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 ...
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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! 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 thesemodern techniques available to us all.

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Product Details

  • ISBN-13: 9780943396354
  • Publisher: Willmann-Bell, Incorporated
  • Publication date: 1/28/1991
  • Pages: 429

Table of Contents

Some Symbols and abbreviations5
Chapter 1: Hints and Tips.....7
Chapter 2: about accuracy.....15
Chapter 3: Interpolation.....23
Chapter 4: Curve Fitting.....35
Chapter 5: Iteration.....47
Chapter 6: Sorting Numbers.....55
Chapter 7: Julian Day.....59
Chapter 8: Date of Easter.....67
Chapter 9: Jewish and Moslem Calendars.....71
Chapter 10: Dynamical Time and Universal Time.....77
Chapter 11: The Earth's Globe.....81
Chapter 12: Sidereal Time at Greenwich.....87
Chapter 13: Transformation of Coordinates.....91
Chapter 14: The Parallactic angle, and three other Topics.....97
Chapter 15: Rising, Transit, and Setting.....101
Chapter 16: atmospheric Refraction.....105
Chapter 17: angular Separation.....109
Chapter 18: Planetary Conjunctions.....117
Chapter 19: Bodies in Straight Line.....121
Chapter 20: Smallest Circle containing three Celestial Bodies.....127
Chapter 21: Precession.....131
Chapter 22: Nutation and the Obliquity of the Ecliptic.....143
Chapter 23: apparent Place of a Star.....149
Chapter 24: Reduction of Ecliptical Elements from one Equinox to another one.....159
Chapter 25: Solar Coordinates.....163
Chapter 26: Rectangular Coordinates of the Sun.....171
Chapter 27: Equinoxes and Solstices.....177
Chapter 28: Equation of Time.....183
Chapter 29: Ephemeris for Physical Observations of the Sun.....189
Chapter 30: Equation of Kepler.....193
Chapter 31: Elements of the Planetary Orbits.....209
Chapter 32: Positions of the Planets.....217
Chapter 33: Elliptic Motion.....223
Chapter 34: Parabolic Motion.....241
Chapter 35: Near-parabolic Motion.....245
Chapter 36: The Calculation of some Planetary Phenomena.....249
Chapter 37: Pluto.....263
Chapter 38: Planets in Perihelion and in aphelion.....269
Chapter 39: Passages through the nodes.....275
Chapter 40: Correction for Parallax.....279
Chapter 41: Illuminated Fraction of the Disk and Magnitude of a Planet.....283
Chapter 42: Ephemeris for Physical Observations of Mars.....287
Chapter 43: Ephemeris for Physical Observations of Jupiter.....293
Chapter 44: Positions of the Satellites of Jupiter.....301
Chapter 45: The Ring of Saturn.....317
Chapter 46: Positions of the Satellites of Saturn.....323
Chapter 47: Position of the Moon.....337
Chapter 48: Illuminated Fraction of the Moon's Disk.....345
Chapter 49: Phases of the Moon.....349
Chapter 50: Perigee and apogee of the Moon.....355
Chapter 51: Passages of the Moon through the Nodes.....363
Chapter 52: Maximum Declinations of the Moon.....367
Chapter 53: Ephemeris for Physical Observations of the Moon.....371
Chapter 54: Eclipses.....379
Chapter 55: Semidiameters of the Sun, Moon, and Planets.....389
Chapter 56: Stellar Magnitudes.....393
Chapter 57: Binary Stars.....397
Chapter 58: Calculation of a Planar Sundial.....401
appendix I: Constants.....407
appendix 11: 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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When, in 1978, I wrote the first (Belgian) edition of my astronomical Formulae for Calculators, the industry of microcomputers was just starting its worldwide expansion. Because these "personal computers" were not yet within reach of everybody, the aforesaid book was written mainly for the users of pocket calculating machines and therefore calculation methods requiring a large amount of computer memory, or many steps in a program, were avoided as far as possible, or kept to a minimum.

The present work is a greatly revised version of the former one. It is, in fact, a completely new book. The subjects have been expanded and the content has been improved. Changes were needed to take into account new resolutions of the International astronomical Union, particularly the adoption of the new standard epoch J2000.0, while moreover I profited by the new planetary and lunar theories constructed at the Bureau des Longitudes, Paris.

as Gerard Bodifee wrote in the Preface of my previous work:

anyone who endeavours to make astronomical calculations has to be very familiar with the essential astronomical conceptions and rules and he must have sufficient knowledge of elementary mathematical techniques. as a matter of fact he must have a perfect command of his calculating machine, knowing all possibilities it offers the competent user. However, all these necessities don't suffice. Creating useful, successful and beautiful programs requires much practice. Experience is the mother of all science. This general truth is certainly valid for the art of programming. Only by experience and practice can one learn the innumerable tricks and dodges that are so useful and often essential in agood program.

astronomical algorithms intends to be a guide for the (professional or amateur) astronomer who wants to do calculations. an algorithm (from the arabic mathematician al-Khltrezmi) is a set of rules for getting something done; for us it is a mathematical procedure, a sequence of reasonings and operations which provides the solution to a given problem.

This book is not a general textbook on astronomy. The reader will find no theoretical derivations. Some definitions are kept to a minimum. Nor is this a textbook on mathematics or a manual for microcomputers. The reader is assumed to be able to use his machine properly.

Except in a few rare cases, no programs are given in this book. The reasons are clear. a program is useful only for one computer language. Even if we consider BaSIC only, there are so many versions of this language that a given program cannot be used as such by everybody without making the necessary changes. Every calculator thus must learn to create his own programs. There is the added circumstance that the precise contents of a program usually depend on the specific goals of the computation, that are impossible to anticipate by anybody else.

The few programs we give are in standard BaSIC. They can easily be converted into FORTRaN or any other programming language.

Of course, in the formulae we still use the classical mathematical symbols and notations, not the symbolism used in program languages. For example, we write instead of SQR(a), or a (1 - e) instead of a * (I - E), or cos2x instead of COS (X)" 2 or cos(X) * * 2.

The writing of a program to solve some astronomical problem will require a study of more than one chapter of this book. For instance, in order to create a program for the calculation of 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 is restricted to the "classical", mathematical astronomy, although a few astronomy oriented mathematical techniques are dealt with, such as interpolation, fitting curves, and sorting data. But astrophysics is not considered at all. Moreover, it is clear that not all topics of mathematical astronomy could have been covered in this book. So nothing is said about orbit determination, occultations of stars by the Moon, meteor astronomy, or eclipsing binaries. For solar eclipses, the interested reader will find Besselian elements and many useful formulae in Elements of Solar Eclipses 1951 to 2200 by the undersigned (1989). Elements and formulae about transits of Mercury and Venus across the Sun's disk are provided in my Transits (1989). These two books are published by Willmann-Bell, Inc.

The author wishes to express his gratitude to Dr. S. De Meis (Milan, Italy), to a. Dill (Germany), and to E. Goffin and C. Steyaert (Belgium), for their valuable advice and assistance.

Jean Meeus

Note to the second edition

In this second edition several misprints and errors have been corrected. The principal change in the new edition is the addition of some material, such as expressions for the times of the stations of the planets (Chapter 36), a list of constants (appendix I), expressions for the heliocentric coordinates of the giant planets from 1998 to 2025 (appendix IV), and new chapters about the Jewish and Moslem Calendars, and the satellites of Saturn.


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