USNO Circular 179 - U.S. Naval Observatory

A Few Words about Constants
This circular does not contain a list of adopted fundamental astronomical constants, because the
IAU is no longer maintaining such a list. The last set of officially adopted constant values was the
IAU (1976) System of Astronomical Constants. That list is almost entirely obsolete. For a while,
an IAU working group maintained a list of “best estimates” of various constant values, but the IAU
General Assembly of 2003 did not renew that mandate. It can be argued that a list of fundamental
astronomical constants is no longer possible, given the complexity of the models now used and the
many free parameters that must be adjusted in each model to fit observations. That is, there are
more constants now to consider, and their values are theory dependent. In many cases, it would be
incorrect to attempt to use a constant value, obtained from the fit of one theory to observations,
with another theory.
We are left with three defining constants with IAU-sanctioned values that are intended to be
fixed:
1. The Gaussian gravitational constant: k = 0.01720209895. The dimensions of k2 are
AU3M −1
○· d−2 where AU is the astronomical unit, M○· is the solar mass, and d is the day
of 86400 seconds.
2. The speed of light: c = 299 792 458 m s −1 .
3. The fractional difference in rate between the time scales TT and TCG: LG = 6.969290134×10 −10 .
Specifically, the derivative dTT/dTCG = 1 − LG. (See Chapter 3.)
The IERS Conventions (2003) includes a list of constants as its Table 1.1. Several useful ones
from this list that are not highly theory dependent (for astronomical use, at least) are:
1. Equatorial radius of the Earth: aE = 6 378 136.6 m.
2. Flattening factor of the Earth: f = 1/298.25642.
3. Dynamical form factor of the Earth: J2 = 1.0826359×10 −3 .
4. Nominal mean angular velocity of Earth rotation: ω = 7.292115×10 −5 rad s −1 .
5. Constant of gravitation: G = 6.673×10 −11 m 3 kg −1 s −2 (CODATA 2002 recommended
value: 6.6742×10 −11 m 3 kg −1 s −2 ).
The first four values above were recommended by Special Commission 3 of the International
Association of Geodesy; the first three are so-called “zero tide” values. (The need to introduce
the concept of “zero tide” values indicates how theory creeps into even such basic constants as
the radius of the Earth as the precision of measurement increases. See section 1.1 of the IERS
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