IAU Division I Working Group
Numerical Standards for Fundamental Astronomy
Astronomical Constants : Current Best Estimates (CBEs)


This list of Current Best Estimates is made up of the "defining constants" which are not fixed by convention but measurable and determined by the NSFA Working Group. The NSFA WG will update these constants as and when research produces better values.

Click on one of the following constants to jump to the section with the current best estimate and all the relevant details and references.


MEASURABLE Gravitation Const.
OTHER LC
BODY CONSTANTS Earth Radius Dynamical F.F. J2 Variation in J2
Geocentric Grav. Potential of Geoid Earth Velocity
Solar Mass Mass Moon / Earth
Mass Mercury Mass Venus Mass Mars
Mass Jupiter Mass Saturn Mass Uranus Mass Neptune
Mass Pluto Mass Eris
Mass Ceres Mass Pallas Mass Vesta
INITIAL VALUES Obliquity of Ecliptic

The List of Current Best Estimates - SI Units

-->
 
Constant of gravitation G = 6.674 28 x 10−11 m3kg−1s−2 G
Uncertainty: 6.7 x 10−15 m3kg−1s−2
Status:
  • Natural measurable constant.
  • IAU 2009 adopted constant.
  • Adopted CBE 2009 August 10.
Notes:
  1. The value for the constant of gravitation, G, has been changed from the CODATA 1998 value to the value adopted by CODATA 2006.
References:
  1. CODATA 2006, physics.nist.gov/cuu/Constants
  2. Mohr, P. J. and Taylor, B. N., 2000, "CODATA recommended values of the fundamental physical constants: 1998," Rev. Mod. Phys., 72, pp. 351-495.
  3. Mohr, P. J., Taylor, B. N., and Newell, D. B., 2008, "The CODATA recommended values of the fundamental physical constants: 2006," Rev. Mod. Phys., 80, pp. 633-730.
Top
Average value of
1−d(TCG)/d(TCB)		 LC = 1.480 826 867 41 x 10−8 LC
Uncertainty: 2 x 10−17
Status:
  • Other constant.
  • IAU 2009 adopted constant.
  • Adopted CBE 2009 August 10.
Notes:
  1. The value for LC is taken from Irwin and Fukushima (1999) and is the most recent published determination. It is based on the DE405.
  2. LC is used in some analtical formulas for the transformation between TCG and TCB.
  3. Before 2006, LC was used to compute LB but since the adoption of IAU 2006 Resolution B3, that is no longer true.
  4. Before IAU 2006, LB was computed as LB = LC + LG − LC × LG. This relation does not hold [exactly] between the defining values of LB and LG and a value of LC computed from an ephemeris.
References:
  1. Irwin, A. and Fukushima, T., 1999, "A numerical time ephemeris of the Earth," Astron. Astrophys., 348, pp. 642-652.
Top
Solar mass parameter GMS = 1.327 124 420 99 x 1020 m3s−2 [TCB-compatible]
GMS = 1.327 124 400 41 x 1020 m3s−2 [TDB-compatible]		 GMS
Uncertainty: 1.0 x 1010 m3s−2 [TCB-compatible]
1.0 x 1010 m3s−2 [TDB-compatible]
Status:
  • Body constant.
  • 2012 August 30, IAU GA 2012 Resolution B2; name and status changed.
  • IAU 2009 adopted constant.
  • Adopted CBE 2009 August 10.
Notes:
  1. The IAU GA 2012 Resolution B2 defined the astronomical unit (au) as a conventional value, thus breaking the historical relationship between GMS, k, and the au. Thus noting (3) and recommends (4) of the resolution states that GMS, the solar mass parameter, previously know as the heliocentric gravitational constant be determined observationally in SI units.
  2. This value for GMS given is taken from the Folkner et al. (2008) fit to the DE421 ephemerides. It was not derived using the value of au, but the TDB-compatible value of GMS given is consistent with the value of au given (Pitjeva and Standish, 2009) to within the errors of the estimate.
  3. The previous definitions for GMS, k and the au are given in the archive.
References:
  1. Folkner, W.M., Williams, J.G., and Boggs, D.H., 2008, "The Planetary and Lunar Ephemeris DE 421," Memorandum IOM 343R-08-003, 31 pp.
