USNO Circular 179 - U.S. Naval Observatory

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A Few Words about Constants This circular does not contain a list of adopted fundamental astronomical constants, because the IAU is no longer maintaining such a list. The last set of officially adopted constant values was the IAU (1976) System of Astronomical Constants. That list is almost entirely obsolete. For a while, an IAU working group maintained a list of “best estimates” of various constant values, but the IAU General Assembly of 2003 did not renew that mandate. It can be argued that a list of fundamental astronomical constants is no longer possible, given the complexity of the models now used and the many free parameters that must be adjusted in each model to fit observations. That is, there are more constants now to consider, and their values are theory dependent. In many cases, it would be incorrect to attempt to use a constant value, obtained from the fit of one theory to observations, with another theory. We are left with three defining constants with IAU-sanctioned values that are intended to be fixed: 1. The Gaussian gravitational constant: k = 0.01720209895. The dimensions of k2 are AU3M −1 ○· d−2 where AU is the astronomical unit, M○· is the solar mass, and d is the day of 86400 seconds. 2. The speed of light: c = 299 792 458 m s −1 . 3. The fractional difference in rate between the time scales TT and TCG: LG = 6.969290134×10 −10 . Specifically, the derivative dTT/dTCG = 1 − LG. (See Chapter 3.) The IERS Conventions (2003) includes a list of constants as its Table 1.1. Several useful ones from this list that are not highly theory dependent (for astronomical use, at least) are: 1. Equatorial radius of the Earth: aE = 6 378 136.6 m. 2. Flattening factor of the Earth: f = 1/298.25642. 3. Dynamical form factor of the Earth: J2 = 1.0826359×10 −3 . 4. Nominal mean angular velocity of Earth rotation: ω = 7.292115×10 −5 rad s −1 . 5. Constant of gravitation: G = 6.673×10 −11 m 3 kg −1 s −2 (CODATA 2002 recommended value: 6.6742×10 −11 m 3 kg −1 s −2 ). The first four values above were recommended by Special Commission 3 of the International Association of Geodesy; the first three are so-called “zero tide” values. (The need to introduce the concept of “zero tide” values indicates how theory creeps into even such basic constants as the radius of the Earth as the precision of measurement increases. See section 1.1 of the IERS viii
CONSTANTS ix Conventions (2003).) Planetary masses, the length of the astronomical unit, and related constants used in or obtained from the Jet Propulsion Laboratory DE405/LE405 ephemeris are listed with its description in Chapter 4. The rate of general precession in longitude (the “constant of precession”) is given in Chapter 5 on the precession and nutation theories. The World Geodetic System 1984 (WGS 84), which is the basis for coordinates obtained from GPS, uses an Earth ellipsoid with aE = 6378137 m and f = 1/298.257223563. Some astronomical “constants” (along with reference data such as star positions) actually represent quantities that slowly vary, and the values given must therefore be associated with a specific epoch. That epoch is now almost always 2000 January 1, 12 h (JD 2451545.0), which can be expressed in any of the usual time scales. If, however, that epoch is considered an event at the geocenter and given in the TT time scale, the epoch is designated J2000.0. See Chapter 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 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 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 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 46 and 47: 32 EPHEMERIDES scaling. LB = 1.550
Page 48 and 49: 34 PRECESSION & NUTATION 5.1 Aspect
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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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