Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.atnf.csiro.au/iau-comm31/pdf/2009_IAUGA_JD6/JD06_capitaine_wallace.pdf Дата изменения: Fri Aug 6 03:06:19 2010 Дата индексирования: Mon Feb 4 09:58:26 2013 Кодировка: Поисковые слова: retrograde motion

Implementation of the IAU 2000 definition of UT1 in astronomy
N. Capitaine, P. Wallace
SYRTE, Observatoire de Paris, STFC/RAL

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Outline

Review of the:
-

concepts, definitions and nomenclature associated with the IAU 2000 definition of the ERA conventional numerical values associated with the IAU 2000 definition of UT1 IAU 2006 expressions for the position of the celestial intermediate origin and the equation of the origins CIO and equinox-based procedures for transforming between celestial and terrestrial coordinates (SOFA and IERS implementation)

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IAU 2000/2006 and IUGG 2003/2007 resolutions regarding Earth's rotation
1) Definition of the celestial and terrestrial coordinate systems in the framework of GR IAU 2000 Resolution B1.3 Definition of BCRS and GCRS IUGG 2007 Resolution 2 Definition of GTRS and ITRS

2) Adoption of precession-nutation model with a microarcsecond precision IAU 2000 Resolution B1.6 IAU 2000 Precession-Nutation Model IAU 2006 Resolution B1 Adoption of the P03 Precession and
definition of the ecliptic

3) Realization of the pole with microarcsecond accuracy IAU 2000 Resolution B1.7 Definition of Celestial Intermediate Pole 4) Definition of the ERA and UT1 for an accurate estimation of the EOPs IAU 2000 Resolution B1.8 IAU 2006 Resolution B2, Rec 1 Definition and use of CEO and TEO

Harmonizing « intermediate » to the pole and the origin Celestial/Terrestrial intermediate origin: CIO, TIO

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The Earth Rotation Angle (ERA) and the IAU 2000 conventional definition of UT1 (IAU 2000 Resolution B1.8)
· ·

The Earth Rotation Angle (ERA) is the angle between the CIO and the TIO The conventional linear relationship that defines UT1 from ERA is : ERA (UT1) = 2 [ 0.7790572732640 + 1.00273781191135448 x (Julian UT1date - 2451545.0) ] This expression from (Capitaine, Guinot, McCarthy, 2000) was derived from (i) the GMST1982(UT1) expression based on the IAU 1976 precession and (ii) the expression for the GCRS position of the CIO 0.7790572732640 and 1.00273781191135448 rev/day are defining constants
(conventional values) which have replaced the factor between GMST and UT1

·

(The ERA/UT1 relationship involves not only the Earth angular velocity but also what UT1 is intended to represent, i.e. the hour angle of the « fictitious mean » Sun)

JD06, IAU GA 2009, Rio de Janeiro, Brazil, August 2009


concepts

The Earth rotation angle
ecliptic J2000

J2000 equinox: 0

+



A

+

A



0

90°+E

(TIO)
d

CIP equator

equinox at t:

A

A

A+ A

s



1

EO

CIO

ERA

TIO

GCRS equator

ERA: Earth rotation angle = hour angle of the CIO from the TIO meridian

GST: Greenwich sidereal time= hour angle of the equinox from the TIO meridian GST = ERA - EO EO: equation of the origins: distance from the CIO to the equinox s: CIO locator
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Concepts associated with the IAU 2000 resolutions
concept of the NRO
C0
E

equinox versus the NRO
ecliptic

d

PC

P0
Equator of P

Equator

N



0



of
0

equator equator at t
equator at t

at t
2

1

1 2

1

2 3

P

0

3 3

speed of

kinematical definition of the NRO , dependent on the CIP (i.e. equator) motion CIO: celestial intermediate origin : NRO in the GCRS TIO: terrestrial intermediate origin : NRO in the ITRS

geometrical definition of the equinox, , dependent on both the equator and ecliptic motions Complexities: - definition of the ecliptic in the GCRS - definition of the mean equinox

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ERA based expression for Greenwich sidereal time
GST : ERA (UT1)
+ accumulated precession in RA (in TT) + scross (GMST)
x nutation

+ accumulated nutation in RA (in TT) + precession x nutation (in TT) (kinematical equation of equinoxes)

(GST= GMST (UT1, TT) + "equation of the equinoxes")

= ERA (UT1) - EO

EO can also be derived from the expression for s (from Wallace & Capitaine 2006):

