Astronomical constant

Besides the IAU list of units and constants, also the International Earth Rotation and Reference Systems Service defines constants relevant to the orientation and rotation of the Earth, in its technical notes.

The IAU system of constants defines a system of astronomical units for length, mass and time (in fact, several such systems), and also includes constants such as the speed of light and the constant of gravitation which allow transformations between astronomical units and SI units. Slightly different values for the constants are obtained depending on the frame of reference used. Values quoted in barycentric dynamical time (TDB) or equivalent time scales such as the T_eph of the Jet Propulsion Laboratory ephemerides represent the mean values that would be measured by an observer on the Earth's surface (strictly, on the surface of the geoid) over a long period of time. The IAU also recommends values in SI units, which are the values which would be measured (in proper length and proper time) by an observer at the barycentre of the Solar System: these are obtained by the following transformations:

${\displaystyle {\tau }_A(\mathrm{S}\mathrm{I})=(1+L_{\mathrm{B}}{)}^{\frac{1}{3}}{\tau }_A(\mathrm{T}\mathrm{D}\mathrm{B})}$

${\displaystyle GE(\mathrm{S}\mathrm{I})=(1+L_{\mathrm{B}})GE(\mathrm{T}\mathrm{D}\mathrm{B})}$

${\displaystyle GS(\mathrm{S}\mathrm{I})=(1+L_{\mathrm{B}})GS(\mathrm{T}\mathrm{D}\mathrm{B})}$

Astronomical system of units

The astronomical unit of time is a time interval of one day (D) of 86400 seconds. The astronomical unit of mass is the mass of the Sun (S). The astronomical unit of length is that length (A) for which the Gaussian gravitational constant (k) takes the value 0.01720209895 when the units of measurement are the astronomical units of length, mass and time.