IAU WG on NSFA
Current Best Estimates

Below are the CBEs as determined by the NSFA WG. This is a work in progress and the constants in the list and their associated values are subject to (possibly frequent) change. The values will not be considered final until the 2009 IAU General Assembly makes a decision concerning these values.

The items in blue are new from the previous IAU list of current best estimates. Unless otherwise noted, the constants should be considered to be in terms of the Système International d'Unités (SI). [Work in Progress]

Defining Constants (SI)
ConstantDescriptionValueReferenceAdopted
Natural Defining Constants
cSpeed of light2.997 924 58 x 108 ms-1[7]IAU, IERS
Auxiliary Defining Constants
k[1]Gaussian gravitational constant1.720 209 895 x 10-2[14, 11]IAU
LG1-d(TT)/d(TCG)6.969 290 134 x 10-10[15, 25]IAU, IERS
LB1-d(TDB)/d(TCB)1.550 519 768 x 10-8[16]IAU
TDB0[2]TDB - TCB at T0-6.55 x 10-5 s[16]IAU
θ0[3]Earth Rotation Angle at J2000.00.779 057 273 264 0 revolutions[15, 4]IAU
dθ/dt[3]Rate of advance of Earth Rotation Angle1.002 737 811 911 354 48 revolutions UT1-day-1[15, 4]IAU

Current Best Estimates (SI)
ConstantDescriptionValueUncertaintyReferenceAdopted
Natural Measurable Constants
GConstant of gravitation6.674 28 x 10-11 m3kg-1s-26.7 x 10-15 m3kg-1s-2[7]
Derived Constants
au[4]Astronomical unit1.495 978 707 00 x 1011 m3 m[26]
LCAverage value of 1-d(TCG)/d(TCB)1.480 826 867 41 x 10-82 x 10-17[18]IAU, IERS
Body Constants[5]
MM/MERatio of the mass of the Moon to the Earth1.230 003 71 x 10-24 x 10-10[26]
MS/MMeRatio of the mass of the Sun to Mercury6.023 6 x 1063 x 102[1]IERS
MS/MVRatio of the mass of the Sun to Venus4.085 237 19 x 1058 x 10-3[23]
MS/MMaRatio of the mass of the Sun to Mars3.098 703 59 x 1062 x 10-2[24]
MS/MJRatio of the mass of the Sun to Jupiter1.047 348 644 x 1031.7 x 10-5[20]
MS/MSaRatio of the mass of the Sun to Saturn3.497 901 8 x 1031 x 10-4[21]
MS/MURatio of the mass of the Sun to Uranus2.290 298 x 1043 x 10-2[19]IERS
MS/MNRatio of the mass of the Sun to Neptune1.941 226 x 1043 x 10-2[22]
MS/MPRatio of the mass of the Sun to Pluto1.365 66 x 1082.8 x 104[29]
MS/MErisRatio of the mass of the Sun to Eris1.191 x 1081.4 x 106[2]
MCeres/MSRatio of the mass of Ceres to the Sun4.72 x 10-103 x 10-12[26]
MPallas/MSRatio of the mass of Pallas to the Sun1.03 x 10-103 x 10-12[26]
MVesta/MSRatio of the mass of Vesta to the Sun1.35 x 10-103 x 10-12[26]
aE[6]Equatorial radius of the Earth6.378 136 6 x 106 m1 x 10-1 m[12, 3]IERS
J2[6]Dynamical form factor1.082 635 9 x 10-31 x 10-10[12]IERS
dJ2/dtLong-term variation in J2-3.001 x 10-9 cy-16 x 10-10 cy-1[16]
GMSHeliocentric gravitational constant1.327 124 420 99 x 1020 m3s-2 (TCB-compatible)
1.327 124 400 41 x 1020 m3s-2 (TDB-compatible)		1.0 x 1010 m3s-2 (TCB-compatible)
1.0 x 1010 m3s-2 (TDB-compatible)		[8]
GMEGeocentric gravitational constant3.986 004 418 x 1014 m3s-2 (TCB-compatible)
3.986 004 415 x 1014 m3s-2 (TT-compatible)
3.986 004 356 x 1014 m3s-2 (TDB-compatible)		8 x 105 m3s-2 (TCB-compatible)
8 x 105 m3s-2 (TT-compatible)
8 x 105 m3s-2 (TDB-compatible)		[27]IERS
W0Potential of the geoid6.263 685 60 x 107 m2s-25 x 10-1 m2s-2[12]IERS
ω[7]Nominal mean angular velocity of the Earth7.292 115 x 10-5 rad s-1[12]IERS
Initial Values at J2000.0
εJ2000[8]Obliquity of the ecliptic at J2000.08.438 140 6 x 104 "1 x 10-3 "[16, 13, 6]IAU

