Ashish Tewari - Foundations of Space Dynamics

To the loving memory of my daughter, Manya (24.1.2000 ‐ 9.7.2019)

This edition first published 2021

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Library of Congress Cataloging‐in‐Publication Data

Names: Tewari, Ashish, author.

Title: Foundations of space dynamics / Ashish Tewari.

Description: First edition. | Hoboken, NJ : Wiley, [2020] | Series:

Aerospace series | Includes bibliographical references and index.

Identifiers: LCCN 2020033397 (print) | LCCN 2020033398 (ebook) | ISBN

9781119455349 (paperback) | ISBN 9781119455332 (adobe pdf) | ISBN

9781119455325 (epub) | ISBN 9781119455301 (obook)

Subjects: LCSH: Aerospace engineering. | Astrodynamics. | Orbital

mechanics.

Classification: LCC TL545 .T385 2020 (print) | LCC TL545 (ebook) | DDC

629.4/11–dc23

LC record available at https://lccn.loc.gov/2020033397

LC ebook record available at https://lccn.loc.gov/2020033398

Cover Design: Wiley

Cover Image: © Philip Wallick/Getty Images

To the loving memory of my daughter, Manya (24.1.2000 ‐ 9.7.2019)

Foundations of Space Dynamics is written as a textbook for students, as well as a ready reference covering the essential concepts for practicing engineers and researchers. It introduces a reader to the basic aspects of both orbital mechanics and attitude dynamics. While many good textbooks are available on orbital mechanics and attitude dynamics, there is a need for a direct, concise, yet rigorous treatment of both the topics in a single textbook. Important derivations from basic principles are highlighted, while offering insights into the physical principles which can often be hidden by mathematical details. While the emphasis is on analytical derivations, the essential computational tools are presented wherever required, such as the iterative root‐finding methods and the numerical integration of ordinary differential equations.

The objective of this book is to provide a physically insightful presentation of space dynamics. The usage of simple ideas and numerical tools to illustrate advanced concepts is inspired by the work of the original masters (Newton, Liebnitz, Laplace, Gauss, etc.), and is combined with the application and terminology of modern space dynamics.

A student of space dynamics in the past generally possessed a strong background in analytical mechanics, often reinforced by such classical treatises as those by Whittaker, Lanczos, Truesdell, and Mach. Today, the exposure to analytical dynamics is often based upon a single undergraduate course. This book therefore includes a basic introduction to analytical mechanics by both Newtonian and Lagrangian approaches.

The contents of the textbook are arranged such that they may be covered in two successive courses: Space Dynamics I could focus on Chaps. 1–7 and 11, while the following course, Space Dynamics II , could cover Chaps. 8–10 and 12, supplemented by a semester project exploring a specific research topic. However, the arrangement of the chapters in the book offers sufficient flexibility for them to be covered in a single comprehensive course, if so required. There are a multitude of exercises at the end of the chapters which can serve as homework assignments and quiz problems. Solutions to selected exercises is also provided.

I would like to thank the editorial and production staff of Wiley, Chichester, for their constructive suggestions and valuable insights during the preparation of the manuscript.

Ashish Tewari

May 2020

This chapter gives an introduction to the basic features of space flight, which is predominated by the quiet space environment and gravity. The essential differences with atmospheric flight are discussed, and the important time scales and frames of reference for space flight are described. Topics in space dynamics are classified as the translational motion (orbital mechanics) and rotational motion (attitude dynamics) of a rigid spacecraft. Classification of the various practical spacecraft is given according to their missions.

Space flight refers to motion outside the confines of a planetary atmosphere. It is different from atmospheric flight in that no assistance can be derived from the atmospheric forces to support a vehicle, and no benefit of planetary oxygen can be utilized for propulsion. Apart from these major disadvantages, space flight has the advantage of experiencing no (or little) drag due to the resistance of the atmosphere; hence a spacecraft can achieve a much higher flight velocity than an aircraft. Since atmospheric lift is absent to sustain space flight, a spacecraft requires such high velocities to balance the force of gravity by a centrifugal force in order to remain in flight. The trajectories of spacecraft (called orbits ) – being governed solely by gravity – are thus much better defined than those of aircraft. Since gravity is a conservative force, space flight involves a conservation of the sum of kinetic and potential energies, as well as that of the angular momentum about a fixed point. Therefore, space flight is much easier to analyze mathematically when compared to atmospheric flight.