USNO Circular 179 - U.S. Naval Observatory

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ii 3.4.4 Relationship to Other Systems . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.4.5 Data in the ICRS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.5 Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4 Ephemerides of the Major Solar System Bodies 29 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.1 The JPL Ephemerides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.2 DE405 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 4.3 Sizes, Shapes, and Rotational Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.4 DE405 Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 5 Precession and Nutation 33 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 5.1 Aspects of Earth Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 5.2 Which Pole? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 5.3 The New Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 5.4 Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 5.4.1 Formulas for Precession . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 5.4.2 Formulas for Nutation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 5.4.3 Alternative Combined Transformation . . . . . . . . . . . . . . . . . . . . . . 48 5.4.4 Observational Corrections to Precession-Nutation . . . . . . . . . . . . . . . . 49 6 Modeling the Earth’s Rotation 50 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 6.1 A Messy Business . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 6.2 Non-Rotating Origins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 6.3 The Path of the CIO on the Sky . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 6.4 Transforming Vectors Between Reference Systems . . . . . . . . . . . . . . . . . . . . 55 6.5 Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 6.5.1 Location of Cardinal Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 6.5.1.1 CIO Location Relative to the Equinox . . . . . . . . . . . . . . . . . 59 6.5.1.2 CIO Location from Numerical Integration . . . . . . . . . . . . . . . 60 6.5.1.3 CIO Location from the Arc-Difference s . . . . . . . . . . . . . . . . 61 6.5.2 Geodetic Position Vectors and Polar Motion . . . . . . . . . . . . . . . . . . . 63 6.5.3 Complete Terrestrial to Celestial Transformation . . . . . . . . . . . . . . . . 64 6.5.4 Hour Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Text of IAU Resolutions of 1997 67 Text of IAU Resolutions of 2000 70 References 82 URLs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 IAU 2000A Nutation Series 88 Errata & Updates 104
Introduction The series of resolutions passed by the International Astronomical Union at its General Assemblies in 1997 and 2000 are the most significant set of international agreements in positional astronomy in several decades and arguably since the Paris conference of 1896. The approval of these resolutions culminated a process — not without controversy — that began with the formation of an intercommission Working Group on Reference Systems at the 1985 IAU General Assembly in Delhi. The resolutions came at the end of a remarkable decade for astrometry, geodesy, and dynamical astronomy. That decade witnessed the successes of the Hipparcos satellite and the Hubble Space Telescope (in both cases, after apparently fatal initial problems), the completion of the Global Positioning System, 25-year milestones in the use of very long baseline interferometry (VLBI) and lunar laser ranging (LLR) for astrometric and geodetic measurements, the discovery of Kuiper Belt objects and extra-solar planets, and the impact of comet Shoemaker-Levy 9 onto Jupiter. At the end of the decade, interest in near-Earth asteroids and advances in sensor design were motivating plans for rapid and deep all-sky surveys. Significant advances in theory also took place, facilitated by inexpensive computer power and the Internet. Positional and dynamical astronomy were enriched by a deeper understanding of chaos and resonances in the solar system, advances in the theory of the rotational dynamics of the Earth, and increasingly sophisticated models of how planetary and stellar systems form and evolve. It is not too much of an exaggeration to say that as a result of these and similar developments, the old idea that astrometry is an essential tool of astrophysics was rediscovered. The IAU resolutions thus came at a fortuitous time, providing a solid framework for interpreting the modern high-precision measurements that are revitalizing so many areas of astronomy. This circular is an attempt to explain these resolutions and provide guidance on their implementation. This publication is the successor to USNO Circular 163 (1982), which had a similar purpose for the IAU resolutions passed in 1976, 1979, and 1982. Both the 1976–1982 resolutions and those of 1997–2000 provide the specification of the fundamental astronomical reference system, the definition of time scales to be used in astronomy, and the designation of conventional models for Earth orientation calculations (involving precession, nutation, and Universal Time). It will certainly not go unnoticed by readers familiar with Circular 163 that the current publication is considerably thicker. This reflects both the increased complexity of the subject matter and the wider audience that is addressed. Of course, the IAU resolutions of 1997–2000 did not arise in a vacuum. Many people participated in various IAU working groups, colloquia, and symposia in the 1980s and 1990s on these topics, and some important resolutions were in fact passed by the IAU in the early 1990s. Furthermore, any set of international standards dealing with such fundamental matters as space and time must to some extent be based on, and provide continuity with, existing practice. Therefore, many of the new resolutions carry “baggage” from the past, and there is always the question of how much of this history (some of it quite convoluted) is important for those who simply wish to implement the latest iii
Page 1: UNITED STATES NAVAL OBSERVATORY CIR
Page 6 and 7: iv INTRODUCTION recommendations. Ma
Page 8 and 9: vi INTRODUCTION that are available
Page 10 and 11: A Few Words about Constants This ci
Page 12 and 13: Abbreviations and Symbols Frequentl
Page 14 and 15: xii ABBREVIATIONS & SYMBOLS s CIO l
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
Page 24 and 25: 10 TIME SCALES were computed in a b
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
Page 32 and 33: 18 TIME SCALES through the local ge
Page 34 and 35: 20 CELESTIAL REFERENCE SYSTEM 3.1 T
Page 36 and 37: 22 CELESTIAL REFERENCE SYSTEM the i
Page 38 and 39: 24 CELESTIAL REFERENCE SYSTEM 3.4 I
Page 40 and 41: 26 CELESTIAL REFERENCE SYSTEM withi
Page 42 and 43: 28 CELESTIAL REFERENCE SYSTEM the p
Page 44 and 45: 30 EPHEMERIDES DE200 nor DE405 have
Page 46 and 47: 32 EPHEMERIDES scaling. LB = 1.550
Page 48 and 49: 34 PRECESSION & NUTATION 5.1 Aspect
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40 PRECESSION & NUTATION the pole o
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42 PRECESSION & NUTATION and the re
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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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100 NUTATION SERIES Term i j= 1 Fun
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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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