USNO Circular 179 - U.S. Naval Observatory

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vi INTRODUCTION that are available on the World Wide Web. These URLs are numbered and they are referred to in the text by number — for example, a PDF version of this circular can be found at URL 1. It is assumed that readers have a basic knowledge of positional astronomy; that the terms right ascension, declination, sidereal time, precesssion, nutation, equinox, ecliptic, and ephemeris are familiar. Some experience in computing some type of positional astronomy data is useful, because the ultimate purpose of the circular is to enable such computations to be carried out in accordance with the 1997 and 2000 IAU resolutions. The explanatory narratives deal primarily with new or unfamiliar concepts introduced by the resolutions — concepts that would not generally be described in most introductory textbooks on positional astronomy. This circular is not a substitute for such textbooks. IAU resolutions are referred to in the text in the form “res. N of year”, for example, “res. B1.2 of 2000”. The year refers to the year of the IAU General Assembly that passed the resolution. The proceedings of each General Assembly, including the text of the resolutions, are usually published the following year. The References section of this circular lists the various proceedings volumes under “IAU”. An online reference for the text of IAU resolutions (beginning with those passed at the 1994 General Assembly) is the IAU Information Bulletin (IB) series, at URL 2. Resolutions are printed in the January IB following a General Assembly, i.e., IB numbers 74, 81, 88, 94, etc. This circular contains two appendices containing the complete text of the resolutions passed by the 1997 and 2000 General Assemblies, which are the main focus of attention here. Errata in this circular and updates to it are provided at URL 1. Other Resources An increasing number of publications, data, and software related to the recent IAU resolutions are becoming available. A major online resource for implementing the IAU resolutions involving Earth rotation and time (Chapters 2, 5, and 6 here) is the document of conventions used by the International Earth Rotation and Reference Systems Service (IERS): IERS Conventions (2003), IERS Technical Note No. 32, edited by D. D. McCarthy and G. Petit. It is available in printed form from the IERS and also on the web at URL 3. The online document contains links to Fortran subroutines that implement the recommended models. The document also contains algorithms specific to geodetic applications, such as tidal and geopotential models, that have not been the subject of IAU action and are not discussed in this circular. The IERS also maintains an online list of FAQs on the IAU resolutions (URL 4). The IAU Working Group on Nomenclature for Fundamental Astronomy (2003–2006) has a website (URL 6) with many helpful documents, including a list of definitions (some of which are used in this circular) and other educational material. In addition to the IERS software, two other packages of computer subroutines are available for implementing the IAU resolutions: the Standards of Fundamental Astronomy (SOFA), at URL 7, and the Naval Observatory Vector Astrometry Subroutines (NOVAS), at URL 8. SOFA is a collection of routines managed by an international panel, the SOFA Reviewing Board, that works under the auspices of IAU Division 1 and is chaired by P. Wallace. The board has adopted a set of Fortran coding standards for algorithm implementations (C versions are contemplated for the future) and is soliciting code from the astrometric and geodetic communities that implements IAU models. Subroutines are adapted to the coding standards and validated for accuracy before being added to the SOFA collection. NOVAS is an integrated package of subroutines, available in Fortran and
INTRODUCTION vii C, for the computation of a wide variety of common astrometric quantities and transformations. NOVAS dates back to the 1970s but has been continually updated to adhere to subsequent IAU resolutions. The Astronomical Almanac, beginning with the 2006 edition, is also a resource for implementing the IAU resolutions. Not only does it list various algorithms arising from or consistent with the resolutions, but its tabular data serve as numerical checks for independent developments. Both SOFA and NOVAS subroutines are used in preparing the tabulations in The Astronomical Almanac, and various checks have been made to ensure the consistency of the output of the two software packages. Acknowledgments Many people have contributed in some way to this circular. I have had many interesting and enlightening discussions with James Hilton, Victor Slabinski, and Patrick Wallace. I wish to thank Bill Tangren for setting me straight on some of the basic concepts of general relativity, and Sergei Klioner and Sergei Kopeikin for patiently trying to explain to me the relativistic aspects of the 2000 IAU resolutions. Sergei Klioner provided some text that I have used verbatim. I hope that the final product properly represents their input. The e-mail discussions within the IAU Working Group on Nomenclature for Fundamental Astronomy have also been quite valuable and have contributed to what is presented here. The many scientific papers written by Nicole Capitaine and her collaborators have been essential references. Victor Slabinski and Dennis McCarthy of the U.S. Naval Observatory, Ken Seidelmann of the University of Virginia, Catherine Hohenkerk of Her Majesty’s Nautical Almanac Office, and Myles Standish of the Jet Propulsion Laboratory carefully reviewed drafts of this circular and made many substantive suggestions for improvement. The remaining defects in the circular are, of course, my sole responsibility. — George Kaplan
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Page 4 and 5: ii 3.4.4 Relationship to Other Syst
Page 6 and 7: iv INTRODUCTION recommendations. Ma
Page 10 and 11: A Few Words about Constants This ci
Page 12 and 13: Abbreviations and Symbols Frequentl
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Page 16 and 17: 2 RELATIVITY In 1991, the IAU made
Page 18 and 19: 4 RELATIVITY Geocentric Celestial R
Page 20 and 21: 6 RELATIVITY 1.4 Concluding Remarks
Page 22 and 23: 8 TIME SCALES star across a certain
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Page 26 and 27: 12 TIME SCALES Clearly UT1-UTC and
Page 28 and 29: 14 TIME SCALES From the perspective
Page 30 and 31: 16 TIME SCALES method and the time
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Page 46 and 47: 32 EPHEMERIDES scaling. LB = 1.550
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44 PRECESSION & NUTATION 2. A rotat
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46 PRECESSION & NUTATION ∆ɛ = N
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48 PRECESSION & NUTATION S1 = sin (
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Chapter 6 Modeling the Earth’s Ro
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52 MODELING THE EARTH’S ROTATION
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68 IAU RESOLUTIONS 1997 reference f
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Text of IAU Resolutions of 2000 Ado
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72 IAU RESOLUTIONS 2000 Resolution
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74 IAU RESOLUTIONS 2000 integrals t
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76 IAU RESOLUTIONS 2000 g0i = − 4
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78 IAU RESOLUTIONS 2000 3. that sem
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80 IAU RESOLUTIONS 2000 Recommends
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References Journal abbreviations: A
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84 REFERENCES Høg, E., Fabricius,
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86 REFERENCES Nelson, R. A., McCart
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IAU 2000A Nutation Series The nutat
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90 NUTATION SERIES Term i j= 1 Fund
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102 NUTATION SERIES Term i j= 1 Fun
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Errata & Updates Errata in this cir
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USNO Circular 179 - U.S. Naval Observatory

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