USNO Circular 179 - U.S. Naval Observatory

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Abbreviations and Symbols Frequently Used and index to most relevant sections α right ascension 3.2 δ declination 3.2 ∆ψ nutation in [ecliptic] longitude (usually expressed in arcseconds) 5.3, 5.4.2 ∆ɛ nutation in obliquity (usually expressed in arcseconds) 5.3, 5.4.2 ɛ mean obliquity of date 5.4.1 ɛ ′ true obliquity of date (= ɛ + ∆ɛ) 5.4.2 ɛ0 mean obliquity of J2000.0 5.3, 5.4.1 θ Earth Rotation Angle 2.3, 6.2 µas microarcecond (= 10 −6 arcsecond ≈ 4.8×10 −12 radian) σ a non-rotating origin or, specifically, the CIO 6.2 σ unit vector toward a non-rotating origin or, specifically, the CIO 6.5.1 Υ the equinox 3.2, 6.2 Υ unit vector toward the equinox 6.5.1 as or ′′ arcsecond (= 1/3600 degree ≈ 4.8×10 −6 radian) AU astronomical unit(s) B frame bias matrix 3.5 BCRS Barycentric 1 Celestial Reference System 1.2 BIPM Bureau International des Poids et Mesures C matrix for transformation from GCRS to Eσ 5.4.3, 6.5.3 cen century, specifically, the Julian century of 36525 days of 86400 seconds CIO Celestial Intermediate Origin 2 3 6.2, 6.5.1 CIP Celestial Intermediate Pole 5.2, 6.5.1 CIRS (See Eσ) E Υ instantaneous (true) equator and equinox of date 6.4, 6.5.3 Eσ Celestial Intermediate Reference System (CIRS) 6.4, 6.5.3 Eϖ Terrestrial Intermediate Reference System (TIRS) 6.4, 6.5.3 EΥ equation of the equinoxes 2.3, 2.6.2 Eo equation of the origins 6.5.1.1, 6.5.4 ESA European Space Agency FKn n th Fundamental Catalog (Astronomisches Rechen-Institut, Heidelberg) 3.3 GAST Greenwich apparent sidereal time 2.3, 2.6.2 GCRS Geocentric Celestial Reference System 1.2 x
ABBREVIATIONS & SYMBOLS xi GMST Greenwich mean sidereal time 2.3, 2.6.2 GPS Global Positioning System HCRF Hipparcos Celestial Reference Frame 3.1, 3.4 IAG International Association of Geodesy IAU International Astronomical Union ICRF International Celestial Reference Frame 3.1, 3.4 ICRS International Celestial Reference System 3.1, 3.4 IERS International Earth Rotation and Reference System Service ITRF International Terrestrial Reference Frame 6.4 ITRS International Terrestrial Reference System 6.4, 6.5.2 IUGG International Union of Geodesy and Geophysics J2000.0 the epoch 2000 January 1, 12h TT (JD 2451545.0 TT) at the geocenter 2.2 (“J2000.0 system” is shorthand for the celestial reference system defined 3.2 by the mean dynamical equator and equinox of J2000.0.) JD Julian date (time scale used should be specified) JPL Jet Propulsion Laboratory mas milliarcsecond (= 10 −3 arcsecond ≈ 4.8×10 −9 radian) N nutation matrix (for transformation from mean to true system of date) 5.4, 5.4.2 n unit vector toward the CIP (celestial pole) 5.4,6.5.1 NOVAS <strong>Naval</strong> <strong>Observatory</strong> Vector Astrometry Subroutines (software) P precession matrix (for transformation from J2000.0 system to mean system of date) R1(φ) rotation matrix to transform column 3-vectors from one cartesian coordinate system to another. Final system is formed by rotating original system about its own x-axis by angle φ (counterclockwise as viewed from the +x direction): R1(φ) = ⎛ ⎜ ⎝ 1 0 0 0 cos φ sin φ 0 − sin φ cos φ R2(φ) rotation matrix to transform column 3-vectors from one cartesian coordinate system to another. Final system is formed by rotating original system about its own y-axis by angle φ (counterclockwise as viewed from the +y direction): R2(φ) = ⎛ ⎜ ⎝ cos φ 0 − sin φ 0 1 0 sin φ 0 cos φ R3(φ) rotation matrix to transform column 3-vectors from one cartesian coordinate system to another. Final system is formed by rotating original system about its own z-axis by angle φ (counterclockwise as viewed from the +z direction): R3(φ) = ⎛ ⎜ ⎝ cos φ sin φ 0 − sin φ cos φ 0 0 0 1 ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ 5.4, 5.4.2
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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 8 and 9: vi INTRODUCTION that are available
Page 10 and 11: A Few Words about Constants This ci
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
Page 50 and 51: 36 PRECESSION & NUTATION 5.2 Which
Page 52 and 53: 38 PRECESSION & NUTATION Figure 5.2
Page 54 and 55: 40 PRECESSION & NUTATION the pole o
Page 56 and 57: 42 PRECESSION & NUTATION and the re
Page 58 and 59: 44 PRECESSION & NUTATION 2. A rotat
Page 60 and 61: 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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