# Physics: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 It superseded the IAU's previous recommendations of 1964 (see IAU (1964) System of Astronomical Constants), became in effect in the Astronomical Almanac from 1984 onward,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 In 1994[3] the IAU recognized that the parameters became outdated, but retained the 1976 set for sake of continuity, but also recommended to start maintaining a set of "current best estimates".[4]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

Number Quantity Symbol Value Unit Relative
uncertainty
Ref.
Defining Constants
1 Gaussian gravitational constant k 0.017 202 098 95 A3/2S−1/2D−1 defined [6]
Primary Constants
2 Speed of light c 299 792 458 ±1.2 m s−1 4×109 [16]
3 light time for unit distance τA 499.004 782 ±0.000 002 s 4×109 [6]
4 equatorial radius for Earth ae 6 378 140 ±5 m 8×107 [6]
5 dynamical form-factor for Earth J2 (108 263 ±1)×108 1×105 [6]
6 geocentric gravitational constant GE (3 986 005 ±3)×10+8 m3s−2 8×107 [6]
7 constant of gravitation G (6 672 ±4.1)×1014 m3kg−1s−2 6.1×104 [17]
8 Earth/Moon mass ratio 1/μ 81.300 7 ±0.000 3 4×106 [6]
Moon/Earth mass ratio μ 0.012 300 02 4×106 [6]
9 general precession in longitude p 5 029.0966 ±0.15 " cy−1 3×105 [6]
10 obliquity of the ecliptic ε 23°26'21.448" ±0.10 " 1×106 [6]
11 constant of nutation at standard epoch J2000 N 9.2055 [18] " 3×105 [10][12]
Derived Constants
12 unit distance (astronomical unit) A = cτA (149 597 870 ±2)×10+3 m 1×108 [6]
13 solar parallax π = arcsin(ae/A) 8.794 148 ±0.000 007 " 8×107 [6]
14 constant of aberration for standard epoch J2000 κ 20.495 52 " [2][6]
15 flattening factor for the Earth f 0.003 352 81 ±0.000 000 02 6×106 [2][6]
reciprocal flattening 1/f (298 257 ± 1.5)×103 5×106 [2][6]
16 heliocentric gravitational constant GS = A3k2/D2 (132 712 438 ±5)×10+12 m3s−2 4×108 [6]
17 Sun/Earth mass ratio S/E = GS/GE 332 946.0 ± 0.3 9×107 [6]
18 mass ratio Sun to Earth+Moon (S/E)/(1+μ) 328 900.5 ±0.5 1.5×106 [6]
19 mass of the Sun S = GS/G (19 891 ±12)×10+26 kg 6×104 [6]
20 ratios of mass of Sun to planets+satellites 1/S [2][6]
Mercury 6 023 600
Venus 408 523.5
Earth+Moon 328 900.5
Mars 3 098 710
Jupiter 1 047.355
Saturn 3 498.5
Uranus 22 869
Neptune 19 314
Pluto 3 000 000

### Other quantities for use in the preparation of ephemerides

Number Name Mass in solar mass 1. Masses of minor planets (1) Ceres (5.9 ±0.3)×10−10 (2) Pallas (1.1 ±0.2)×10−10 (4) Vesta (1.2 ±0.1)×10−10
Planet Number Satellite Satellite/Planet mass 2. Masses of satellites Jupiter I Io (4.70 ±0.06)×10−5 II Europa (2.56 ±0.06)×10−5 III Ganymedes (7.84 ±0.08)×10−5 IV Callisto (5.6 ±0.17)×10−5 Saturnus I Titan (2.41 ±0.018)×10−4 Neptune I Triton 2×10−3
Object Equatorial radius (km) 3. Equatorial radii Mercury 2 439 ±1 Venus 6 052 ±6 Earth 6 378.140 ±0.005 Mars 3 397.2 ±1 Jupiter 71 398 Saturn 60 000 Uranus 25 400 Neptune 24 300 Pluto 2 500 Moon 1 738 Moon's disk, ratio to Earth's equatorial radius k = 0.272 5076 ae [19] Sun 696 000
Planet J2 J3 J4 C22 S22 S31 4. Gravity fields of the planets 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
Quantity Symbol Value 5. Gravity field of the Moon average inclination of equator on ecliptic I 5 552.7" moment of inertia C/MR2 0.392 (C-A)/B β 0.000 6313 (B-A)/C γ 0.000 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", Transactions of the IAU, Dordrecht: D.Reidel, p. 31, ISBN 90-277-0836-3
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", Transactions of the International Astronomical Union: Proceeding of the Twenty-Second General Assembly, the Hague 1994, Transactions of the IAU, Kluwer Academic, ISBN 0-7923-3842-1
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., Highlights of Astronomy, Dordrecht: Kluwer
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 (2): 165–177. doi:10.1007/BF01228598. Bibcode1977CeMec..16..165S.
7. Wayman, P., ed. (1980), "IAU (1979): Proceedings of the 17th General Assembly, XVII B", Transactions of the International Astronomical Union, Volume XVIIB, Transactions of the IAU, Dordrecht: D.Reidel, ISBN 90-277-1159-3
8. West, R, ed. (1982), "IAU (1982): Proceedings of the 18th General Assembly, XVIII B", Transactions of the International Astronomical Union: Proceeding of the Twenty-Second General Assembly, the Hague 1994, Transactions of the IAU, Dordrecht: D.Reidel, ISBN 0-7923-3842-1
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. Bibcode1980MitAG..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. CODATA System of Physical Constants of 1973, CODATA Bulletin No. 11 [1]
17. originally (Seidelmann 1977) listed as 9.2109", derived from Woolard
18. IAU(1982) ibidem, Resolution No. C 10