The following resolutions were adopted by the IAU in 2000 and the IUGG in 2003.

• B1.3 - Definition of the Barycentric Celestial Reference System (BCRS) and the Geocentric Celestial Reference System (GCRS)
• B1.5 - Extended Relativistic framework for time transformation
• B1.6 - IAU 2000 Precession-Nutation Model. The nutation model was designated MHB2000A.
• B1.7 - Definition of Celestial Intermediate Pole (CIP)
• B1.8 - Definition and use of Celestial Ephemeris Origin (CEO) and Terrestrial Ephemeris Origin (TEO)
• B1.9 - Re-definition of Terrestrial Time (TT)

Definition of barycentric celestial reference system (BCRS) and geocentric celestial reference system (GCRS)

The following link provides the IAU 2000 Resolution document that was passed by the General Assembly. This resolution is complex with metric tensor equations and thus is best studied by downloading the document.

Extended relativistic framework for time transformations and realisation of coordinate times in the solar system

The following link provides the IAU 2000 Resolution document that was passed by the General Assembly. This resolution is complex with metric tensor equations and thus is best studied by downloading the document.

IAU 2000 precession-nutation model

The following English version is extracted from the IAU 2000 Resolution document that was passed by the General Assembly.

The IAU Accepts

the conclusions of the IAU-IUGG WG on Non-rigid Earth Nutation Theory published by Dehant et al., 1999, Celest. Mech., 72 (4), 245-310 and the recent comparisons between the various possibilities, and

Recommends

• that, beginning on 1 January 2003, the IAU 1976 Precession Model and IAU 1980 Theory of Nutation, be replaced by the precession-nutation model IAU 2000A (MHB2000 based on the transfer functions of Mathews, Herring and Buffett, 2000 - submitted to the Journal of Geophysical Research) for those who need a model at the 0.2 mas level, or its shorter version IAU 2000B for those who need a model only at the 1 mas level, together with their associated precession and obliquity rates, and their associated celestial pole offsets at J2000.0, to be published in the IERS Conventions 2000, and

Encourages

1. the continuation of theoretical developments of non-rigid Earth nutation series,
2. the continuation of VLBI observations to increase the accuracy of the nutation series and the nutation model, and to monitor the unpredictable free core nutation, and
3. the development of new expressions for precession consistent with the lAU 2000A model.

Definition of Celestial Intermediate Pole

The following English version is extracted from the IAU 2000 Resolution document that was passed by the General Assembly.

The IAU recommends

1. that the Celestial Intermediate Pole (CIP) be the pole, the motion of which is specified in the Geocentric Celestial Reference System (GCRS, see Resolution B1.3) by motion of the Tisserand mean axis of the Earth with periods greater than two days,
2. that the direction of the CIP at J2000.0 be offset from the direction of the pole of the GCRS in a manner consistent with the IAU 2000A (see Resolution B1.6) precession-nutation model,
3. that the motion of the CIP in the GCRS be realised by the IAU 2000 A model for precession and forced nutation for periods greater than two days plus additional time-dependent corrections provided by the International Earth Rotation Service (IERS) through appropriate astro-geodetic observations,
4. that the motion of the CIP in the International Terrestrial Reference System (ITRS) be provided by the IERS through appropriate astro-geodetic observations and models including high-frequency variations,
5. that for highest precision, corrections to the models for the motion of the CIP in the ITRS may be estimated using procedures specified by the IERS, and
6. that implementation of the CIP be on 1 January 2003.

Notes

• The forced nutations with periods less than two days are included in the model for the motion of the CIP in the ITRS.
• The Tisserand mean axis of the Earth corresponds to the mean surface geographic axis, quoted B axis, in Seidelmann, 1982, Celest. Mech., 27, 79-106.
• As a consequence of this resolution, the Celestial Ephemeris Pole is no longer necessary.

Definition and use of celestial and terrestrial ephemeris origins

The following English version is extracted from the IAU 2000 Resolution document that was passed by the General Assembly.

