# Astronomical constant

An astronomical constant is a physical constant used in astronomy. Formal sets of constants, along with recommended values, have been defined by the International Astronomical Union (IAU) several times: in 1964[1] and in 1976[2] (with an update in 1994[3]). In 2009 the IAU adopted a new current set, and recognizing that new observations and techniques continuously provide better values for these constants, they decided [4] to not fix these values, but have the Working Group on Numerical Standards continuously maintain a set of Current Best Estimates [5] . The set of constants is widely reproduced in publications such as the Astronomical Almanac of the United States Naval Observatory and HM Nautical Almanac Office.

Besides the IAU list of units and constants, also the International Earth Rotation and Reference Systems Service defines constants relevant to the orientation and rotation of the Earth, in its technical notes .[6]

The IAU system of constants defines a system of astronomical units for length, mass and time (in fact, several such systems), and also includes constants such as the speed of light and the constant of gravitation which allow transformations between astronomical units and SI units. Slightly different values for the constants are obtained depending on the frame of reference used. Values quoted in barycentric dynamical time (TDB) or equivalent time scales such as the Teph of the Jet Propulsion Laboratory ephemerides represent the mean values that would be measured by an observer on the Earth's surface (strictly, on the surface of the geoid) over a long period of time. The IAU also recommends values in SI units, which are the values which would be measured (in proper length and proper time) by an observer at the barycentre of the Solar System: these are obtained by the following transformations:[3]

${\displaystyle \tau _{A}({\rm {SI}})=(1+L_{\rm {B}})^{\frac {1}{3}}\tau _{A}({\rm {TDB}})\,}$
${\displaystyle GE({\rm {SI}})=(1+L_{\rm {B}})GE({\rm {TDB}})\,}$
${\displaystyle GS({\rm {SI}})=(1+L_{\rm {B}})GS({\rm {TDB}})\,}$

## Astronomical system of units

The astronomical unit of time is a time interval of one day (D) of 86400 seconds. The astronomical unit of mass is the mass of the Sun (S). The astronomical unit of length is that length (A) for which the Gaussian gravitational constant (k) takes the value 0.017 202 098 95 when the units of measurement are the astronomical units of length, mass and time.[2]

## Table of astronomical constants

Quantity Symbol Value Relative
uncertainty
Ref.
Defining constants
Gaussian gravitational constant k 0.017 202 098 95 A3/2S−1/2D−1 defined [2]
Speed of light c 299 792 458 m s−1 defined [7]
Mean ratio of the TT second to the TCG second 1 − LG 1 − 6.969 290 134×10−10 defined [8]
Mean ratio of the TCB second to the TDB second 1 − LB 1 − 1.550 519 767 72×10−8 defined [9]
Primary constants
Mean ratio of the TCB second to the TCG second 1 − LC 1 − 1.480 826 867 41×10−8 1.4×10−9 [8]
Light-time for unit distance τA 499.004 786 3852 s 4.0×10−11 [10][11]
Equatorial radius for Earth ae 6.378 1366×106 m 1.6×10−8 [11]
Potential of the geoid W0 6.263 685 60×107 m2 s−2 8.0×10−9 [11]
Dynamical form-factor for Earth J2 0.001 082 6359 9.2×10−8 [11]
Flattening factor for Earth 1/ƒ 0.003 352 8197
= 1/298.256 42
3.4×10−8 [11]
Geocentric gravitational constant GE 3.986 004 391×1014 m3 s−2 2.0×10−9 [10]
Constant of gravitation G 6.673 84×10−11 m3 kg−1 s−2 1.2×10−4 [10][12]
Ratio of mass of Moon to mass of Earth μ 0.012 300 0383
= 1/81.300 56
4.0×10−8 [10][11]
General precession in longitude, per Julian century, at standard epoch 2000 ρ 5029.796 195″ * [13]
Obliquity of the ecliptic, at standard epoch 2000 ε 23° 26′ 21.406″ * [13]
Derived constants
Constant of nutation, at standard epoch 2000 N 9.205 2331″ * [14]
Unit distance = A A 149 597 870 691 m 4.0×10−11 [10][11]
Solar parallax = arcsin(ae/A) π 8.794 1433″ 1.6×10−8 [2]
Constant of aberration, at standard epoch 2000 κ 20.495 52″ [2]
Heliocentric gravitational constant = A3k2/D2 GS 1.327 2440×1020 m3 s−2 3.8×10−10 [11]
Ratio of mass of Sun to mass of Earth = (GS)/(GE) S/E 332 946.050 895 [10]
Ratio of mass of Sun to mass of (Earth + Moon) (S/E)
(1 + μ)
328 900.561 400 [10]
Mass of Sun = (GS)/G S 1.9818×1030 kg 1.0×10−4 [2]
System of planetary masses: Ratios of mass of Sun to mass of planet[10]
Mercury 6 023 600
Venus 408 523.71
Earth + Moon 328 900.561 400
Mars 3 098 708
Jupiter 1047.3486
Saturn 3497.898
Uranus 22 902.98
Neptune 19 412.24
Pluto 135 200 000
Other constants (outside the formal IAU System)
Parsec = A/tan(1") pc 3.085 677 581 28×1016 m 4.0×10−11 [15]
Light-year = 365.25cD ly 9.460 730 472 5808×1015 m defined [15]
Hubble constant H0 70.1 km s−1 Mpc−1 0.019 [16]
Solar luminosity L 3.939×1026 W
= 2.107×10−15 S D−1
variable,
±0.1%
[17]
Notes