  2. Pitjeva, E.V. and Standish, E.M., 2009, "Proposals for the masses of the three largest asteroids, the Moon-Earth mass ratio and the astronomical unit," Celest. Mech. Dyn. Astr., 103, pp. 365-372, doi: 10.1007/s10569-009-9203-8.
  3. The IAU GA 2012 Resolution B2
Top
Equatorial radius of the Earth aE = 6.378 1366 x 106 m [TT-compatible] aE
Uncertainty: 1 x 10−1 m [TT-compatible]
Status:
  • Body constant.
  • IAU 2009 adopted constant.
  • Adopted CBE 2009 August 10.
Notes:
  1. aE is taken from Burša, et al. (1998) and was included in the International Association of Geodesy (IAG) Special Commission 3 (SC3) Report in Groten (2000).
  2. The value of aE is the "zero tide" value. See the IERS Conventions for more explanation of the terminology "zero tide".
  3. Although the value is listed as TT-compatible, the TCG-compatible value is equivalent to the number of decimal places listed.
References:
  1. Groten, E., 2000, Geodesists Handbook 2000, Part 4, www.gfy.ku.dk/~iag/HB2000/part4/groten.htm. See also "Parameters of Common Relevance of Astronomy, Geodesy, and Geodynamics," J. Geod., 74, pp. 134-140.
  2. Burša, M., Kouba, J., Radej, K., True, S.A., Vatrt, V., Vojtišková, M., 1998, "Mean Earth's Equipotential Surface from Topex/Poseidon Altimetry," Studia Geoph. et Geod., 42, pp. 459-466, doi: 10.1023/A:1023356803773.
  3. IERS Conventions, 2003, McCarthy, D.D. and Petit, G., IERS Technical Note 32., Verlag des Bundesamts für Kartographie und Geodäsie, Frankfurt am Main, 127 pp.
Top
Dynamical form factor J2 = 1.082 6359 x 10−3 J2
Uncertainty: 1 x 10−10
Status:
  • Body constant.
  • IAU 2009 adopted constant.
  • Adopted CBE 2009 August 10.
Notes:
  1. The dynamical form factor is taken from the International Association of Geodesy (IAG) Special Commission 3 (SC3) Report provided by Groten (2000).
  2. The value for J2 is the "zero tide" value (see IERS Conventions for an explanation of the terminology). Values according to other conventions can be found in Groten (2000).
References:
  1. Groten, E., 2000, Geodesists Handbook 2000, Part 4, www.gfy.ku.dk/~iag/HB2000/part4/groten.htm. See also "Parameters of Common Relevance of Astronomy, Geodesy, and Geodynamics," J. Geod., 74, pp. 134-140.
  2. IERS Conventions, 2003, McCarthy, D.D. and Petit, G., IERS Technical Note 32., Verlag des Bundesamts für Kartographie und Geodäsie, Frankfurt am Main, 127 pp.
Top
Time rate of change in J2 dJ2/dt = −3.0 x 10−9 cy−1 dJ2/dt
Uncertainty: 6 x 10−10 cy−1
Status:
  • Body constant.
  • IAU 2009 adopted constant.
  • Adopted CBE 2009 August 10.
Notes:
  1. The time rate of change in J2 is a value adopted in IAU 2006 Resolution B1 that is consistent with the adopted IAU 2006 precession model.
  2. The value is taken from Capitaine et al. (2005).
  3. A discussion about the uncertainty can be found in Bourda and Capitaine (2004) and in Hilton et al. (2006) while a discussion about the components of the J2 variation can be found in Cheng and Tapley (2004) with a 2008 AGU update ( 2008AGUFM.G33A0673C).
References:
  1. International Astronomical Union (IAU), 2006, "Proceedings of the Twenty-Sixth General Assembly," Transactions of the IAU, XXVIB.
  2. Capitaine, N., Wallace, P.T., and Chapront, J., 2005, "Improvement of the IAU 2000 precession model," Astron. Astrophys., 432, pp. 355-367.
  3. Bourda, G. and Capitaine, N., 2004, "Precession, nutation and space geodetic determination of the Earth's variable gravity field," Astron. Astrophys., 428, pp. 691-702.
  4. Cheng and Tapley, 2004, "Variations in the Earth's oblateness during the past 28 years," Journ. Goephys. Res., 109, B09402, doi: 10.1029/2004JB003028.