The IAU recommends

1. the use of the non-rotating origin in the Geocentric Celestial Reference System (GCRS) and that this point be designated as the Celestial Ephemeris Origin (CEO) on the equator of the Celestial Intermediate Pole (CIP),
2. the use of the non-rotating origin in the International Terrestrial Reference System (ITRS) and that this point be designated as the Terrestrial Ephemeris Origin (TEO) on the equator of the CIP,
3. that UT1 be linearly proportional to the Earth Rotation Angle defined as the angle measured along the equator of the CIP between the unit vectors directed toward the CEO and the TEO,
4. that the transformation between the ITRS and GCRS be specified by the position of the CIP in the GCRS, the position of the CIP in the ITRS, and the Earth Rotation Angle,
5. that the International Earth Rotation Service (IERS) take steps to implement this by 1 January 2003, and
6. that the IERS will continue to provide users with data and algorithms for the conventional transformations.

Note

• The position of the CEO can be computed from the IAU 2000A model for precession and nutation of the CIP and from the current values of the offset of the CIP from the pole of the ICRF at J2000.0 using the development provided by Capitaine et al. (2000).
• The position of the TEO is only slightly dependent on polar motion and can be extrapolated as done by Capitaine et al. (2000) using the IERS data
• The linear relationship between the Earth's rotation angle θ and UT1 should ensure the continuity in phase and rate of UT1 with the value obtained by the conventional relationship between Greenwich Mean Sidereal Time (GMST) and UT1. This is accomplished by the following relationship :

θ(UT1) = 2 π (0.779057 2732640 + 1.002737 811911 35448 x (Julian UT1 date − 245 1545.0))

References

• Guinot, B., 1979, in D.D. McCarthy and J.D. Pilkington (eds.), Time and the Earth's Rotation, D. Reidel Pub. 7-18.
• Capitaine, N., Guinot, B. and Mc Carthy, D. D., 2000, Astron. Astrophys., 335, 398-405.

Updated IAU 2006 -- Harmonising the name of the pole and origin to intermediate

The first recommendation of the 2006 IAU Resolution B2 re-named both the Celestial Ephemeris Origin (CEO) and Terrestrial Ephemeris Origin (TEO) as the Celestial Intermediate Origin (CIO) and the Terrestrial Intermediate Origin (TIO), respectively.

Re-definition of Terrestrial Time TT

The following English version is extracted from the IAU 2000 Resolution document that was passed by the General Assembly.

The IAU recommends

• that TT be a time scale differing from TCG by a constant rate: dTT/dTCG = 1 − L_G
  where L_G = 6.969 290 134 x 10⁻¹⁰ is a defining constant.

Note L_G was defined by the IAU Resolution A4 (1991) in its Recommendation 4 as equal to U_G / c² where U_G is the geopotential at the geoid. L_G is now used as a defining constant.

IAU 2006 resolutions:

• B1 - Adoption of the P03 Precession Theory and Definition of the Ecliptic
• B2 - Supplement to the IAU 2000 Resolutions on reference systems
  1. Harmonizing intermediate to the pole and the origin
  2. Default orientation of the BCRS/GCRS
• B3 - Re-definition of Dynamical Barycentric Time (TDB)

IUGG 2007 Resolution 2:

• The definition of Geocentric Terrestrial Reference System (GTRS) and International Terrestrial Reference System (ITRS) as a specific GTRS.

Adoption of the P03 Precession Theory and Definition of the Ecliptic

The following is extracted from the English version of the IAU 2006 Resolution document that was passed by the General Assembly.

The IAU Accepts

the conclusions of the IAU Division I Working Group on Precession and the Ecliptic published in Hilton et al. (2006, Celest. Mech. 94, 351), and

Recommends

1. that the terms lunisolar precession and planetary precession be replaced by precession of the equator and precession of the ecliptic, respectively,
2. that, beginning on 1 January 2009, the precession component of the IAU 2000A precession-nutation model be replaced by the P03 precession theory, of Capitaine et al. (2003, A&A, 412, 567-586) for the precession of the equator (Eqs. 37) and the precession of the ecliptic (Eqs. 38); the same paper provides the polynomial developments for the P03 primary angles and a number of derived quantities for use in both the equinox based and CIO based paradigms,
3. that the choice of precession parameters be left to the user, and
4. that the ecliptic pole should be explicitly defined by the mean orbital angular momentum vector of the Earth-Moon barycenter in the Barycentric Celestial Reference System (BCRS), and this definition should be explicitly stated to avoid confusion with other, older definitions.

