IAU (1976) System of Astronomical Constants

The International Astronomical Union at its XVIth General Assembly in Grenoble in 1976, accepted (Resolution No. 1 [1]) a whole new consistent set of astronomical constants [2] recommended for reduction of astronomical observations, and for computation of ephemerides. It superseded the IAU's previous recommendations of 1964 (see IAU (1964) System of Astronomical Constants), became in effect in the Astronomical Almanac from 1984 onward, and remained in use until the introduction of the IAU (2009) System of Astronomical Constants. In 1994 [3] the IAU recognized that the parameters became outdated, but retained the 1976 set for sake of continuity, but also recommended to start maintaining a set of "current best estimates"

[4]

this "sub group for numerical standards" had published a list, which included new constants (like those for relativistic time scales) [5] .

The system of constants was prepared [6] by Commission 4 on ephemerides led by P. Kenneth Seidelmann (after whom asteroid 3217 Seidelmann is named).

At the time, a new standard epoch (J2000.0) was accepted; followed later [7] [8] by a new reference system with fundamental catalogue (FK5), and expressions for precession of the equinoxes, and in 1979 by new expressions for the relation between Universal Time and sidereal time [9] [10] [11] , and in 1979 and 1980 by a theory of nutation [12] [13] . There were no reliable rotation elements for most planets,[2][6] but a joint working group on Cartographic Coordinates and Rotational Elements was installed to compile recommended values [14] [15] .

Units

The IAU(1976) system is based on the astronomical system of units:

  • The astronomical unit of time is the day (D) of 86,400 SI seconds, which is close to the mean solar day of civil clock time.
  • The astronomical unit of mass is the mass of the Sun (S).
  • The astronomical unit of length is known as the astronomical unit (A or au), which in the IAU(1976) system is defined as the length for which the gravitational constant, more specifically the Gaussian gravitational constant k expressed in the astronomical units (i.e. k2 has units A3S−1D−2), takes the value of 0.017 202 098 95 . This astronomical unit is approximately the mean distance between the Earth and the Sun. The value of k is the angular velocity in radians per day (i.e. the daily mean motion) of an infinitesimally small mass that moves around the Sun in a circular orbit at a distance of 1 AU.

Table of constants
NumberQuantitySymbolValueUnitRelative
uncertainty		Ref.
Defining Constants
1Gaussian gravitational constantk0.017 202 098 95A3/2S−1/2D−1defined[6]
Primary Constants
2Speed of lightc299 792 458 ±1.2m s−14×10−9[16]
3light time for unit distanceτA499.004 782 ±0.000 002s4×10−9[6]
4equatorial radius for Earthae6 378 140 ±5m8×10−7[6]
5dynamical form-factor for EarthJ2(108 263 ±1)×10−81×10−5[6]
6geocentric gravitational constantGE(3 986 005 ±3)×10+8m3s−28×10−7[6]
7constant of gravitationG(6 672 ±4.1)×10−14m3kg−1s−26.1×10−4[17]
8Earth/Moon mass ratio1/μ81.300 7 ±0.000 34×10−6[6]
Moon/Earth mass ratioμ0.012 300 024×10−6[6]
9general precession in longitudep5 029.0966 ±0.15" cy−13×10−5[6]
10obliquity of the eclipticε23°26'21.448" ±0.10"1×10−6[6]
11constant of nutation at standard epoch J2000N9.2055 [18]"3×10−5[10][12]
Derived Constants
12unit distance (astronomical unit)A = cτA(149 597 870 ±2)×10+3m1×10−8[6]
13solar parallaxπ◌ = arcsin(ae/A)8.794 148 ±0.000 007"8×10−7[6]
14constant of aberration for standard epoch J2000κ20.495 52"[2][6]
15flattening factor for the Earthf0.003 352 81 ±0.000 000 026×10−6[2][6]
reciprocal flattening1/f(298 257 ± 1.5)×10−35×10−6[2][6]
16heliocentric gravitational constantGS = A3k2/D2(132 712 438 ±5)×10+12m3s−24×10−8[6]
17Sun/Earth mass ratioS/E = GS/GE332 946.0 ± 0.39×10−7[6]
18mass ratio Sun to Earth+Moon(S/E)/(1+μ)328 900.5 ±0.51.5×10−6[6]
19mass of the SunS = GS/G(19 891 ±12)×10+26kg6×10−4[6]
20ratios of mass of Sun to planets+satellites1/S[2][6]
Mercury6 023 600
Venus408 523.5
Earth+Moon328 900.5
Mars3 098 710
Jupiter1 047.355
Saturn3 498.5
Uranus22 869
Neptune19 314
Pluto3 000 000