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nomenclature

IAU 2000/2006 Nomenclature

The Nomenclature in Fundamental Astronomy IAU WG provided an IAU 2006 Glossary including a set of detailed definitions (compliant with GR) that best explain all the terms required for implementing the IAU 2000 and 2006 resolutions

http://syrte.obspm.fr/iauWGnfa/NFA_Glossary.html
Barycentric Celestial Reference System (BCRS) Barycentric Dynamical Time (TDB) Celestial Intermediate Origin (CIO) Celestial Intermediate Reference System (CIRS) CIO locator CIO right ascension and declination epoch equation of the origins (EO) equinox right ascension Geocentric Celestial Reference System (GCRS) Geocentric Terrestrial Reference System (GTRS) ICRS place intermediate equator intermediate place intermediate right ascension and declination International Celestial Reference Frame (ICRF) International Celestial Reference System (ICRS) International Terrestrial Reference Frame (ITRF) International Terrestrial Reference System (ITRS) Julian century Julian date Julian year right ascension Teph Terrestrial Intermediate Origin (TIO) Terrestrial Intermediate Reference System (TIRS) Terrestrial Time (TT) TIO locator

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The IAU 2006 NFA Glossary a few examples of newly proposed terms
http://syrte.obspm.fr/iauWGnfa/NFA_Glossary.html

non-rotating origin: in the context of the GCRS or the ITRS, the point on the intermediate equator such that its instantaneous motion with respect to the system (GCRS or ITRS as appropriate) has no component along the intermediate equator (i.e. its instantaneous motion is perpendicular to the intermediate equator). It is called the CIO and TIO in the GCRS and ITRS, respectively. Earth Rotation Angle (ERA): angle measured along the intermediate equator of the Celestial Intermediate Pole (CIP) between the Terrestrial Intermediate Origin (TIO) and the Celestial Intermediate Origin (CIO), positively in the retrograde direction. It is related to UT1 by a conventionally adopted expression in which ERA is a linear function of UT1 (see IAU 2000 Resolution B1.8). Its time derivative is the Earth's angular velocity. Previously, it has been referred to as the stellar angle.

Celestial Intermediate Origin (CIO): origin for right ascension on the intermediate equator in the celestial intermediate reference system. It is the non-rotating origin in the GCRS that is recommended by the IAU 2000 Resolution B 1.8, where it was designated the Celestial Ephemeris Origin. The CIO was originally set close to the GCRS meridian and throughout 1900-2100 stays within 0.1 arcseconds of this alignment. Terrestrial Intermediate Origin (TIO): origin of longitude in the Intermediate Terrestrial Reference System. It is the nonrotating origin in the ITRS that is recommended by the IAU 2000 Resolution B1.8, where it was designated Terrestrial Ephemeris Origin. The name Terrestrial Intermediate Origin was adopted by IAU 2006 Resolution B2. The TIO was originally set at the ITRF origin of longitude and throughout 1900-2100 stays within 0.1 mas of the ITRF prime meridian.
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The IAU 2006 NFA Glossary a few examples of newly proposed terms
http://syrte.obspm.fr/iauWGnfa/NFA_Glossary.html
CIO locator (denoted s) : the difference between the GCRS right ascension and the intermediate right ascension of the intersection of the GCRS and intermediate equators. The CIO was originally set close to the mean equinox at J2000.0. As a consequence of precession-nutation the CIO moves according to the kinematical property of the non-rotating origin. The CIO is currently located by using the quantity s. TIO locator (denoted s): the difference between the ITRS longitude and the instantaneous longitude of the intersection of the ITRS and intermediate equators. The TIO was originally set at the ITRF origin of longitude. As a consequence of polar motion the TIO moves according to the kinematical property of the non-rotating origin. The TIO is currently located using the quantity s, whose rate is of the order of 50 mas/cy which is due to the current polar motion.

equation of the origins: distance between the CIO and the equinox along the intermediate equator; it is the CIO right ascension of the equinox; alternatively the difference between the Earth rotation angle and Greenwich apparent sidereal time (ERA ­ GAST).

Greenwich mean sidereal time (GMST): Greenwich hour angle of the mean equinox defined by a conventional relationship to Earth rotation angle or equivalently to UT1.

Greenwich sidereal time (GST): Greenwich apparent sidereal time (GAST), the hour angle of the true equinox from the Terrestrial Intermediate Origin (TIO) meridian (Greenwich or International meridian).

