USNO Circular 179 - U.S. Naval Observatory

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32 EPHEMERIDES scaling. LB = 1.550 519 767 72×10 −8 =⇒ K = 1.000 000 015 505 198 (4.1) The value of LB is taken from note 3 of res. B1.5 of 2000. These conversions also depend on assumptions about what constants are truly fundamental and what their values are (Klioner 2005); therefore, the SI value of the astronomical unit in meters is not given below. The planetary masses below include contributions from satellites and atmospheres. Constant Symbol DE405 Value Equivalent SI value astronomical unit in seconds τA 499.004 783 806 1 s 499.004 786 385 2 s astronomical unit in meters A or cτA 149 597 870 691 m heliocentric gravitational GS or GM ○· 1.327 124 400 2×10 20 1.327 124 420 8×10 20 constant m 3 s −2 m 3 s −2 Moon/Earth mass ratio µ 1/81.30056 Sun/planet mass ratios: Mercury 6 023 600 Venus 408 523.71 Earth + Moon 328 900.561400 Earth 332 946.050895. . . Mars 3 098 708 Jupiter 1 047.3486 Saturn 3 497.898 Uranus 22 902.98 Neptune 19 412.24 Pluto 135 200 000
Chapter 5 Precession and Nutation Relevant IAU resolutions: B1.6, B1.7 of 2000 Summary Precession and nutation are really two aspects of a single phenomenon, the overall response of the spinning, oblate, elastic Earth to external gravitational torques from the Moon, Sun, and planets. As a result of these torques, the orientation of the Earth’s rotation axis is constantly changing with respect to a space-fixed (locally inertial) reference system. The motion of the celestial pole among the stars is conventionally described as consisting of a smooth long-term motion called precession upon which is superimposed a series of small periodic components called nutation. The algorithms for precession used generally from about 1980 through 2000 (in The Astronomical Almanac from the 1984 through 2005 editions) were based on the IAU (1976) value for the rate of general precession in ecliptic longitude (5029.0966 arcseconds per Julian century at J2000.0). Nutation over most of the same time period was given by the 1980 IAU Theory of Nutation. However, not long after these algorithms were widely adopted, it became clear that the IAU (1976) rate of precession had been overestimated by approximately 3 milliarcseconds per year. Further observations also revealed periodic errors of a few milliarcseconds in the 1980 IAU Theory of Nutation. For many applications these errors are negligible, but they are significant at the level of the best ground-based astrometry and geodesy. As part of the 2000 IAU resolutions, the IAU 2000A precession-nutation model was introduced, based on an updated value for the rate of precession and a completely new nutation theory. As before, the model actually consists of two parts, a precession algorithm describing the smooth secular motion of the celestial pole and a nutation algorithm describing the small periodic variations in the pole’s position. The precession algorithm consists of short polynomial series for the values of certain angles. The sines and cosines of these angles, in combination, then define the elements of a precession matrix, P. The nutation algorithm consists of a rather long series expansion in Fourier terms for the angular offsets, in ecliptic longitude and latitude, of the actual celestial pole (as modeled) from the precession-only pole (true pole – mean pole). The sines and cosines of these offsets, in combination, then define the elements of a nutation matrix, N. The P and N matrices are applied to the coordinates of celestial objects, expressed as 3-vectors, to transform them from the equator and equinox of one epoch to the equator and equinox of another. 33
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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 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
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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
Page 32 and 33: 18 TIME SCALES through the local ge
Page 34 and 35: 20 CELESTIAL REFERENCE SYSTEM 3.1 T
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Page 38 and 39: 24 CELESTIAL REFERENCE SYSTEM 3.4 I
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Page 42 and 43: 28 CELESTIAL REFERENCE SYSTEM the p
Page 44 and 45: 30 EPHEMERIDES DE200 nor DE405 have
Page 48 and 49: 34 PRECESSION & NUTATION 5.1 Aspect
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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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Page 66 and 67: 52 MODELING THE EARTH’S ROTATION
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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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USNO Circular 179 - U.S. Naval Observatory

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