Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.gao.spb.ru/english/as/j2014/presentations/capitaine.pdf Äàòà èçìåíåíèÿ: Tue Oct 21 10:07:11 2014 Äàòà èíäåêñèðîâàíèÿ: Sun Apr 10 05:54:27 2016 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: ð ï ð ï ð ï ð ï ð ï ð ï ð ï ð ï ð ï ð ï ð ï ð ï ð ï ð ï

On the definition and use of the ecliptic in modern astronomy
(1) (2)

Nicole Capitaine
(1) (2)

,

Michael Soffel

: Observatoire de Paris / SYRTE

: Lohrmann Observatory, Dresden Technical University


Introduction
- The ecliptic was a fundamental reference plane for astronomy (astrometry,

solar system dynamics and measurements), from antiquity unto the realization of the FK5 reference system. - The situation has changed considerably with the adoption of the International Celestial Reference system (ICRS) by the IAU since 1998 and the IAU resolutions on reference systems that were adopted between 2000 and 2009. These correspond to major improvements in concepts and realizations of astronomical reference systems, in the use of observational data and the accuracy of the models for the motions of the solar system objects and Earth's rotation. - In that modern context, consistent with GR, the ecliptic is no more a fundamental plane. Although IAU 2006 Resolution B1 clarifies some aspects of the definition of the ecliptic, the concept of an ecliptic is not as clear as those of the ICRS, the intermediate equator, etc.. It is therefore necessary to review in which works such a concept is still required and whether a definition in the GR framework is needed.
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1) The adoption of the ICRS and ICRF

(IAU 1997 Resolution B2)

International Celestial Reference System (ICRS)*: the idealized barycentric coordinate system to which celestial positions are referred. It is kinematically non-rotating with respect to the ensemble of distant extragalactic objects. It has no intrinsic orientation but was aligned close to the mean equator and dynamical equinox of J2000.0 for continuity with previous fundamental reference systems. Its orientation is independent of epoch, ecliptic or equator and is realized by a list of adopted coordinates of extragalactic sources. International Celestial Reference Frame (ICRF)*: a set of extragalactic objects whose adopted positions and uncertainties realize the ICRS axes and give the uncertainties of the axes. It is also the name of the radio catalog whose 212 defining sources is currently the most accurate realization of the ICRS. Successive revisions of the ICRF are intended to minimize rotation from its original orientation. Other realizations of the ICRS have specific names (e.g. Hipparcos Celestial Reference Frame). ICRS and ICRF were adopted by the IAU since 1998 as the replacement of the FK5 system and the fundamental catalogue of stars FK5 (based on the determination of the ecliptic, the equator and the equinox) *: definitions from the IAU 2006 NFA Glossary, http://syrte.obspm.fr/iauWGnfa/
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2) The IAU 2000/2006 definitions and models

IAU 2000 Resolutions
----------------------------------------------Resolution B1.3 Definition of BCRS and GCRS ----------------------------------------------Resolution B1.6 IAU 2000 Precession-Nutation Model ----------------------------------------------Resolution B1.7 Definition of Celestial Intermediate Pole (CIP) Resolution B1.8 Definition and use of CEO and TEO

----------------------------------------------

IAU 2006 Resolutions

----------------------------------------------------------

----------------------------------------------------------

Resolution B1 Adoption of the P03 Precession and definition of the ecliptic

Resolution B2 Harmonization of the names to CIO and TIO

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3) The IAU 2009 Resolutions

Resolution
Adoption of the IAU 2009 System of astronomical constants

Aim
to adopt an improved system of astronomical constants consistent with the current measurement accuracy

Adoption of the 2d realization of the International Celestial Reference Frame

to improve the realization of the ICRF with densification of the frame and a more precise definition of the axes

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The Barycentric and Geocentric celestial reference systems, BCRS and GCRS
IAU 2000 Resolution B1.3: Definition of BCRS and GCRS as coordinate systems in the framework of GR
- a) for Solar System (BCRS) which can be considered to be a global coordinate system

e.g. to be used for planetary ephemerides
- b) for the Earth (GCRS) which can only be considered as a local coordinate system

e.g. to be used for Earth rotation, precession-nutation of the equator
Transformation BCRS/GCRS: extension of the Lorentz transformation (PN approximation) BCRS GCRS TCB TCG