Notes

  1. The Gaussian gravitational constant, k, defines au.
  2. This constant comes from the expression TDB = TCB - LB x ( JDTCB - T0 ) x 86400 + TDB0, where T 0 = 2443144.5003725.
  3. This constant comes from the expression θ(UT1) = 2π (0.7790572732640+1.00273781191135448×(Julian UT1 date−2451545.0))
  4. The value for au is TDB-compatible. An accepted definition for the TCB-compatible value of au is still under discussion.
  5. All values of the masses from Mars to Eris are the sum of the masses of the celestial bodies and its satellites.
  6. The values for aE and J2 are "zero tide" values (see IERS Conventions for an explanation of the terminology). Values according to other conventions can be found in Groten (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 of the IAU 2006 precession model, which includes expressions that are time dependent.
  9. The rate of precession appearing in previous lists of constants is no longer appropriate given the IAU 2006 precession model [16].

References

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  2. Brown, M.E. and Schaller, E.L., 2007, "The mass of Dwarf Planet Eris," Science, 316, p. 1585, doi: 10.1126/science.1139415.

  3. Burša, M., Kouba, J., Radej, K., True, S.A., Vatrt, V., Vojtiškova, M., 1998, "Mean Earth's Equipotential Surface from Topex/Poseidon Altimetry," Studia Geoph. et Geod., 42, pp. 459-466, doi 10.1023/A:1023356803773.

  4. Capitaine, N., Guinot, B., and McCarthy, D.D., 2000, "Definition of the Celestial Ephemeris Origin and of UT1 in the International Celestial Reference Frame," Astron. Astrophys., 355, pp. 398-405.

  5. Capitaine, N., Wallace, P., and Chapront, J., 2003, "Expressions for IAU 2000 precession quantities," Astron. Astrophys., 412, pp. 567-586.

  6. 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.

  7. CODATA, 2006, http://physics.nist.gov/cuu/Constants/index.html

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  9. Fukushima, T., 2000, "Report on Astronomical Constants," Proc. IAU Colloquium 180, Johnston, K.J., McCarthy, D.D., Luzum, B.J., and Kaplan, G.H. (eds.), pp. 417-427.

  10. Fukushima, T., 2003, "Report on Astronomical Constants," Highlights of Astronomy, Vol. 13, International Astronomical Union, 2002, Rickman, H. (ed.), pp. 107-112.

  11. Gauss, C.F., 1857, Theory of the Motion of the Heavenly Bodies Moving About the Sun in Conic Sections, Boston: Little, Brown and Company, p. 2.

  12. Groten, E., 2000, Geodesists Handbook 2000, Part 4, http://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.

  13. 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.

  14. International Astronomical Union (IAU), 1976, "Proceedings of the Sixteenth General Assembly," Transactions of the IAU, XVIB, p. 31, pp. 52-66.

  15. International Astronomical Union (IAU), 2000, "Proceedings of the Twenty- Fourth General Assembly, Transactions of the IAU, XXIVB, pp. 34-57.

  16. International Astronomical Union (IAU), 2006 "Proceedings of the Twenty- Sixth General Assembly, Transactions of the IAU, XXVIB.

  17. IERS Conventions, McCarthy, D.D. and Petit, G., 2003, IERS Technical Note 32.

  18. Irwin, A. and Fukushima, T., 1999, "A numerical time ephemeris of the Earth,"Astron. Astrophys., 348, pp. 642-652.

  19. Jacobson, R.A., Campbell, J.K., Taylor, A.H., and Synott, S.P., 1992, "The Masses of Uranus and its Major Satellites from Voyager Tracking Data and Earth-based Uranian Satellite Data," Astron. J., 103(6), pp. 2068-2078.

  20. 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.

  21. 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.

  22. 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.

  23. Konopliv, A.S., Banerdt, W.B., and Sjogren, W.L., 1999, "Venus Gravity: 180th Degree and Order Model," Icarus, 139, pp. 3-18.

  24. 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.

  25. Petit, G., 2000, "Report of the BIPM/IAU Joint Committee on relativity for space-time reference systems and metrology," in Proc. of IAU Colloquium 180, Johnston, K. J., McCarthy, D. D., Luzum, B. J., Kaplan, G. H. (eds.), U. S. Naval Observatory, Washington, D. C., pp. 275-282.

  26. Pitjeva, E. 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.

  27. 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.

  28. Standish, E.M., 1995, "Report of the IAU WGAS Sub- group on Numerical Standards," Highlights in Astronomy, Vol. 12, International Astronomical Union, 1994, Appenzeller, I. (ed.), pp. 180-184.

  29. Tholen, D.J., Buie, M.W., and Grundy, W., 2008, "Masses of Nix and Hydra," Astron. J., 135(3), pp. 777-784.

Last updated 10 August 2009.