Unknown - Fundamentals of Astronomy A guide for Olympiads nodrm

Flavio Salvati Fundamentals of Astronomy A guide for Olympiads ii Copyright c 2020 Flavio Salvati All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of the author, or as expressly permitted by law, or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the author. You must not circulate this book in any other binding or cover and you must impose the same conditions on any buyer. Experience suggests that it is close to impossible for the book to be error-free. If something looks amiss, please check the webpage www.astrolympiad.com for a list of typos, updates and additional problems.

If you have any questions or suggestions, dont hesitate to contact me at astrolympiad@gmail.com. ISBN: 979-8688791433 Published on the autumnal equinox, 2020. To my parents Contents ix iv Contents v vi Contents Contents vii viii Contents Preface ix Preface Chances are you too have gazed in awe and wonder at the night sky, with endless questions drifting through your mind: how did the universe begin, how did life spark on Earth, are there any other intelligent beings in the universe and, if so, why hasnt anyone visited our planet? These are questions one can hardly ignore and, while our chances of finding a definitive answer within our lifetime are slim, we can make progress and enable future generations to do so. This book will teach you the fundamentals of astronomy, passing on the discoveries of countless scientists who lived before us, giving you the tools to continue along this endless journey. Maybe you will be writing the next chapter. I have tried to make this book accessible to a large audience, with the only prerequisites being basic high school mathematics and physics.

Slightly more advanced mathematical tools are covered in the appendix, making the book self-contained. At the same time, there are plenty of exercises and problems which will help you become familiar with the concepts explained throughout the theory. The book is specifically aimed at students preparing for the regional and national phases of the Astronomy Olympiads, but will still represent a valuable resource for those chosen to represent their countries at the international competition (IOAA and IAO). While the book contains a lot of information, you are encouraged to supplement it with online resources and other textbooks that might cover some topics in more detail. The book has been divided into 4 parts. Part I (Positional Astronomy) covers the celestial coordinate systems, the transformation and perturbation of coordinates, observation and instruments, the time systems and the Moon.

Part II (Radiation Mechanisms) explains electromagnetic radiation, flux, stellar magnitudes and the cosmological ladder. Part III (Celestial mechanics) introduces gravitation and Keplers laws, the motion of the planets, the rocket equation, orbital manoeuvres and binary systems. Finally, Part IV (Solutions) presents detailed solutions to all the exercises and problems. I decided to distinguish between exercises, which require you to apply the concepts learned throughout the theory (aimed at sharpening your problem solving skills), and problems, which will guide you through the derivation of entirely new concepts (targeting your creative thinking). The difficulty of the exercises and problems is denoted by asterisks, from zero (easy) to four (extremely challenging). Of course, you may disagree with my judgement of difficulty, but I think that an arbitrary weighting scheme is better than none at all.

Some problems are extremely hard, so it is normal you will get stuck. In this case, dont be discouraged, just set the problem aside for some time and get back to it later. You will find that thinking about the possible solutions over and over again will strengthen what you learned and resolve new doubts. x Preface If you need some guidance, try reading the solution line-by-line (maybe covering the rest of the page with a piece of paper), pausing where you think you can continue by yourself. I have added interesting discussions at the end of many solutions, so be sure to read them after you solve a question. In the case of questions with 4 asterisks, my aim was to create an almost insurmountable challenge, that will always give you something to think about.

I have also included some exercises of various astronomy competitions, from the national to the international level. The source is stated at the beginning of each problem (see the next page for a list of references), so that you can easily find it online. At the end of the book there are four appendices. Appendix A (Mathematics) covers the necessary concepts to understand the theory and solve most of the exercises. My advice is that you start by studying this part, if you are not familiar with high school mathematics. Appendix B (Kepler laws) contains a proof of Kepler laws from Newtons law of gravitation.

I suggest you read this only after having gone through Appendix A and Part III. Appendix C (Virial theorem) contains a proof of the Virial theorem in its most general form. Finally, Appendix D (Tables and constants) has been included to speed up the process of finding known constants when solving exercises and problems. I want to thank everyone that helped proof-read the book: Alexandra Alexiu and Amar Shah, who read the whole manuscript and made invaluable suggestions, and Je Qin Chooi and Alisa Hathaway for the additional help in the more challenging chapters. I also want to thank my parents, Lidwina and Francesco, and my siblings, Fabiana and Federico, for reading the book and encouraging me to finish this immense project. Despite scrupulous reviews by myself and many other people, it is practically impossible for the book to be error-free.

If something looks amiss, visit www.astrolympiad.com for a list of typos and updates. On the website I will also publish many other problems that, for the sake of brevity, I could not include in the book. If you discover an error that has not yet been published, I would be very grateful if you could report it to me either by filling out the form on the site or by writing to the email address astrolympiad@gmail.com. If you have any questions or suggestions, dont hesitate to contact me. Finally, if you liked the book, I would be grateful if you could leave a review. I hope you enjoy the book! National Olympiads xi National Olympiads Part of the exercises were selected from the following national competitions: ARAO, the All-Russian Astronomy Olympiad; ArmAO, the Armenian Astronomy Olympiad; BAAO, the British Astronomy and Astrophysics Olympiad; CAO, the Canadian Astronomy Olympiad; CzAO, the Czech Astronomy Olympiad; INAO, the Indian National Astronomy Olympiad; INT and NAZ, the Italian regional and national Astronomy Olympiads; MyAO, the Malaysian Astronomy Olympiad; SAO, the Singaporean Astronomy Olympiad; ONAA, the Romanian Astronomy and Astrophysics Olympiad; USAAAO, the U.S.A.

Astronomy and Astrophysics Olympiad. You will also find exercises from the following international competitions: IAO, the International Astronomy Olympiads. IOAA, the International Olympiads on Astronomy and Astrophysics; xii Contents Part I Positional Astronomy Celestial Coordinate Systems In this chapter we aim to study the commonly used astronomical reference systems. In the past, man believed that the universe was confined within a spherical shell and that the stars, fixed on this shell, were all equidistant from the Earth, placed at the centre of the universe. Although we know today that these assumptions are for the most part false, this simple model is still useful today, in many aspects, as it was in the past. In fact, since most of the measurements are taken from Earth, it is useful to place ourselves at the centre of the universe.