FUNDAMENTALS OF ASTRODYNAMICS (original) (raw)
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The Motion of Celestial Bodies
2011
The history of celestial mechanics is first briefly surveyed, identifying the major contributors and their contributions. The Ptolemaic and Copernican world models, Kepler’s laws of planetary motion and Newton’s laws of universal gravity are presented. It is shown that the orbit of a body moving under the gravitational attraction of another body can be represented by a conic section. The six orbital elements are defined, and it is indicated how they can be determined from observed positions of the body on the sky. Some special cases, permitting exact solutions of the motion of three gravitating bodies, are also treated. With two-body motion as a first approximation, the perturbing effects of other bodies are next derived and applied to the motions of planets, satellites, asteroids and ring particles. The main effects of the Earth’s oblateness on the motions of artificial satellites are explained, and trajectories for sending a space probe from one planet to another are shown. The in...
Orbital Mechanics and Astrodynamics
2015
The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein.
2002
Before Kepler all men were blind. Kepler had one eye, Newton had two. Voltaire In this chapter we introduce the concept of angular momentum for a particle and show that it is conserved for a particle in a central force field. We then show how the two-particle problem can be reduced to an effective one-particle problem in the center of mass system. After that the we use conservation of energy to find out things about central motion. The Kepler problem for motion in a 1/r 2-force field is solved using the conservation of energy and angular momentum. Some properties of the resulting solutions, the ellipse, the parabola, and the hyperbola are presented. We then discuss the problem of the force-field from an extended body, in particular the spherically symmetric case.
Knowledge of orbital motion is essential for a full understanding of space operations. Motion through space can be visualized using the laws described by Johannes Kepler and understood using the laws described by Sir Isaac Newton. Thus, the objectives of this chapter are to provide a conceptual understanding of orbital motion and discuss common terms describing that motion. The chapter is divided into three sections. The first part focuses on the important information regarding satellite orbit types to provide an understanding of the capabilities and limitations of the spaceborne assets supporting the war fighter. The second part covers a brief history of orbital mechanics, providing a detailed description of the Keplerian and Newtonian laws. The third section discusses the application of those laws to determining orbit motion, orbit geometry, and orbital elements. This section has many facts, figures, and equations that may seem overwhelming at times. However, this information is essential to understanding the fundamental concepts of orbital mechanics and provides the necessary foundation to enable war fighters to better appreciate the challenges of operating in the space domain.
The celestial mechanics approach: theoretical foundations
Journal of Geodesy, 2010
Gravity field determination using the measurements of Global Positioning receivers onboard low Earth orbiters and inter-satellite measurements in a constellation of satellites is a generalized orbit determination problem involving all satellites of the constellation. The celestial mechanics approach (CMA) is comprehensive in the sense that it encompasses many different methods currently in use, in particular so-called short-arc methods, reduced-dynamic methods, and pure dynamic methods. The method is very flexible because the actual solution type may be selected just prior to the combination of the satellite-, arc-and technique-specific normal equation systems. It is thus possible to generate ensembles of substantially different solutions-essentially at the cost of generating one particular solution. The article outlines the general aspects of orbit and gravity field determination. Then the focus is put on the particularities of the CMA, in particular on the way to use accelerometer data and the statistical information associated with it. Keywords Celestial mechanics • Orbit determination • Global gravity field modeling • CHAMP • GRACE 1 Problem description and overview This article has the focus on the theoretical foundations of the so-called celestial mechanics approach (CMA). Applications
PREFACE This book is the outgrowth of courses taught at Stanford University and at the University of California, Los Angeles, and of the authors' professional activities in the field of spacecraft dynamics. It is intended both for use as a textbook in courses of instruction at the graduate level and as a reference work for engineers engaged in research, design, and development in this field. The choice and arrangement of topics was dictated by the following considerations.
General-relativistic celestial mechanics. IV. Theory of satellite motion
Physical Review D, 1994
The basic equations needed for developing a complete relativistic theory of artificial Earth satellites are explicitly written down. These equations are given both in a local, geocentric frame and in the global, barycentric one. They are derived within our recently introduced general-relativistic celestial mechanics framework. Our approach is more satisfactory than previous ones, especially with regard to its consistency, completeness, and flexibility. In particular, the problem of representing the relativistic gravitational effects associated with the quadrupole and higher multipole moments of the moving Earth, which caused difficulties in several other approaches, is easily dealt with in our approach thanks to the use of previously developed tools: the definition of relativistic multipole moments and transformation theory between reference frames. With this last paper in a series we hope to indicate the way of using our formalism in specific problems in applied celestial mechanics and astrometry.
Mathematical Problems in Engineering, 2009
The space activity in the world is one of the most important achievements of mankind. It makes possible live communications, exploration of Earth resources, weather forecast, accurate positioning and several other tasks that are part of our lives today.
Modern Celestial Mechanics: From Theory to Applications
2002
t the opening of the "Third Meeting on Celestial Mechanics - CELMEC III", strong sensations hit our minds. The conference (18-22 June 2001) was being held in Villa Mondragone, a beautiful complex of buildings and gardens located within the township of Monte Porzio Catone, on the hills surrounding Rome. A former papal residence, the building has been recently restored by the University of Rome "Tor Vergata" to host academic activities and events