  5. Hilton, J.L., Capitaine, N., Chapront, J., Ferrandiz, J.M., Fienga, A., Fukushima, T., Getino, J., Mathews, P., Simon, J.-L., Soffel, M., Vondrak, J., Wallace, P., and Williams, J., 2006, "Report of the International Astronomical Union Division I Working Group on Precession and the Ecliptic," Celest. Mech. Dyn. Astr., 94, pp. 351-367, doi: 10.1007/s10569-006-0001-2.
Top
Geocentric gravitational constant GME = 3.986 004 418 x 1014 m3s−2 [TCB-compatible]
GME = 3.986 004 415 x 1014 m3s−2 [TT-compatible]
GME = 3.986 004 356 x 1014 m3s−2 [TDB-compatible]		 GME
Uncertainty: 8 x 105 m3s−2 [TCB-compatible]
8 x 105 m3s−2 [TT-compatible]
8 x 105 m3s−2 [TDB-compatible]
Status:
  • Body constant.
  • IAU 2009 adopted constant.
  • Adopted CBE 2009 August 10.
References:
  1. Ries, J. C., Eanes, R. J., Shum, C. K., and Watkins, M. M., 1992, "Progress in the Determination of the Gravitational Coefficient of the Earth," Geophys. Res. Lett., 19(6), pp. 529-531.
Top
Potential of the geoid W0 = 62 636 853.4 m2s−2 W0
Uncertainty: The formal error is 0.02 m2s−2; however, as convention the adopted value is understood free of error.
Status:
  • Body constant.
  • Adopted 2015 July 2 at XXVI IUGG General Assembly by IAG Resolution 1
  • Adopted CBE 2018 August 31.
References:
  1. Sánchez L., Cunderlík R., Dayoub N., Mikula K., Minarechová Z., Šíma Z., Vatrt V., Vojtíšková M., 2016, "A conventional value for the geoid reference potential W0", Journal of Geodesy, 10.1007/s00190-016-0913-x https://www.math.sk/mikula/W0_JoGE.pdf. See also Working Group on Vertical Datum Standardization http://ggos.org/en/focus-areas/unified-height-system/working-group/011-vds/
Top
Nominal mean angular velocity of the Earth ω = 7.292 115 x 10−5 rad s−1 [TT-compatible] ω
Uncertainty: (see Notes)
Status:
  • Body constant.
  • IAU 2009 adopted constant.
  • Adopted CBE 2009 August 10.
Notes:
  1. 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.
  2. Although the value is listed as TT-compatible, the TCG-compatible value is equivalent to the number of decimal places listed.
References:
  1. Groten, E., 2000, Geodesists Handbook 2000, Part 4, www.gfy.ku.dk/~iag/HB2000/part4/groten.htm. See also "Parameters of Common Relevance of Astronomy, Geodesy, and Geodynamics," J. Geod., 74, pp. 134-140.
Top
Ratio mass of the Moon to the Earth MM/ME = 1.230 003 71 x 10−2 MM/ME
Uncertainty: 4 x 10−10
Status:
  • Body constant.
  • IAU 2009 adopted constant.
  • Adopted CBE 2009 August 10.
Notes:
  1. This value is equivalent to ME / MM = 81.300 5678 ± 2.7 × 10-6.
References:
  1. Pitjeva, E.V. and Standish, E.M., 2009, "Proposals for the masses of the three largest asteroids, the Moon-Earth mass ratio and the astronomical unit," Celest. Mech. Dyn. Astr., 103, pp. 365-372, doi: 10.1007/s10569-009-9203-8.
Top
Ratio of the mass of the Sun to Mercury MS/MMe = 6.023657330 x 106 MS/MMe
Uncertainty: 2.35 x 10−1
Status:
  • Body constant.
  • Adopted CBE 2015 May 25.
References:
  1. Mazarico, E., Genova, A., Goossens, S., Lemoine, F.G., Neumann, G.A., Zuber, M.T., Smith, D.E., Solomon, S.C., 2014, "The gravity field, orientatation, and ephemeris of Mercury from MESSENGER observations after three years in orbit," J. Geophys. Res.: Planets, 119, pp. 337-349, doi:10.1002/2014JE004675.
Top
Ratio of the mass of the Sun to Venus MS/MVe = 4.085 237 19 x 105 MS/MVe
Uncertainty: 8 x 10−3
Status:
  • Body constant.
