IAU (1976) System of Astronomical Constants

The International Astronomical Union at its 16th General Assembly in Grenoble in 1976, accepted Resolution No. 1{{Citation

| editor-last=Müller | editor-first=Edith A.

| editor2-last=Jappel | editor2-first=A.

| year=1977

| title=Proceedings of the Sixteenth General Assembly Grenoble 1976

| series=Transactions of the International Astronomical Union

| section=Resolution No. 1

| volume=16B

| page=31

| url=https://archive.org/details/proceedingsofsix0016inte/page/31/

| publisher=D. Reidel

| place=Dordrecht, Holland

| isbn=90-277-0836-3

}} regarding a "New System of Astronomical Constants"{{Citation

| editor-last=Müller | editor-first=Edith A.

| editor2-last=Jappel | editor2-first=A.

| year=1977

| title=Proceedings of the Sixteenth General Assembly Grenoble 1976

| series=Transactions of the International Astronomical Union

| section=Report of Joint Meeting of Commissions 4, 8, 31 on the New System of Astronomical Constants

| volume=16B

| pages=52–67

| url=https://archive.org/details/proceedingsofsix0016inte/page/52/

| publisher=D. Reidel

| place=Dordrecht, Holland

| isbn=90-277-0836-3

}}. Refer to subsection "Recommendations to IAU General Assembly, 1976" on pages 58-61 for specific values. recommended for reduction of astronomical observations, and for computation of ephemerides. It superseded the IAU's previous recommendations of 1964 (see IAU (1964) System of Astronomical Constants), became in effect in the Astronomical Almanac from 1984 onward, and remained in use until the introduction of the IAU (2009) System of Astronomical Constants. In 1994

{{Citation | editor-last=Appenzeller | editor-first=I | contribution=IAU (1994): Proceedings of the 22nd General Assembly, XXII B | series=Transactions of the IAU | year=1994 | publisher=Kluwer Academic | contribution-url=http://www.iau.org/static/resolutions/IAU1994_French.pdf | isbn=0-7923-3842-1 | title=Transactions of the International Astronomical Union: Proceeding of the Twenty-Second General Assembly, the Hague 1994 }}

the IAU recognized that the parameters became outdated, but retained the 1976 set for sake of continuity and also recommended to start maintaining a set of "current best estimates".IAU(1994) ibidem, Resolution No. C 6 This "sub group for numerical standards" had published a list, which included new constants (like those for relativistic time scales).

{{citation|author=Standish, E.M. |contribution=Report of the IAU WGAS Sub-group on Numerical Standards |url=http://iau-comm4.jpl.nasa.gov/iausgnsrpt.pdf |title=Highlights of Astronomy |editor=Appenzeller, I. |location=Dordrecht |publisher=Kluwer |year=1995 |url-status=dead |archive-url=https://web.archive.org/web/20120907165000/http://iau-comm4.jpl.nasa.gov/iausgnsrpt.pdf |archive-date=2012-09-07 }}

The system of constants was prepared

{{cite journal | last=Seidelmann | first=P. Kenneth | title=Numerical values of the constants of the Joint Report of the Working Groups of IAU Commission 4 | journal=Celestial Mechanics | volume=16 | pages=165–177 | date=1977 | issue=2 | doi=10.1007/BF01228598 | url=http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977CeMec..16..165S&link_type=ARTICLE | bibcode=1977CeMec..16..165S| s2cid=123361221 }}

by Commission 4 on ephemerides led by P. Kenneth Seidelmann after whom asteroid 3217 Seidelmann is named.

At the time, a new standard epoch (J2000.0) was accepted; followed later

{{Citation | editor-last=Wayman | editor-first=P. | contribution=IAU (1979): Proceedings of the 17th General Assembly, XVII B | series=Transactions of the IAU | year=1980 | publisher=D.Reidel | place=Dordrecht | contribution-url=http://www.iau.org/static/resolutions/IAU1979_French.pdf | isbn=90-277-1159-3| title=Transactions of the International Astronomical Union, Volume XVIIB }}

