eCosmology

Does anyone know any good books about mathematical astronomy?

I am really interested in mathematical astronomy. It seems that no one publishes any good books about it. I would like to learn a bit more about it. Does anyone know any good books about it?

Public Comments

1. Of course they publish books. Where did you look? Did you actually look anywhere? Typing "mathematical astronomy" in to the search page at amazon.com brings up a whole pile of interesting-looking books. I own copies of several of them. Books by Jean Meeus are good ones to start with.
2. You need a firm basis in mathematics to do any kind of advanced astronomy, so in a sense every astronomy book (except books geared to non-scientists) is mathematical. Here are five books that you might be interested in: 1) Astronomical Algorithms, by Jean Meeus (available from Willman Bell http://www.willbell.com ) 2) Mathematical Astronomy Morsels, by Jean Meeus (available from Willman Bell) 3) Explanatory Supplement to the Astronomical Almanac, edited by P. Kenneth Seidelmann (available from Amazon) 4) Textbook on Spherical Astronomy, by W.M. Smart (available from Amazon) 5) Statistical Astronomy, by Robert J. Trumpler and Harold F. Weaver (out of print, used copies available from Amazon) Astronomical Algorithms explains how to do calculations useful for amateur and professional astronomy. It's especially useful if you're interested in writing astronomy software; but if you enjoy mathematics, the book is interesting even if you don't implement the algorithms. It covers topics like the following: - sidereal time - rising and setting of objects - precession - calculating coordinates of sun, moon, and planets - eclipses - sundials The other book by Meeus, Mathematical Astronomy Morsels, is quite different. Meeus is a superb celestial mechanic and calculator. In this book, he covers a wide assortment of topics -- the moon and planets, the celestial sphere, and eclipses. For instance: - How often do eclipses occur? - How often does an observer in one location see a total eclipse? - Where is the barycenter of the solar system? - How often are planets aligned (more or less)? - When do you see the shadows of three satellites on the disk of Jupiter? When are all of the satellites invisible? Meeus has written three additional books in the "Morsels" series. If you like the first one, you might take a look at the others also. The Astronomical Almanac is an annual publication of the Naval Observatory that has high-precision astronomical data, such as the coordinates of objects in the solar system. The book I mentioned above, the Explanatory Supplement, explains the astronomy behind the Astronomical Almanac. This might sound esoteric, but much of the book is understandable to anyone with a decent knowledge of astronomy and some mathematics. There are interesting sections, for example, on time and calendars. All of astronomy is based on observations on the celestial sphere. The normal trigonometry you learn in high school is "plane trigonometry". A different set of mathematics is necessary to understand spherical trigonometry, so that you can do calculations based on triangles on the celestial sphere, such as the following: - calculating the azimuth and altitude of a star for a particular time and location - converting equatorial coordinates (based on the earth's equator) into ecliptic coordinates (based on the plane of the earth's orbit) If you understand plane trigonometry, you can understand the basic principles of spherical trigonometry without too much effort. There are a number of books on this subject, but one classic (old but still in print) is Textbook on Spherical Astronomy, by W.M. Smart If you find this book on Amazon, you can search through the table of contents and see if it looks interesting. The last book I mentioned, Statistical Astronomy, is the most difficult one here. It's a graduate-level book and quite heavy in mathematics; also, it's an old book (1953) and out-of-print, although used copies are available. Here are some examples of "statistical astronomy": - The stars we see are not a good statistical sample, because it is easier to see intrinsically bright stars than intrinsically faint stars. From the stars we see, how do we construct a model of the actual distributions of various stellar types. - The motions of stars are due to various sources -- the motion of the sun, the motions of the stars themselves, and the rotation of the galaxy. How do we disentangle these effects? How can we use stellar motions to determine distances (in a statistical sense) to a class of stars? -- edit I see from your profile that you're in high school. If you enjoy math and astronomy, I'd recommend Mathematical Astronomy Morsels first, and maybe the Explanatory Supplement. If you're very good at math and thoroughly understand trigonometry, you might want to tackle a book on spherical astronomy. Statistical Astronomy is a difficult book and really shouldn't be included in this answer, but some of the same topics are covered briefly in good introductory astronomy textbooks (particularly the ones that are not afraid to include a little mathematics).