Notes

1. Formulas for constructing the precession matrix using various parameterizations are given in Eqs. 1, 6, 7, 11, 12 and 22 of Hilton et al. (2006, Celest. Mech., 94, 351). The recommended polynomial developments for the various parameters are given in Table 1 of the same paper, including the P03 expressions set out in expressions (37) to (41) of Capitaine et al. (2003) and Tables 3-5 of Capitaine et al. (2005, A&A, 432, 355).
2. The time rate of change in the dynamical form factor in P03 is dJ2/dt = −0.3001 x 10⁻⁹ century⁻¹.

Supplement to the IAU 2000 Resolutions on reference systems

The following two recommendations are extracted from the English version of the IAU 2006 Resolution document that was passed by the General Assembly.

RECOMMENDATION 1. Harmonizing the name of the pole and origin to intermediate

The IAU recommends

1. that, the designation intermediate be used to describe the moving celestial and terrestrial reference systems defined in the 2000 IAU Resolutions and the various related entities, and
2. that the terminology Celestial Intermediate Origin (CIO) and Terrestrial Intermediate Origin (TIO) be used in place of the previously introduced "Celestial Ephemeris Origin" (CEO) and "Terrestrial Ephemeris Origin" (TEO), and
3. that authors carefully define acronyms used to designate entities of astronomical reference systems to avoid possible confusion.

RECOMMENDATION 2. Default orientation of the Barycentric Celestial Reference System (BCRS) and Geocentric Celestial Reference System (GCRS)

The IAU recommends

• that the BCRS definition is completed with the following: "For all practical applications, unless otherwise stated, the BCRS is assumed to be oriented according to the ICRS axes. The orientation of the GCRS is derived from the ICRS-oriented BCRS."

Re-definition of Barycentric Dynamical Time, TDB

The following is extracted from the English version of the IAU 2006 Resolution document that was passed by the General Assembly.

The IAU recommends

• that, in situations calling for the use of a coordinate time scale that is linearly related to Barycentric Coordinate Time (TCB) and, at the geocenter, remains close to Terrestrial Time (TT) for an extended time span, TDB be defined as the following linear transformation of TCB:

  TDB = TCB − L_B x ( JD_TCB − T₀ ) x 86400 + TDB₀
  where T₀ = 244 3144.5003 725, and L_B = 1.550 519 768 x 10⁻⁸ and TDB₀ = − 6.55 x 10⁻⁵ s are defining constants.

Notes

1. JD_TCB is the TCB Julian date. Its value is T₀ = 244 3144.5003 725 for the event 1977 January 1 00^h 00^m 00^s TAI at the geocenter, and it increases by one for each 86400s of TCB.
2. The fixed value that this definition assigns to L_B is a current estimate of L_C + L_G − L_C x L_G, where L_G is given in IAU Resolution B1.9 (2000) and L_C has been determined (Irwin & Fukushima, 1999, A&A 348, 642) using the JPL ephemeris DE405. When using the JPL Planetary Ephemeris DE405, the defining L_B value effectively eliminates a linear drift between TDB and TT, evaluated at the geocenter. When realizing TCB using other ephemerides, the difference between TDB and TT, evaluated at the geocenter, may include some linear drift, not expected to exceed 1 ns per year.
3. The difference between TDB and TT, evaluated at the surface of the Earth, remains under 2 ms for several millennia around the present epoch.
4. The independent time argument of the JPL ephemeris DE405, which is called T_eph (Standish, A&A, 336, 381, 1998), is for practical purposes the same as TDB defined in this Resolution.
5. The constant term TDB₀ is chosen to provide reasonable consistency with the widely used TDB − TT formula of Fairhead & Bretagnon (A&A 229, 240, 1990). n.b. The presence of TDB₀ means that TDB is not synchronized with TT, TCG and TCB at 1977 Jan 1.0 TAI at the geocenter.
6. For solar system ephemerides development the use of TCB is encouraged.