{{Citation | editor-last=West | editor-first=R | contribution=IAU (1982): Proceedings of the 18th General Assembly, XVIII B | series=Transactions of the IAU | year=1982 | publisher=D.Reidel | place=Dordrecht | contribution-url=http://www.iau.org/static/resolutions/IAU1982_French.pdf | isbn=0-7923-3842-1 | title=Transactions of the International Astronomical Union: Proceeding of the Twenty-Second General Assembly, the Hague 1994 }}

by a new reference system with fundamental catalogue (FK5), and expressions for precession of the equinoxes,

and in 1979 by new expressions for the relation between Universal Time and sidereal time,IAU(1979) ibidem, recommendation by Commissions 4 (Ephemerides), 8 (Positional Astronomy), 19 (Rotation of the Earth), 31 (Time)

{{cite journal | last=Lederle | first=Trudpert | title=The IAU (1976) System of Astronomical Constants | journal=Mitteilungen des Astronomisches Gesellschaft | volume=48 | pages=59..65 | date=1980 | url=http://articles.adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980MitAG..48...59L&link_type=ARTICLE | bibcode=1980MitAG..48...59L}}

IAU(1982) ibidem, Resolution No. C 5 and in 1979 and 1980 by a theory of nutation.IAU(1979) ibidem, recommendation by Commissions 4 (Ephemerides), 19 (Rotation of the Earth), 31 (Time)IAU(1982) ibidem, Resolution No. R 3 There were no reliable rotation elements for most planets, but a joint working group on Cartographic Coordinates and Rotational Elements was installed to compile recommended values.{{Citation

| editor-last=Müller | editor-first=Edith A.

| editor2-last=Jappel | editor2-first=A.

| year=1977

| title=Proceedings of the Sixteenth General Assembly Grenoble 1976

| series=Transactions of the International Astronomical Union

| section=Commision 4: Ephemerides, Report of Meeting 25 August 1976

| volume=16B

| pages=49–52

| url=https://archive.org/details/proceedingsofsix0016inte/page/49/

| publisher=D. Reidel

| place=Dordrecht, Holland

| isbn=90-277-0836-3

}}. See page 50, specifically.IAU(1979) ibidem, recommendation by Commissions 4 (Ephemerides) and 16 (Physical Study of Planets and Satellites)

Units

The IAU(1976) system is based on the astronomical system of units:

  • The astronomical unit of time is the day (D) of 86,400 SI seconds, which is close to the mean solar day of civil clock time.
  • The astronomical unit of mass is the mass of the Sun (S).
  • The astronomical unit of length is known as the astronomical unit (A or au), which in the IAU(1976) system is defined as the length for which the gravitational constant, more specifically the Gaussian gravitational constant k expressed in the astronomical units (i.e., k2 has units A3S−1D−2), takes the value of {{nowrap|0.017 202 098 95}}. This astronomical unit is approximately the mean distance between the Earth and the Sun. The value of k is the angular velocity in radians per day (i.e. the daily mean motion) of an infinitesimally small mass that moves around the Sun in a circular orbit at a distance of 1 AU.

