Information sheet n°27c :

The definition of the astronomical unit and the other units of distance in astronomy

The unit of length of the international system (SI) is the meter, defined as follows:

- the meter is the length of the way traversed in the vacuum by the light throughout one 1/299 792 458 second.

The basic unit used in astronomy to measure the distances is the "astronomical unit", defined as follows:

- the unit of length or unit of distance is the semi-major axis of an orbit described by a non disturbed planet with a negligeable mass around the Sun, whose mean motion is equal to "k" radians per day, "k" being the constant of Gauss, the unit of time being the day and the unit of mass, the mass of the Sun.

It is seen here that the basic unit in astronomy is linked to the dimension of the solar system and to the motion of the Earth. Indeed, all the distances in the solar system may be deduced from only one of them thanks to the laws from Kepler. The perturbations generated by the Moon and other planets on the Earth, are known only through a dynamic modeling of the solar system. One will avoid the problems generated by these not well-known perturbations by using a fictitious planet having a simple motion which is connected through this modeling to the solar system. To define the astronomical unit from the Earth itself would make us depending on the knowledge of the Earth-Moon system.

From there, it remains to evaluate the value of astronomical unit with the unit of length of the system SI, the meter. That is done by calculation of parallaxes or using radar on close planets. The use of the astronomical unit makes it possible to preserve the same numerical quantities in the modeling of the solar system, even if the value of the astronomical unit itself evolves and is improved by increasingly precise measurements.

The unit derived from the astronomical unit is the solar parallax defined as follows:

- the solar parallax is the arc sine of the terrestrial radius divided by the astronomical unit. One will note finally the existence of auxiliary units of length defined as follows:

- the parsec is the distance of a star whose annual parallax is equal to one second of degree, i.e. the distance to which an astronomical unit is seen under an angle of one second of degree; - the year of light is the distance covered by the light during one julian year (365.25 days) in an empty matter space time.

Only the meter corresponds to a constant of definition whose value is fixed arbitrarily; the other units have derived values, whose determination can vary with time. The Gauss’ constant has as a value (UAI, 1976 and IERS, 1992)of 0,017 202 098 95 radian per day, that is to say 0,985 607 668 601 425 degree per day.

The following tables give the current values of these constants.

 Solar parallaxe Astronomical unit symbol p0 au unit Second of degree meter Newcomb 1895 8,790 Paris 1896 8,80 De Sitter 1938 8,8030 149 453 000 000 Clemence 1948 8,790 149 670 000 000 UAI 1964 8,79405 149 600 000 000 UAI 1976 8,794148 149 597 870 000 JPL DE200 1982 149 597 870 660 IERS 1992 8,794142 149 597 870 610 JPL DE403 1995 149 597 870 691

Finally, for a value of the astronomical unit corresponding to the one of  IERS (1992) i.e.  149 597 870 610 meters, the auxiliary units of measure of length are :

1 year of light = 63 241,077 10 au

1 parsec = 206 264,806 248 au