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2.7.2 Astronomical units and constants
The IAU and IERS systems of astronomical units and constants
The current IAU system of values of the principal constants of the Solar System was adopted by the International Astronomical Union in 1976, and was introduced in the principal national and international almanacs from 1984 onwards. The system includes adopted relationships between SI units and the astronomical units of length, mass and time that are used in almost all theories of the motions of the members of the Solar System. The 1976 system differs in one fundamental respect from the previous 1964 system in that the astronomical unit of time is defined as one day (D) of 86 400 SI seconds, rather than as an ephemeris day. The definitions of the other astronomical units were not changed: the astronomical unit of mass is the mass of the Sun (S), while the astronomical unit of length is that length (A) for which the Gaussian gravitational constant (k) takes the value 0.017 202 098 095 in these units. The dimensions of k2 are those of the constant of gravitation, G. The length A is approximately the mean distance of the Earth from the Sun.
The high precision that has been achieved in recent years in the monitoring of the rotation of the Earth has led the International Earth Rotation Service to introduce a comprehensive set of ‘IERS Standards’ that specify the numerical models to be used in the reduction of the observations. The values of some of the constants in the 1992 version of the IERS standards differ from those in the current IAU system and are given in the third column of the table.
Notes: (1) For the definitions of J2 and
f see section
Other units and the standard epoch
The unit of time in the fundamental formulae for precession (and in similar expressions) is the Julian century of 36 525 days (the tropical century is not to be used). The new standard epoch is designated J2000.0 and is the calendar date 2000 January ld.5, which is the Julian date JD 245 1545.0.
An alternative unit for use in Newtonian dynamics of the solar system and binary stars is the Gaussian year, which is the sidereal period of a particle of negligible mass moving around the Sun in an orbit with a mean distance of 1 au; it is equal to 2π/k ( = 365.256 898) days. Kepler’s law for the relative motion of two isolated particles of mass M and m is then, simply,
a3 = P2(M + m)
where a is the semi-major axis of the orbit in au, P is the period in Gaussian years, and the unit of mass is the mass of the Sun.
A convenient unit for the measurement of the distances of nearby stars is the parsec (pc); this is the distance at which 1 au subtends an angle of 1 second of arc. Hence
1 parsec = l/(sin 1″) au = 2.063 × 105 au = 3.086 × 1016 m
The multiple units kiloparsec (kpc) and megaparsec (Mpc) are more appropriate for most galactic and extragalactic objects respectively. The ‘light-year’ is normally only used in popular astronomical texts:
1 light-year = 0.307 pc = 6.32 × 104 au = 9.46 × 1015 m
Constants relating to time
The following relationships hold in all time systems:
1 day = 24 hours = 1440 minutes = 86
The rate of rotation of the Earth is
72 921 151.467 − 0.844 ΔD picoradians/second,
where ΔD is the difference measured in
milliseconds between the duration of the mean solar day and 86 400 SI seconds.
The current value of ΔD is about 3.
Universal time is related to Greenwich mean sidereal time through the expression:
GMST at 0h UT = 6h 41m 50s.548 41 + 8640 184s.812 866Tu + 0s.093 104Tu2 − 6.2 × 10−6Tu3
where Tu is measured in centuries of 36 525 mean solar
days from 2000 January 1 at 12h UT (JD 245 1545.0 UT).
The precessional motion of the celestial equator (plane normal to the axis of rotation of the Earth) around the ecliptic (mean plane of the Earth's orbit around the Sun) has a period of about 25 725 years, and gives rise to the luni-solar precession in celestial longitude of 5037 per year. There is also a slow precessional motion of the ecliptic due to planetary perturbations; this gives both a change in the obliquity (inclination of the ecliptic to the equator) and a motion of the equinox (direction of the line of intersection of equator and ecliptic) along the equator of 0''.12 per year. The combined effect is known as the general precession.
Obliquity of ecliptic = 23° 26′ 21″.45
- 46″.81 T = 23°.439 291 − 0°.013 00 T
Where T is measured in Julian centuries from 2000.0. For a star with right ascension α and declination δ the annual precessions in right ascension and declination are m + n sin α tan δ and n cos α, respectively, where
m = 3s.074 96 + 0s.001 86 T, n = 1s.336 21 − 0s.000 57 T= 20″.0431 − 0″.0085 T
The nutation of the axis of rotation of the Earth is normally specified by its effects in celestial longitude and obliquity. The principal terms in the trigonometric series for the nutation are:
The Explanatory Supplement to the Astronomical Almanac (ed. P. K.
Seidelmann, 1992, University Science Books, Mill Valley, California, ISBN
0-935702-68-7) contains detailed accounts of astronomical time and coordinate
systems and of the IAU system of astronomical units and constants.
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