IAU Division 1 Working Group
Numerical Standards for Fundamental Astronomy
IAU 2009 System of Astronomical Constants


The following table lists the IAU 2009 constants that was adopted by the 2009 IAU GA in Resolution B2. The full details are contained in the report The IAU 2009 System of Astronomical Constants . The best estimates page lists the latest values of these constants that have been approved by the IAU NSFA Working Group.

The table lists the name of the quantity, the symbol usually used, the value in SI units (unless stated otherwise) and the uncertainty, which is given in the same units as the value. The last column gives the reference numbers, which are also links to the references that are listed below.

IAU 2009 System of Astronomical Constants
QuantitySymbolValueUncertaintyRef(s).
Natural Defining Constants
Speed of Light c 2.997 924 58 x 108 m s−1 defined 10
Auxiliary Defining Constants
Gaussian gravitation constant [a] k 1.720 209 895 x 10−2 defined 18,15
1−d(TT)/d(TCG) LG 6.969 290 134 x 10−10 defined 19,32
1−d(TDB)/d(TCB) LB 1.550 519 768 x 10−8 defined 20
TDB − TCB at T0 [b] TDB0 −6.55 x 10−5 s defined 20
Earth rotation angle at J2000.0 [c] θ0 0.779 057 273 2640 revolutions defined 19,5
Rate of advance of Earth rotation angle [c] dθ/dUT1 1.002 737 811 911 354 48 revolutions UT1-day−1 defined 19,5
Natural Measurable Constants
Constant of gravitation G 6.674 28 x 10−11 m3 kg−1 s−2 6.7 x 10−15 10
Other Constants
Astronomical unit [d] au 1.495 978 707 00 x 1011 m 3 m 33
Average value of 1−d(TCG)/d(TCB) LC 1.480 826 867 41 x 10−8 2 x 10−17 22
Body Constants [e]
Heliocentric gravitational constant GMS 1.327 124 420 99x1020 m3 s−2 [TCB-compatible]
1.327 124 400 41x1020 m3 s−2 [TDB-compatible]
1.0 x 1010
1.0 x 1010  
12
Equatorial radius of the Earth [f] aE 6.378 1366 x 106 m [TT-compatible] 1 x 10−1 16,4
Dynamical form factor [f] J2 1.082 6359 x 10−3 1 x 10−10 16
Time rate of change in J2 dJ2/dt −3.0 x 10−9 cy−1 6 x 10−10 20,7
Geocentric gravitational constant
GME 3.986 004 418 x 1014 m3 s−2 [TCB-compatible]
3.986 004 415 x 1014 m3 s−2 [TT-compatible]
3.986 004 356 x 1014 m3 s−2 [TDB-compatible]
8 x 105
8 x 105
8 x 105
34
Potential of the geoid W0 6.263 685 60 x 107 m2 s−2 5 x 10−1 16
Nominal mean angular velocity of the Earth[g] ω 7.292 115 x 10−5 rad s−1 [TT-compatible]  — 16
Ratio mass of the Moon to the Earth MM/ME 1.230 003 71 x 10−2 4 x 10−10 33
Ratio of the mass of the Sun to the mass of the Body [e]
Mercury MS/MMe 6.0236 x 106 3 x 102 1
Venus MS/MVe 4.085 237 19 x 105 8 x 10−3 28
Mars MS/MMa 3.098 703 59 x 106 2 x 10−2 29
Jupiter MS/MJ 1.047 348 644 x 103 1.7 x 10−5 25
Saturn MS/MSa 3.497 9018 x 103 1 x 10−4 26
Uranus MS/MU 2.290 298 x 104 3 x 10−2 24
Neptune MS/MN 1.941 226 x 104 3 x 10−2 23
(134340) Pluto MS/MP 1.365 66 x 108 2.8 x 104 36
(136199) Eris MS/MEris 1.191 x 108 1.4 x 106 3
Ratio of the mass of the Body to the mass of the Sun
(1) Ceres MCeres/MS 4.72 x 10−10 3 x 10−12 33
(2) Pallas MPallas/MS 1.03 x 10−10 3 x 10−12 33
(4) Vesta MVesta/MS 1.35 x 10−10 3 x 10−12 33
Initial Values at J2000.0
Obliquity of the ecliptic at J2000.0 [h] εJ2000 8.438 1406 x 104 " 1 x 10−3 " 20,17,8
Brief Notes:
Detailed notes and explanations are contained in The IAU 2009 System of Astronomical Constants .
  1. The Gaussian gravitational constant, k, is listed as an auxiliary defining constant as it continues to be used to define the relationship between au and GMS. This value from the IAU 1976 System of Astronomical Constants is retained in Table 1 and has been used to derive the GMS value given in Table 1 (Folkner et al., 2008). However, other estimates of GMS can be determined directly by fitting modern planetary ephemerides (e.g. INPOP08, DE423, EPM2008) to observations. See discussion below regarding the Gaussian gravitation constant, k, and heliocentric gravitation constant, GMS.
  2. This constant comes from the expression TDB = TCB − LB x (JDTCB − T0 ) x 86400 + TDB0, where T0 = 2443144.5003725.
  3. This constant comes from the IAU 2000 Resolution B1.8 expression
    θ(UT1) = 2π (0.7790 5727 32640 + 1.0027 3781 1911 35448 (Julian UT1 date − 2451545.0))
  4. The value for the au is TDB-compatible. An accepted definition for the TCB-compatible value of the au is still under discussion.
  5. All values of the masses from Mars to Eris are the sum of the masses of of the celestial body and its satellite(s).
  6. The value of aE and J2 are the "zero tide" values (see IERS Conventions for an explanation of the terminology). Values according to other conventions can be found in Groten et al. (2000).
  7. ω is a nominal value and was chosen to have the number of significant digits limited to those for which the value can be considered constant.
  8. εJ2000 is a component of the IAU 2006 precession model, which includes expressions that are time dependent.
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