Geocentric and International Terrestrial Reference Systems (GTRS and ITRS)

The following is extracted from the IUGG 2007 Resolution document.

The International Union of Geodesy and Geophysics (IUGG)

Endorses

1. The definition of a Geocentric Terrestrial Reference System (GTRS) in agreement with the 2000 IAU resolution B1.3,
2. the definition of the International Terrestrial Reference System (ITRS) as the specific GTRS for which the orientation is operationally maintained in continuity with past international agreements (BIH orientation), and

Adopts

• the ITRS as preferred GTRS for scientific and technical applications, and

Urges

• Other communities such as geo-spatial information and navigation communities to do the same.

IAU 2009 resolutions:

• B2 - Adoption of the IAU 2009 System of Astronomical Constants
• B3 - Adoption of the Second Realization of the International Celestial Reference Frame, ICRF2

IAU 2009 Astronomical Constants

The following is extracted from the English version of the IAU 2009 Resolution document that was passed by the General Assembly.

The IAU recommends

1. that the list of previously published constants compiled in the report of the Working Group on Numerical Standards of Fundamental Astronomy (NSFA) be adopted as the IAU 2009 System of Astronomical Constants.
2. that Current Best Estimates of Astronomical Constants be permanently maintained as an electronic document,
3. that, in order to ensure the integrity of the CBEs, IAU Division I (now Division A) develop a formal procedure to adopt new values and archive older versions of the CBEs, and
4. that the IAU establish within IAU Division I (now Division A) a permanent body to maintain the CBEs for fundamental astronomy.

These recommends have been enhanced by adding the links to the web pages that have been developed by the permanent body designated in item 4 above, the IAU Functional Working Group for Numerical Standards for Fundamental Astronomy (NSFA).

The Second Realization of the International Celestial Reference Frame (ICRF2)

The following is extracted from the English version of the IAU 2009 Resolution document that was passed by the General Assembly.

The IAU resolves

1. that from 01 January 2010 the fundamental astrometric realization of the International Celestial Reference System (ICRS) shall be the Second Realization of the International Celestial Reference Frame (ICRF2) as constructed by the IERS/IVS working group on the ICRF in conjunction with the IAU Division I (now Division A) Working Group on the Second Realization of the International Celestial Reference Frame (see note 1),
2. that the organizations responsible for astrometric and geodetic VLBI observing programs (e.g. IERS, IVS) take appropriate measures to continue existing and develop improved VLBI observing and analysis programs to both maintain and improve ICRF2,
3. that the IERS, together with other relevant organizations continue efforts to improve and densify high accuracy reference frames defined at other wavelengths and continue to improve ties between these reference frames and ICRF2.

Note 1: The Second Realization of the International Celestial Reference Frame by Very Long Baseline Interferometry, Presented on behalf of the IERS / IVS Working Group, Alan Fey, David Gordon and Christopher S. Jacobs (eds.). IERS Technical Note 35 Frankfurt am Main: Verlag des Bundesamts für Kartographie und Geodäsie, 2009.

The Re-definition of the astronomical unit of length (au)

The following is extracted from the English version of the IAU 2012 Resolution document that was passed by the General Assembly.

The IAU recommends

1. that the astronomical unit be re-defined to be a conventional unit of length equal to
   149 597 870 700 m exactly, in agreement with the value adopted in IAU 2009 Resolution B2,
2. that this definition of the astronomical unit be used with all time scales such as TCB, TDB, TCG, TT, etc.,
3. that the Gaussian gravitational constant k be deleted from the system of astronomical constants,
4. that the value of the solar mass parameter, GM_S, be determined observationally in SI units, and
5. that the unique symbol "au" be used for the astronomical unit.

Details about constants, and the astronomical unit in particular, is given by the IAU WG for Numerical Standards for Fundamental Astronomy (NSFA) and is listed in Table 6 of the SI Brochure: The International System of Units (SI) (8th edition, updated 2014).