by Jean Meeus, 6.00" by 9.00"

477 pages, hardbound

2nd Edition published 1999

$34.95

Errata: 1st Edition

Errata: 2nd Edition

Note: All printings, with a 2005 printing date or later have no known errors.

**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.

*—Choice*

…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

Index