IAU WG on NSFA Current Best Estimates

# 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)
Constant | Description | Value | Reference | Adopted
--- | --- | --- | --- | ---
Natural Defining Constants
c | Speed of light | 2.997 924 58 x 108 ms-1 | [7] | IAU, IERS
Auxiliary Defining Constants
k[1] | Gaussian gravitational constant | 1.720 209 895 x 10-2 | [14, 11] | IAU
LG | 1-d(TT)/d(TCG) | 6.969 290 134 x 10-10 | [15, 25] | IAU, IERS
LB | 1-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 J2000.0 | 0.779 057 273 264 0 revolutions | [15, 4] | IAU
dθ/dt[3] | Rate of advance of Earth Rotation Angle | 1.002 737 811 911 354 48 revolutions UT1-day-1 | [15, 4] | IAU

Current Best Estimates (SI)
Constant | Description | Value | Uncertainty | Reference | Adopted
--- | --- | --- | --- | --- | ---
Natural Measurable Constants
G | Constant of gravitation | 6.674 28 x 10-11 m3kg-1s-2 | 6.7 x 10-15 m3kg-1s-2 | [7]
Derived Constants
au[4] | Astronomical unit | 1.495 978 707 00 x 1011 m | 3 m | [26]
LC | Average value of 1-d(TCG)/d(TCB) | 1.480 826 867 41 x 10-8 | 2 x 10-17 | [18] | IAU, IERS
Body Constants[5]
MM/ME | Ratio of the mass of the Moon to the Earth | 1.230 003 71 x 10-2 | 4 x 10-10 | [26]
MS/MMe | Ratio of the mass of the Sun to Mercury | 6.023 6 x 106 | 3 x 102 | [1] | IERS
MS/MV | Ratio of the mass of the Sun to Venus | 4.085 237 19 x 105 | 8 x 10-3 | [23]
MS/MMa | Ratio of the mass of the Sun to Mars | 3.098 703 59 x 106 | 2 x 10-2 | [24]
MS/MJ | Ratio of the mass of the Sun to Jupiter | 1.047 348 644 x 103 | 1.7 x 10-5 | [20]
MS/MSa | Ratio of the mass of the Sun to Saturn | 3.497 901 8 x 103 | 1 x 10-4 | [21]
MS/MU | Ratio of the mass of the Sun to Uranus | 2.290 298 x 104 | 3 x 10-2 | [19] | IERS
MS/MN | Ratio of the mass of the Sun to Neptune | 1.941 226 x 104 | 3 x 10-2 | [22]
MS/MP | Ratio of the mass of the Sun to Pluto | 1.365 66 x 108 | 2.8 x 104 | [29]
MS/MEris | Ratio of the mass of the Sun to Eris | 1.191 x 108 | 1.4 x 106 | [2]
MCeres/MS | Ratio of the mass of Ceres to the Sun | 4.72 x 10-10 | 3 x 10-12 | [26]
MPallas/MS | Ratio of the mass of Pallas to the Sun | 1.03 x 10-10 | 3 x 10-12 | [26]
MVesta/MS | Ratio of the mass of Vesta to the Sun | 1.35 x 10-10 | 3 x 10-12 | [26]
aE[6] | Equatorial radius of the Earth | 6.378 136 6 x 106 m | 1 x 10-1 m | [12, 3] | IERS
J2[6] | Dynamical form factor | 1.082 635 9 x 10-3 | 1 x 10-10 | [12] | IERS
dJ2/dt | Long-term variation in J2 | -3.001 x 10-9 cy-1 | 6 x 10-10 cy-1 | [16]
GMS | Heliocentric gravitational constant | 1.327 124 420 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]
GME | Geocentric gravitational constant | 3.986 004 418 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
W0 | Potential of the geoid | 6.263 685 60 x 107 m2s-2 | 5 x 10-1 m2s-2 | [12] | IERS
ω[7] | Nominal mean angular velocity of the Earth | 7.292 115 x 10-5 rad s-1 |  | [12] | IERS
Initial Values at J2000.0
εJ2000[8] | Obliquity of the ecliptic at J2000.0 | 8.438 140 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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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.

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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.

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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.

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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.