Astronomical Algorithms, 2nd edition

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About the book Astronomical Algorithms

In the field of celestial calculations, Jean Meeus has enjoyed wide acclaim and respect since long before microcomputers and pocket calculators appeared on the market. When he brought out his Astronomical Formulae for Calculators in 1979, it was practically the only book of its genre. It quickly became the "source among sources," even for other writers in the field. Many of them have warmly acknowledged their debt (or should have), citing the unparalleled clarity of his instructions and the rigor of his methods.

And now this Belgian astronomer has outdone himself yet again with Astronomical Algorithms! Virtually every previous handbook on celestial calculations (including his own earlier work) was forced to rely on formulae for the Sun, Moon, and planets that were developed in the last century — or at least before 1920. The past 10 years, however, have seen a stunning revolution in how the world's major observatories produce their almanacs. The Jet Propulsion Laboratory in California and the U.S. Naval Observatory in Washington, D.C., have perfected powerful new machine methods for modeling the motions and interactions of bodies within the solar system. At the same time in Paris, the Bureau des Longitudes has been a beehive of activity aimed at describing these motions analytically, in the form of explicit equations.

Yet until now the fruits of this exciting work have remained mostly out of reach of ordinary people. The details have existed mainly on reels of magnetic tape in a form comprehensible only to the largest brains, human or electronic. But Astronomical Algorithms changes all that. With his special knack for computations of all sorts, the author has made the essentials of these modern techniques available to us all.

The second edition contains new chapters about the Jewish and Moslem Calendars, and on the satellites of Saturn, and a new Appendix giving expressions (polynomials) for the heliocentric coordinates of the giant planets Jupiter to Neptune from 1998 to 2025.

From the Reviews

…There is no doubt that the book is very good value for the money…computer-minded astronomers will never want to be without it.

                                                                                                                                     —The Observatory

…There are times when an amateur astronomer wants to perform the computations that support his or her observations. Astronomical Algorithms is the reference to have for this. Jean Meeus’ concise volume collects most of the algorithms and computational techniques an observer might want—covering coordinate transformations, the apparent place of a star, the positions of solar system bodies, eclipse predictions, and much more. Discussions are complete enough to make the equations fully understandable to the novice, and virtually every algorithm includes a fully worked numerical example….This is a very handy reference, well worth owning, even if you never have to perform a specific calculation. The text alone is helpful for understanding how the theories of celestial mechanics are applied in practice.

                                                                                                                                                                                —Sky & Telescope

…Indispensable for any student of astronomy, amateur or professional, who enjoys computation.


…Already celebrated for his contributions to the literature of astronomical calculating, Belgian meteorologist Jean Meeus has authored another helpful, though technical, compendium for the mathematically minded. Taking advantage of new astrodynamic models, he has transformed complex techniques into a series of recipes that will permit the motivated, computerized cognoscienti to calculate just about anything they wish. Between the Urania-ornamented covers of this book you get all kinds of time, atmospheric refraction, conjuctions, obliquity of the ecliptic, equinoxes and solstices, planetary ephemerides, lunar phases, eclipses, binary stars, and a whole lot more.

                                                                                                                                                                             —Griffith Observer

Table of Contents

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

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