  • IAU 2009 adopted constant.
  • Adopted CBE 2009 August 10.
References:
  1. Konopliv, A.S., Banerdt, W.B., and Sjogren, W.L., 1999, "Venus Gravity: 180th Degree and Order Model," Icarus, 139, pp. 3-18.
Top
Ratio of the mass of the Sun to Mars MS/MMa = 3.098 703 59 x 106 MS/MMa
Uncertainty: 2 x 10−2
Status:
  • Body constant.
  • IAU 2009 adopted constant.
  • Adopted CBE 2009 August 10.
Notes:
  1. Includes the sum of the masses of the body and its satellites.
References:
  1. Konopliv, A.S., Yoder, C.F., Standish, E.M., Yuan, D.N., Sjogren, W.L., 2006, "A global solution for the Mars static and seasonal gravity, Mars orientation, Phobos and Deimos masses, and Mars ephemeris," Icarus, 182(1), pp. 23-50.
Top
Ratio of the mass of the Sun to Jupiter MS/MJ = 1.047 348 644 x 103 MS/MJ
Uncertainty: 1.7 x 10−5
Status:
  • Body constant.
  • IAU 2009 adopted constant.
  • Adopted CBE 2009 August 10.
Notes:
  1. Includes the sum of the masses of the body and its satellites.
References:
  1. Jacobson, R.A., Haw, R.J., McElrath, T.P., and Antreasian, P.G., 2000, "A Comprehensive Orbit Reconstruction for the Galileo Prime Mission in the J2000 System," J. Astronaut. Sci., 48(4), pp. 495-516.
Top
Ratio of the mass of the Sun to Saturn MS/MSa = 3.497 9018 x 103 MS/MSa
Uncertainty: 1 x 10−4
Status:
  • Body constant.
  • IAU 2009 adopted constant.
  • Adopted CBE 2009 August 10.
Notes:
  1. Includes the sum of the masses of the body and its satellites.
References:
  1. Jacobson, R.A., Antreasian, P.G., Bordi, J.J., Criddle, K.E., Ionasescu, R., Jones, J.B., Mackenzie, R.A., Pelletier, F.J., Owen Jr., W.M., Roth, D.C. and Stauch, J.R., 2006, "The gravity field of the Saturnian system from satellite observations and spacecraft tracking data," Astron. J., 132(6), pp. 2520-2526.
Top
Ratio of the mass of the Sun to Uranus MS/MU = 2.290 295 1 x 104 MS/MU
Uncertainty: 1.7 x 10−2
Status:
  • Body constant.
  • Adopted CBE 2015 May 25.
Notes:
  1. Includes the sum of the masses of the body and its satellites.
References:
  1. Jacobson, R.A., 2014, "The orbits of the Uranian satellites and rings, the gravity field of the Uranian system, and the orientation of the pole of Uranus," Astron. J., 148:76, 13 pp, doi:10.1088/0004-6256/148/5/76.
Top
Ratio of the mass of the Sun to Neptune MS/MN = 1.941 226 x 104 MS/MN
Uncertainty: 3 x 10−2
Status:
  • Body constant.
  • IAU 2009 adopted constant.
  • Adopted CBE 2009 August 10.
Notes:
  1. Includes the sum of the masses of the body and its satellites.
References:
  1. Jacobson, R.A., 2009, "The Orbits of the Neptunian Satellites and the Orientation of the Pole of Neptune," Astron. J., 137, pp. 4322-4329, doi: 10.1088/004-6256/137/5/4322.
Top
Ratio of the mass of the Sun to (134340) Pluto MS/MP = 1.360 5 x 108 MS/MP
Uncertainty: 2.1 x 105
Status:
  • Body constant.
  • Adopted CBE 2015 May 25.
Notes:
  1. Includes the sum of the masses of the body and its satellites.
References:
  1. Brozović, M., Showalter, M.R., Jacobson, R.A., and Buie, M.W., 2015, "The orbits and masses of satellites of Pluto," Icarus, 246, pp. 317-329.
Top
Ratio of the mass of the Sun to (136199) Eris MS/MEris = 1.191 x 108 MS/MEris
Uncertainty: 1.4 x 106
Status:
  • Body constant.
  • IAU 2009 adopted constant.
