# Celestial Calculations: A Gentle Introduction to Computational Astronomy

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## Book Preface

Introductory astronomy books can generally be placed into 1 of 2 categories. Books in the first category are almost devoid of any mathematics. Such books are descriptive in nature and are typically filled with photographs and artistic impressions of the awe-inspiring, otherworldly vistas that can be found scattered throughout the cosmos. By contrast, books in the second category approach astronomy from a mathematical standpoint and are filled with complex equations for describing celestial motion. Such books can be quite challenging to read because of the level of mathematics and physics required to understand the concepts being discussed.

This book is an attempt to bridge both categories. While mathematical calculations are central, this book concerns itself with applying concepts instead of deriving formulas. As a noncalculus introduction to computational astronomy, it requires relatively little mathematical skill. Rest assured, high school algebra and a little trigonometry are more than sufficient for following the various methods presented in this book! Taking a simplified mathematical approach comes at a cost, however. By avoiding more advanced mathematics, the algorithms and equations presented herein will not produce results that are accurate enough for professional astronomers. Even so, the methods presented are generally accurate to within a few minutes of time or a few arcminutes, which should be sufficient for most amateur astronomers.

Books about celestial mechanics often assume that a reader understands why a calculation is necessary and needs only to be shown how to derive and apply the proper equations. By contrast, this book emphasizes understanding what calculations are required, why they are needed, and how all the pieces fit together. As this book will also demonstrate, the very same principles that describe the motion of the planets and stars can be readily applied to track the man-made satellites and other objects, such as the International Space Station, that orbit Earth. The space around our planet has become increasingly crowded since Sputnik, the world’s first satellite, was hurled into orbit in the fall of 1957. Today more than 500,000 objects over 10 cm in size orbit Earth.

Many of those objects are useful satellites while others are debris and remnants of the rockets used to carry payloads into space. Locating and tracking those objects can be as entertaining a hobby as amateur astronomy itself. The chapters ahead do more than merely present the mathematics necessary to explain a particular concept or predict an astronomical event. A computer is also used to demonstrate the topics and guide the reader through the incredible maze of technical details necessary to locate a star or a planet, or predict when sunrise will occur and what the phase of the Moon will be. By employing the computational power of modern personal computers, the tedium of the lengthy calculations required for virtually every task has been eliminated. When the principles discussed in this book are combined with the use of a computer, the result is a powerful and stimulating environment for enjoying the wonders of astronomy. Using a computer allows readers to concentrate on major concepts rather than getting lost in myriad technical details, and it allows a chapter review as often as necessary while a computer serves as a patient guide.

Source code is provided for all of the book’s example programs, althoughno claim is made that their implementation is the best or most suitable for the problem being solved. In particular, the reader is forewarned that relatively little error checking is done, especially during data entry, so that by virtue of brevity the programs will be clearer and easier to follow. In addition, implementation decisions were sometimes made to simplify porting the programs from one programming language to another; these are decisions that might not have been made if software portability was not also an objective.