IAU Working Group Numerical Standards for Fundamental Astronomy

IAU Division I Working Group

Numerical Standards for Fundamental Astronomy

Astronomical Constants : Fixed by Convention

This list is made up of the "defining constants" fixed by convention. The NSFA Working Group 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.

Speed of Light	L_G	L_B	TDB-TCB at T₀
	Astronomical Unit	Earth Rotation Angle	Rate of ERA

Defining Constants Fixed by Convention - SI Units

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Speed of Light	c = 2.997 924 58 x 10⁸ m s⁻¹	c
Status:	Natural defining constant. IAU 2009 adopted constant. Adopted CBE 2009 August 10. A constant fixed by convention.
Notes:	The speed of light is an (unchanged) defining value for the IAU and the IERS. The reference has been updated from CODATA 1998 to CODATA 2006 to reflect the use of the value of this constant by the current set of CODATA constants.
References:	CODATA 2006, `physics.nist.gov/cuu/Constants` Mohr, P. J. and Taylor, B. N., 2000, "CODATA recommended values of the fundamental physical constants: 1998," Rev. Mod. Phys., 72, pp. 351-495. 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.
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1−d(TT)/d(TCG)	L_G = 6.969 290 134 x 10⁻¹⁰	L_G
Status:	Auxiliary defining constant. IAU 2009 adopted constant. Adopted CBE 2009 August 10. A constant fixed by convention
Notes:	The value for L_G is such that the mean rate of TT is close to the mean rate of the proper time of an observer located on the rotating geoid. It is specified in IAU 2000 Resolution B1.9 as a defining constant.
References:	International Astronomical Union (IAU), 2000, "Proceedings of the Twenty-Fourth General Assembly," Transactions of the IAU, XXIVB, pp. 34-57. 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.
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1−d(TDB)/d(TCB)	L_B = 1.550 519 768 x 10⁻⁸	L_B
Status:	Auxiliary defining constant. IAU 2009 adopted constant. Adopted CBE 2009 August 10. A constant fixed by convention
Notes:	L_B is specified in IAU 2006 Resolution B3 as a defining constant. The fixed value for L_B was derived in 2005 from the expression L_B = L_C + L_G − L_C x L_G, where L_G is given in IAU Resolution B1.9 (2000) and L_C has been determined (Irwin and Fukushima, 1999) using the JPL ephemeris DE405. When using the DE405, the defining L_B value effectively eliminates a linear drift between TDB and TT, evaluated at the geocenter. When realizing TCB using other ephemerides, the difference between TDB and TT, evaluated at the geocenter, may include some linear drift, not expected to exceed 1 ns per year.
References:	International Astronomical Union (IAU), 2006 "Proceedings of the Twenty-Sixth General Assembly," Transactions of the IAU, XXVIB. Irwin, A. and Fukushima, T., 1999, "A numerical time ephemeris of the Earth," Astron. Astrophys., 348, pp. 642-652.
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TDB − TCB at T₀	TDB₀ = −6.55 x 10⁻⁵ s	TDB₀
Status:	Auxiliary defining constant. IAU 2009 adopted constant. Adopted CBE 2009 August 10. A constant fixed by convention
Notes:	TDB − TCB, the difference between TDB and TCB at T₀ (2443144.5003725) is specified in IAU 2006 Resolution B3 as a defining constant. TDB = TCB − L_B x (JD_TCB − T₀) x 86400 + TDB₀, where T₀ = 2443144.5003725. The value for TDB₀ is chosen to provide consistency with the TDB−TT formula of Fairhead and Bretagnon (1990).
References:	International Astronomical Union (IAU), 2006 "Proceedings of the Twenty-Sixth General Assembly," Transactions of the IAU, XXVIB. Fairhead, L. and Bretagnon, P., 1990, "An Analytical Formula for the Time Transformation TB-TT," Astron. Astrophys., 229, pp. 240-247.
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Astronomical unit	au = 1.495 978 707 00 x 10¹¹ m	au
Status:	Auxiliary defining constant. Adopted 2012 August 30, IAU GA 2012 Resolution B2 A constant fixed by convention.
Notes:	The IAU GA 2012 Resolution B2 fixes the value of the astronomical unit (au) in kilometres. The definition states that: The astronomical unit is to be used with all time scales TCB, TDB, TCG, TT, etc., the Gaussian gravitational constant k be deleted from the system of astronomical constants, the value of the solar mass parameter (previously called the heliocentric gravitational constant), GMS, be determined observationally in SI units, the unique symbol au be used for the astronomical unit. This value is the IAU 2009 value adopted 2009 August and it was taken from Pitjeva and Standish (2009) and is an average of recent estimates for the au defined by k.
References:	The IAU GA 2012 Resolution B2 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.
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Earth Rotation Angle at J2000.0 Rate of advance of Earth Rotation Angle	θ₀ = 0.779 057 273 2640 revolutions dθ/dUT1 = 1.002 737 811 911 354 48 revolutions UT1-day⁻¹	θ₀ dθ/dUT1
Status:	Auxiliary defining constants. IAU 2009 adopted constant. Adopted CBE 2009 August 10. Costants fixed by convention
Notes:	These values are specified in IAU 2000 Resolution B1.8 as defining constants. They come from the expression θ(UT1) = 2π (0.779 057 273 2640 + 1.002 737 811 911 354 48 (Julian UT1 date − 2451545.0))
References:	International Astronomical Union (IAU), 2000, "Proceedings of the Twenty-Fourth General Assembly," Transactions of the IAU, XXIVB, pp. 34-57. 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.
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