* The theories of precession and nutation have advanced since 1976, and these also affect the definition of the ecliptic. The values here are appropriate for the older theories, but additional constants are required for current models.

† The definitions of these derived constants have been taken from the references cited, but the values have been recalculated to take account of the more precise values of the primary constants cited in the table.

## References

1. ^ Resolution No.4 of the XIIth General Assembly of the International Astronomical Union, Hamburg, 1964.
2. Resolution No. 1 on the recommendations of Commission 4 on ephemerides in the XVIth General Assembly of the International Astronomical Union, Grenoble, 1976.
3. ^ a b Standish, E. M. (1995), "Report of the IAU WGAS Sub-group on Numerical Standards", in Appenzeller, I., Highlights of Astronomy (PDF), Dordrecht: Kluwer
4. ^ Resolution B2 of the XXVIIth General Assembly of the International Astronomical Union, Rio de Janeiro, 2009.
5. ^ IAU Division I Working Group on Numerical Standards for Fundamental Astronomy and Astronomical Constants: Current Best Estimates (CBEs) [1]
6. ^ Gérard Petit; Brian Luzum, eds. (2010). "Table 1.1: IERS numerical standards" (PDF). IERS technical note no. 36: General definitions and numerical standards. International Earth Rotation and Reference Systems Service. For complete document see Gérard Petit; Brian Luzum, eds. (2010). IERS Conventions (2010): IERS technical note no. 36. International Earth Rotation and Reference Systems Service. ISBN 978-3-89888-989-6.
7. ^ International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), pp. 112–13, ISBN 92-822-2213-6.
8. ^ a b Resolutions Nos. B1.5 and B1.9 of the XXIVth General Assembly of the International Astronomical Union, Manchester, 2000.
9. ^ Resolution 3 of the XXVIth General Assembly of the International Astronomical Union, Prague, 2006.
10. Standish, E. M. (1998), JPL Planetary and Lunar Ephemerides, DE405/LE405 (PDF), JPL IOM 312.F-98-048, archived from the original (PDF) on February 20, 2012
11. McCarthy, Dennis D.; Petit, Gérard, eds. (2004), "IERS Conventions (2003)", IERS Technical Note No. 32, Frankfurt: Bundesamts für Kartographie und Geodäsie, ISBN 3-89888-884-3
12. ^ Mohr, Peter J.; Taylor, Barry N.; Newell, David B. (2008). "CODATA Recommended Values of the Fundamental Physical Constants: 2006". Rev. Mod. Phys. 80 (2): 633–730. arXiv:0801.0028. Bibcode:2008RvMP...80..633M. doi:10.1103/RevModPhys.80.633. Direct link to value.
13. ^ a b Resolution 1 of the XXVIth General Assembly of the International Astronomical Union, Prague, 2006.
14. ^ Resolution No. B1.6 of the XXIVth General Assembly of the International Astronomical Union, Manchester, 2000.
15. ^ a b
16. ^
17. ^ Noedlinger, Peter D., "Solar Mass Loss, the Astronomical Unit, and the Scale of the Solar System", Celest. Mech. Dyn. Astron., arXiv:0801.3807, Bibcode:2008arXiv0801.3807N