This is a cookbook of algorithms for solving a variety of numerical problems that come up in astronomy. Explanations of why the author chose to do things a certain way are not on the agenda, but various numerical examples are. Programs are not included, although it is fairly easy to go from the algorithms presented to code. For that information I recommend the equally affordable Textbook on Spherical Astronomy. That book is a pleasure to read and was written with newcomers to the field in mind. Read that book first. It will tell you most of the "whys" omitted in this book.

To understand some astronomical problems will require studying more than one chapter of this book. For instance, to calculate the altitude of the Sun for a given time on a given date at a given place, one must first convert the date and time to Julian Day (Chapter 7), then calculate the Sun's longitude for that instant (Chapter 25), its right ascension and declination (Chapter 13), the sidereal time (Chapter 12) and finally the required altitude of the Sun (Chapter 13).

This book focuses on classical mathematical astronomy, although a few astronomy oriented mathematical techniques are dealt with, such as interpolation, fitting curves, and sorting data. Astrophysics is not a topic covered in this book. Also, it is plain that not all topics of mathematical astronomy could have been covered in this book. Thus, nothing is said about orbit determination, occultations of stars by the Moon, meteor astronomy, or eclipsing binaries.

The table of contents can be hard to track down, and there are no excerpts available on line, so I present the table of contents next:

Some Symbols and Abbreviations 5
1. Hints and Tips 7
2. About Accuracy 15
3. Interpolation 23
4. Curve Fitting 35
5. Iteration 47
6. Sorting Numbers 55
7. Julian Day 59
8. Date of Easter 67
9. Jewish and Moslem Calendars 71
10. Dynamical Time and Universal Time 77
11. The Earth's Globe 81
12. Sidereal Time at Greenwich 87
13. Transformation of Coordinates 91
14. The Parallactic Angle 97
15. Rising, Transit and Setting 101
16. Atmospheric Refraction 105
17. Angular Separation 109
18. Planetary Conjunctions 117
19. Bodies in a Straight Line 121
20. Smallest Circle Containing Three Celestial Bodies 127
21. Precession 131
22. Nutation and the Obliquity of the Ecliptic 143
23. Apparent Place of a Star 149
24. Reduction of Ecliptical Elements from One Equinox to Another One 159
25. Solar Coordinates 163
26. Rectangular Coordinates of the Sun 171
27. Equinoxes and Solstices 177
28. Equation of Time 183
29. Ephemeris for Physical Observations of the Sun 189
30. Equation of Kepler 193
31. Elements of the Planetary Orbits 197
32. Positions of the Planets 217
33. Elliptic Motion 223
34. Parabolic Motion 241
35. Near-Parabolic Motion 245
36. The Calculation of some Planetary Phenomena 249
37. Pluto 263
38. Planets in Perihelion and Aphelion 269
39. Passages through the Nodes 275
40. Correction for Parallax 279
41. Illuminated Fraction of the Disk and Magnitude of a Planet 283
42. Ephemeris for Physical Observations of Mars 287
43. Ephemeris for Physical Observations of Jupiter 293
44. Positions of the Satellites of Jupiter 301
45. The Ring of Saturn 317
46. Positions of the Satellites of Saturn 323
47. Position of the Moon 337
48. Illuminated Fraction of the Moon's Disk 345
49. Phases of the Moon 349
50. Perigee and Apogee of the Moon 355
51. Passages of the Moon through the Nodes 363
52. Maximum Declinations of the Moon 367
53. Ephemeris for Physical Observations of the Moon 371
54. Eclipses 379
55. Semidiameters of the Sun, Moon and Planets 389
56. Stellar Magnitudes 393
57. Binary Stars 397
58. Calculation of a Planar Sundial 401
Appendix I Constants 407
Appendix II Some Astronomical Terms 409
Appendix III Planets: Periodic Terms 413
Appendix IV Coefficients for the Heliocentric Coordinates of
Jupiter to Neptune, 1998-2025 455
Index

Astronomical Algorithms is the reference you want if you intend implementing all sorts of astronomical calculations, solstices and equinoxes, moon and planetary positions, star positions, and more. The examples provided are useful for checking your own implementation.

It's loaded with numbers and equations. There is no fat, no padding.

This is one of the most powerful tools in the knowledge of celestial mechanics. Either if you really want to compute celestial positions or you don't, this book may help you improving your astronomy skills. The firsts chapters of this book make a very useful aproach to computation, curve fitting, and precision, expressed in a very affordable language, as the whole book. If you are interested in astronomy in general, I think this is the best way of invest 30 bucks.

Impressive collection of algorithms for all types of astronomical calculations. Thorough description of HOW to implement the formulas. Relatively few derivations/explanations of WHY the equations work. Some of the material is a bit disjointed in sequence, but still usable. This appears to be THE reference to buy - save lots of time over trying to find or derive the formulas on your own.

This book is very useful for writing astronomy programs, and it gives an essential foundation for astrology programs. The information is a little dispersed throughout the book. It isn't written as a textbook, but rather as a solid reference, and in this way, it excels. Sometimes, the book gives two or three different ways of arriving at the same result with varying degrees of accuracy. It has something for everyone interested in the movements of the sky, and whether you're casually interested in astronomy or a programmer of ephemerides, you need this book.