorous manner Presents recent astrodynamical advances and describes the challenges ahead The first volume of a series designed to give scientists and engineers worldwide an opportunity to publish their works in this multi-disciplinary field

This textbook covers fundamental and advanced topics in orbital mechanics and astrodynamics to expose the student to the basic dynamics of space flight. The engineers and graduate students who read this class-tested text will be able to apply their knowledge to mission design and navigation of space missions. Through highlighting basic, analytic and computer-based methods for designing interplanetary and orbital trajectories, this text provides excellent insight into astronautical techniques and tools. This book is ideal for graduate students in Astronautical or Aerospace Engineering and related fields of study, researchers in space industrial and governmental research and development facilities, as well as researchers in astronautics. This book also: · Illustrates all key concepts with examples · Includes exercises for each chapter · Explains concepts and engineering tools a student or experienced engineer can apply to mission design and navigation of space missions · Covers fundamental principles to expose the student to the basic dynamics of space flight

These problems and solutions are offered to students of mathematics who have learned real analysis, measure theory, elementary topology and some theory of topological vector spaces. The current widely used texts in these subjects provide the background for the understanding of the problems and the finding of their solutions. In the bibliography the reader will find listed a number of books from which the necessary working vocabulary and techniques can be acquired. Thus it is assumed that terms such as topological space, u-ring, metric, measurable, homeomorphism, etc., and groups of symbols such as AnB, x EX, f: IR 3 X 1-+ X 2 - 1, etc., are familiar to the reader. They are used without introductory definition or explanation. Nevertheless, the index provides definitions of some terms and symbols that might prove puzzling. Most terms and symbols peculiar to the book are explained in the various introductory paragraphs titled Conventions. Occasionally definitions and symbols are introduced and explained within statements of problems or solutions. Although some solutions are complete, others are designed to be sketchy and thereby to give their readers an opportunity to exercise their skill and imagination. Numbers written in boldface inside square brackets refer to the bib liography. I should like to thank Professor P. R. Halmos for the opportunity to discuss with him a variety of technical, stylistic, and mathematical questions that arose in the writing of this book. Buffalo, NY B.R.G.