  • Adopted CBE 2009 August 10.
Notes:
  1. Includes the sum of the masses of the body and its satellites.
  2. Equivalently MEris/MS = 8.396 x 10−9 ± 0.100 x 10−9.
References:
  1. Brown, M.E. and Schaller, E.L., 2007, "The mass of Dwarf Planet Eris," Science, 316, p. 1585, doi: 10.1126/science.1139415.
Top
Ratio of the mass of (1) Ceres to the Sun MCeres/MS = 4.72 x 10−10 MCeres/MS
Uncertainty: 3 x 10−12
Status:
  • Body constant.
  • IAU 2009 adopted constant.
  • Adopted CBE 2009 August 10.
References:
  1. Pitjeva, E.V. and Standish, E.M., 2009, "Proposals for the masses of the three largest asteroids, the Moon-Earth mass ratio and the astronomical unit," Celest. Mech. Dyn. Astr., 103, pp. 365-372, doi: 10.1007/s10569-009-9203-8.
Top
Ratio of the mass of (2) Pallas to the Sun MPallas/MS = 1.03 x 10−10 MPallas/MS
Uncertainty: 3 x 10−12
Status:
  • Body constant.
  • IAU 2009 adopted constant.
  • Adopted CBE 2009 August 10.
References:
  1. Pitjeva, E.V. and Standish, E.M., 2009, "Proposals for the masses of the three largest asteroids, the Moon-Earth mass ratio and the astronomical unit," Celest. Mech. Dyn. Astr., 103, pp. 365-372, doi: 10.1007/s10569-009-9203-8.
Top
Ratio of the mass of (4) Vesta to the Sun MVesta/MS = 1.302 684 6 x 10−10 MVesta/MS
Uncertainty: 9 x 10−17
Status:
  • Body constant.
  • Adopted CBE 2015 May 25.
References:
  1. Konopliv, A.S., Asmar, S.W., Park, R.S., Bills, B.G., Centinello, F., Chamberlin, A.B., Ermakov, A., Gaskell, R.W., Rambaux, N., Raymond, C.A., Russell. C.T., Smith, D.E., Tricarico, P., Zuber, M.T., 2014, "The Vesta gravity field, spin pole and rotatin period, landmark positions, and ephemeris from the Dawn tracking and optical data," Icarus, 240, pp. 103-117,
Top
Obliquity of the ecliptic at J2000.0 εJ2000 = 8.438 1406 x 104 " εJ2000
Uncertainty: 1 x 10−3 "
Status:
  • Initial value at J2000.0.
  • IAU 2009 adopted constant.
  • Adopted CBE 2009 August 10.
Notes:
  1. The obliquity of the ecliptic at J2000.0 is from the Hilton et al. (2006) report from the IAU Working Group on precession and the ecliptic. This value is taken from the P03 precession model of Capitaine et al. (2003) and was adopted in IAU 2006 Resolution B1.
  2. The value was determined by Chapront et al. (2002) using lunar laser ranging observations.
  3. εJ2000 is a component of the IAU 2006 precession model that includes expressions that are time dependent.
References:
  1. International Astronomical Union (IAU), 2006 "Proceedings of the Twenty-Sixth General Assembly", Transactions of the IAU, XXVIB.
  2. Hilton, J.L., Capitaine, N., Chapront, J., Ferrandiz, J.M., Fienga, A., Fukushima, T., Getino, J., Mathews, P., Simon, J.-L., Soffel, M., Vondrak, J., Wallace, P., and Williams, J., 2006, "Report of the International Astronomical Union Division I Working Group on Precession and the Ecliptic," Celest. Mech. Dyn. Astr., 94, pp. 351-367, doi: 10.1007/s10569-006-0001-2.
  3. Capitaine, N., Wallace, P., and Chapront, J., 2003, "Expressions for IAU 2000 precession quantities", Astron. Astrophys., 412, pp. 567-586.
  4. Chapront, J, Chapront-Touze, M., and Francou, G., 2002, "A new determination of lunar orbital parameters, precession constant and tidal acceleration from LLR measurements," Astron. Astrophys., 387, pp. 700-709, doi: 10.1051/0004-6361:20020420.
Top

 © IAU, 2010-2012 Valid HTML 4.01 Transitional Valid CSS! 4.01 Transitional