Table of constants

class="wikitable"
NumberQuantitySymbolValueUnitRelative
uncertainty
Ref.
colspan=7 | Defining Constants
1Gaussian gravitational constantalign=center | k0.017 202 098 95A3/2S−1/2D−1defined
colspan=7 | Primary Constants
2Speed of lightalign=center | c299 792 458 ±1.2m s−14{{e
9}}{{SIbrochure8th|pages=112–13}}.
3light time for unit distancealign=center | τA499.004 782 ±0.000 002s4{{e
9}}
4equatorial radius for Earthalign=center | ae6 378 140 ±5m8{{e
7}}
5dynamical form-factor for Earthalign=center | J2(108 263 ±1){{e
8}}1{{e
5}}
6geocentric gravitational constantalign=center | GE(3 986 005 ±3){{e|+8}}m3s−28{{e
7}}
7constant of gravitationalign=center | G(6 672 ±4.1){{e
14}}m3kg−1s−26.1{{e
4}}CODATA System of Physical Constants of 1973, CODATA Bulletin No. 11 [http://physics.nist.gov/cuu/Archive/1973JPCRD.pdf] {{Webarchive|url=https://web.archive.org/web/20170107070201/http://physics.nist.gov/cuu/Archive/1973JPCRD.pdf |date=2017-01-07 }}
8Earth/Moon mass ratioalign=center | 1/μ81.300 7 ±0.000 34{{e
6}}
Moon/Earth mass ratioalign=center | μ0.012 300 024{{e
6}}
9general precession in longitudealign=center | p5 029.0966 ±0.15" cy−13{{e
5}}
10obliquity of the eclipticalign=center | ε23°26'21.448" ±0.10"1{{e
6}}
11constant of nutation at standard epoch J2000align=center | N9.2055 originally (Seidelmann 1977) listed as 9.2109", derived from Woolard"3{{e
5}}
colspan=7 | Derived Constants
12unit distance (astronomical unit)align=center | A = cτA(149 597 870 ±2){{e|+3}}m1{{e
8}}
13solar parallaxalign=center | π = arcsin(ae/A)8.794 148 ±0.000 007"8{{e
7}}
14constant of aberration for standard epoch J2000align=center | κ20.495 52"
15flattening factor for the Earthalign=center | f0.003 352 81 ±0.000 000 026{{e
6}}
reciprocal flatteningalign=center | 1/f(298 257 ± 1.5){{e
3}}5{{e
6}}
16heliocentric gravitational constantalign=center | GS = A3k2/D2(132 712 438 ±5){{e|+12}}m3s−24{{e
8}}
17Sun/Earth mass ratioalign=center | S/E = GS/GE332 946.0 ± 0.39{{e
7}}
18mass ratio Sun to Earth+Moonalign=center | (S/E)/(1+μ)328 900.5 ±0.51.5{{e
6}}
19mass of the Sunalign=center | S = GS/G(19 891 ±12){{e|+26}}kg6{{e
4}}
20ratios of mass of Sun to planets+satellites1/S
Mercury6 023 600
Venus408 523.5
Earth+Moon328 900.5
Mars3 098 710
Jupiter1 047.355
Saturn3 498.5
Uranus22 869
Neptune19 314
Pluto3 000 000

= Other quantities for use in the preparation of ephemerides =

class="wikitable"
1.colspan=2 | Masses of minor planets
NumberNameMass in solar mass
(1)Ceres(5.9 ±0.3){{e
10}}
(2)Pallas(1.1 ±0.2){{e
10}}
(4)Vesta(1.2 ±0.1){{e
10}}

class="wikitable"
2.colspan=3 | Masses of satellites
PlanetNumberSatelliteSatellite/Planet mass
JupiterIIo(4.70 ±0.06){{e
5}}
IIEuropa(2.56 ±0.06){{e
5}}
IIIGanymedes(7.84 ±0.08){{e
5}}
IVCallisto(5.6 ±0.17){{e
5}}
SaturnusITitan(2.41 ±0.018){{e
4}}
NeptuneITriton2{{e
3}}

class="wikitable"
3.Equatorial radii
ObjectEquatorial radius (km)
Mercury2 439 ±1
Venus6 052 ±6
Earth6 378.140 ±0.005
Mars3 397.2 ±1
Jupiter71 398
Saturn60 000
Uranus25 400
Neptune24 300
Pluto2 500
Moon1 738
Moon's disk, ratio to Earth's equatorial radiusk = 0.272 5076 ae IAU(1982) ibidem, Resolution No. C 10
Sun696 000

class="wikitable"
4.colspan=6 | Gravity fields of the planets
PlanetJ2J3J4C22S22S31
Earth(+108 263 ±1){{e
8}}(−254 ±1){{e
8}}(−161 ±1){{e
8}}
Mars(+1 964 ±6){{e
6}}(+36 ±20){{e
6}}(-55 ±1){{e
6}}(+31 ±2){{e
6}}(+26 ±5){{e
6}}
Jupiter+0.014 75-0.000 58
Saturn+0.016 45-0.0010
Uranus+0.012
Neptune+0.004

class="wikitable"
5.colspan=2 | Gravity field of the Moon
QuantitySymbolValue
average inclination of equator on eclipticI5 552.7"
moment of inertiaC/MR20.392
(C-A)/Bβ0.000 6313
(B-A)/Cγ0.000 2278
C20-0.000 2027
C22+0.000 0223
C30-0.000 006
C31+0.000 029
S31+0.000 004
C32+0.000 0048
S32+0.000 0017
C33+0.000 0018
S33-0.000 001

References

{{Reflist}}