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expressions

IAU 2000/2006 expressions for the fundamental precession parameters
(Capitaine, Wallace, Chapront, 2003)
mas mas/cy mas/cy2 mas/cy3 mas/cy4 mas/cy5

Ecliptic

Equator

CIO based precession quantities
GMST(IAU2000) GMST(P03) 14.506 ERA+4612157.399 1396.6784 - 0. 09344 0.0188

14.506 ERA+4612156.534 1391.5817 - 0.00044 0.029956 -0.0000368 expression dependent on the precession-nutation model

(P03 = IAU 2006)
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IAU 2000 expression for the CIO locator
(Capitaine, Wallace, McCarthy, 2003; IERS Conventions 2003, Ch 5)

and IAU 2006 update
(Capitaine, Wallace, Chapront 2003; IERS Conventions, Ch 5, revised 2009)

largest change w.r.t. the IAU 2000 expression

< 3 µas

JD06, IAU GA 2009, Rio de Janeiro, Brazil, August 2009

1 unit : microarcsecon2d


IAU 2000 expression for GMST
(Capitaine, Wallace, McCarthy, 2003; IERS Conventions 2003, Ch 5)

Greenwich sidereal time: GST= GMST (UT1, TT) + "equation of the equinoxes" = ERA (UT1) - "equation of the origins" (i.e. accumulated precession/nutation in RA)

- using IAU 2000 A precession-nutation model - such that there is equivalence between CIO-based and equinox-based z-rotation : link between s(t) and the equation of the equinoxes EE2000 - such that there is continuity in UT1 on 01/01/2003 0h TT with the previous relationship GMST1982(UT1) and current UT1 estimate

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Differences in UT1
over 2 centuries around J2000 period 1980-2020

unit µs

post-2003 minus pre-2003 procedures (quadratic term: due to the precession rate in obliquity; secular term: due to the variation in TT - UT1)

equinox based VLBI reductions w.r.t CIO-based (due to the incompleteness of the IAU 1994 expression for the equation of equinoxes)
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IAU 2006 expression for the equation of the origins
(Capitaine, Wallace, Chapront, 2003; IERS Conventions, Ch 5, revised 2009)

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transformation

Transformation from ICRS to observed places of stars
ICRS , etc.
space motion annual parallax light deflection annual aberration

ICRS BCRS GCRS
frame bias

barycentric

TCB, TDB

GCRS

geocentric

TCG, TT

precession nutation

GCRS position CIP,CIO

true equinox and equator of date
Greenwich Mean Sidereal Time

Celestial Intermediate Reference System (CIRS)
Earth Rotation Angle ERA

equation of the equinoxes

Terrestrial Intermediate Reference System (TIRS) ITRS

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Forming the celestial to terrestrial matrix transformation based on the IAU 2006 precession

GCRS

RTIRS

vCIO = R 3(ERA) в vCIP в vCIO vCIP

vequinox = R 3(GST) в vCIP в vequinox vCIP
= ERA - EO



Capitaine N., Wallace P.T., (2006, A&A 450, 855-872) "High precision methods for locating the celestial intermediate pole and origin" Wallace P.T., Capitaine N., (2006, A&A 459, 981-985 ) "Precession-nutation procedures consistent with IAU 2006 resolutions"

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Software routines IAU 2000A/2006

to implement the transformations

(Wallace 2008; IERS Conventions, Ch 5, revised 2009)

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angle/time

Complexities of UT1 being considered both as an angle and a time scale
Universal Time (UT): a measure of time that conforms, within a close approximation, to the mean diurnal motion of the Sun and serves as the basis of all civil timekeeping. The term "UT" is used to designate a member of the family of Universal Time scales (e.g. UTC, UT1). Universal Time (UT1): angle of the Earth's rotation about the CIP axis defined by its conventional linear relation to the Earth rotation angle (ERA). It is related to Greenwich apparent sidereal time through the ERA (see equation of the origins). It is determined by observations (currently from VLBI observations of the diurnal motions of distant radio sources). UT1 can be regarded as a time determined by the rotation of the Earth. It can be obtained from the uniform time scale UTC by using the quantity UT1 - UTC, which is provided by the IERS. UT1 ­ UTC: difference between the UT1 parameter derived from observation and the uniform time scale UTC, the latter being currently defined as: UTC = TAI + n, where n is an integer number of seconds, such that |UT1 - UTC| < 0.9 s. (cf. IAU 2006 NFA Glossary)

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GMST expressions in seconds

ERA (UT1) = 2 [0.7790572732640 + 1.00273781191135448 x (Julian UT1date - 2451545.0)]

with 1 s = 15 `'

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