Other quantities for use in the preparation of ephemerides
1.Masses of minor planets
NumberNameMass in solar mass
(1)Ceres(5.9 ±0.3)×10−10
(2)Pallas(1.1 ±0.2)×10−10
(4)Vesta(1.2 ±0.1)×10−10
2.Masses of satellites
PlanetNumberSatelliteSatellite/Planet mass
JupiterIIo(4.70 ±0.06)×10−5
IIEuropa(2.56 ±0.06)×10−5
IIIGanymedes(7.84 ±0.08)×10−5
IVCallisto(5.6 ±0.17)×10−5
SaturnusITitan(2.41 ±0.018)×10−4
NeptuneITriton2×10−3
3.Equatorial radii
ObjectEquatorial radius (km)
Mercury2 439 ±1
Venus6 052 ±6
Earth6 378.140 ±0.005
Mars3 397.2 ±1
Jupiter71 398
Saturn60 000
Uranus25 400
Neptune24 300
Pluto2 500
Moon1 738
Moon's disk, ratio to Earth's equatorial radiusk = 0.272 5076 ae [19]
Sun696 000
4.Gravity fields of the planets
PlanetJ2J3J4C22S22S31
Earth(+108 263 ±1)×10−8(−254 ±1)×10−8(−161 ±1)×10−8
Mars(+1 964 ±6)×10−6(+36 ±20)×10−6(-55 ±1)×10−6(+31 ±2)×10−6(+26 ±5)×10−6
Jupiter+0.014 75-0.000 58
Saturn+0.016 45-0.0010
Uranus+0.012
Neptune+0.004
5.Gravity field of the Moon
QuantitySymbolValue
average inclination of equator on eclipticI5 552.7"
moment of inertiaC/MR20.392
(C-A)/Bβ0.000 6313
(B-A)/Cγ0.000 2278
C20-0.000 2027
C22+0.000 0223
C30-0.000 006
C31+0.000 029
S31+0.000 004
C32+0.000 0048
S32+0.000 0017
C33+0.000 0018
S33-0.000 001

References
  1. Müller, Edith A.; Jappel, A., eds. (1977), "IAU (1976): Proceedings of the 16th General Assembly, XVI B" (PDF), Transactions of the IAU, Dordrecht: D.Reidel, p. 31, ISBN 90-277-0836-3 Missing or empty |title= (help)
  2. IAU(1976) ibidem: Commission 4 (Ephemerides) recommendations 1,2,3,5,6: pp.52..67
  3. Appenzeller, I, ed. (1994), "IAU (1994): Proceedings of the 22nd General Assembly, XXII B" (PDF), Transactions of the IAU, Kluwer Academic, ISBN 0-7923-3842-1 Missing or empty |title= (help)
  4. IAU(1994) ibidem, Resolution No. C 6
  5. Standish, E.M. (1995), "Report of the IAU WGAS Sub-group on Numerical Standards", in Appenzeller, I. (ed.), Highlights of Astronomy (PDF), Dordrecht: Kluwer, archived from the original (PDF) on 2012-09-07
  6. Seidelmann, P. Kenneth (1977). "Numerical values of the constants of the Joint Report of the Working Groups of IAU Commission 4". Celestial Mechanics. 16: 165..177. Bibcode:1977CeMec..16..165S. doi:10.1007/BF01228598.
  7. Wayman, P., ed. (1980), "IAU (1979): Proceedings of the 17th General Assembly, XVII B" (PDF), Transactions of the IAU, Dordrecht: D.Reidel, ISBN 90-277-1159-3 Missing or empty |title= (help)
  8. West, R, ed. (1982), "IAU (1982): Proceedings of the 18th General Assembly, XVIII B" (PDF), Transactions of the IAU, Dordrecht: D.Reidel, ISBN 0-7923-3842-1 Missing or empty |title= (help)
  9. IAU(1979) ibidem, recommendation by Commissions 4 (Ephemerides), 8 (Positional Astronomy), 19 (Rotation of the Earth), 31 (Time)
  10. Lederle, Trudpert (1980). "The IAU (1976) System of Astronomical Constants". Mitteilungen des Astronomisches Gesellschaft. 48: 59..65. Bibcode:1980MitAG..48...59L.
  11. IAU(1982) ibidem, Resolution No. C 5
  12. IAU(1979) ibidem, recommendation by Commissions 4 (Ephemerides), 19 (Rotation of the Earth), 31 (Time)
  13. IAU(1982) ibidem, Resolution No. R 3
  14. IAU(1976) ibidem, recommendation by Commissions 4 (Ephemerides) and 16 (Physical Study of Planets and Satellites)
  15. IAU(1979) ibidem, recommendation by Commissions 4 (Ephemerides) and 16 (Physical Study of Planets and Satellites)
  16. International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), pp. 112–13, ISBN 92-822-2213-6, archived (PDF) from the original on 2017-08-14.
  17. CODATA System of Physical Constants of 1973, CODATA Bulletin No. 11 Archived 2017-01-07 at the Wayback Machine
  18. originally (Seidelmann 1977) listed as 9.2109", derived from Woolard
  19. IAU(1982) ibidem, Resolution No. C 10

IAU commission 4: ,

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