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