IAU 2006 Resolution B2: Fixing the default orientation of the BCRS
The BCRS orientation is such that for all practical applications, unless otherwise stated, the BCRS is assumed to be oriented according to the ICRS axes.
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The Earth's rotation angle

CIO
kinematical definition of the CIO only dependent on the motion of the CIP geometrical definition of the equinox, , dependent on both the equator (GCRS) and ecliptic (BCRS) motions

ERA: Earth rotation angle ERA = Hour angle from the CIO

replaces

GST: Greenwhich sidereal time GST = Hour angle from the equinox GST = ERA - EO EO: equation of the origins

Not dependent of the precession-nutation model
P of Equator C E d C P of speed of Equator 0 N P 0 ! ! 0 P

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Equatorial coordinates
CIP

New - Right ascension referred to the CIO - Right ascension referred to the ICRS
equinox l CIO ecliptic CIP equator

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Precession-nutation parameters
(1) The equinox based case
Parameters referred to the ecliptic of date, or the ecliptic of epoch: · precession quantities: A, A, ... · nutation quantities: , , ... precession of the equator nutation of the equator

^ Referring to the eclitpic of date mixes precession of the ecliptic precession of the ecliptic and precession of the equator.

(2) The CIO based case
Parameters referred to the GCRS (OX0Y0Z0):
1 date of ecliptic m longitude of origin instantaneous O O GST ecliptic fixed epoch of date of equator + 1 A Q A 1 A !" A z + !" A ' date of equator mean epoch of equator mean 1 + A A + A A A

CIP

· x, y-coordinates of the CIP unit vector: X = sind cosE, Y = sind sinE - provide where the pole is in the sky (the GCRS) - contain precession-nutation-bias + cross terms - The definition of these parameters is independent of ecliptic and equinox.
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(Celestial Intermediate Pole): (E,d) or (X, Y)

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IAU 2009 System of astronomical constants
Replacement of the IAU 1976 system: Improvements in: - the classification of the constants, - the accuracy, and uncertainties of the numerical values, - the consistency with the SI units (TDB/TCB/TT/TCG-compatible values)

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The solar system ephemerides - the GR framework · The post-Newtonian equations of motion for a set of "point-masses" (the Einstein-Infeld-Hoffmann (EIH) equations) are the basis of the 3 state-ofthe-art numerical solar system ephemerides:
­ the American one, DE (Development Ephemeris; JPL), ­ the Russian one, EPM (Ephemerides of Planets and the Moon; IPA, St.Petersburg) and ­ the French one, INPOP (IntÈgrateur NumÈrique PlanÈtaire de l'Observatoire de Paris).

· The EIH equations of motion are integrated numerically for the whole solar system including a set of selected minor planets. · The equations are solved in the BCRS .
Ref: DE430 & DE431 (Folkner et al. 2014); EPM2014: Pitjeva et al. 2014; INPOP13b (Fienga et al. 2014)
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The numerical solar system ephemerides - the current tie to the ICRF 3.3. SOLAR SYSTEM EPHEMERIDES
Table 3.1: Overview over the American (DE) and Russian (EPM) solar-system ephemerides; from Pitjeva (2005).
Ephemerides DE118 (1981) DE200 EPM87 (1987) Interval of integration 1599 - 2169 Reference frame FK4 J2000.0 system FK4 Mathematical model Integration: the Sun, the Moon, nine planets + perturbations from three asteroids (two-body problem) Integration: the Sun, the Moon, nine planets + perturbations from five asteroids (two-body problem) Integration: the Sun, the Moon, nine planets + perturbations from 300 asteroids (mean elements) Integration: the Sun, the Moon, nine planets, five asteroids + perturbations from 295 asteroids (mean elements) Integration: the Sun, the Moon, nine planets + perturbations from 300 (integrated) asteroids Type of observations Optical Radar Spacecraft and landers LLR (lunar laser ranging) Total Optical Radar Spacecraft and landers LLR (lunar laser ranging) Total Optical Radar Spacecraft and landers LLR (lunar laser ranging) Total Optical Radar Spacecraft and landers LLR (lunar laser ranging) Total Optical Radar Spacecraft and landers LLR (lunar laser ranging) Total Number of observations 44755 1307 1408 2954 50424 48709 5344 ­ 1855 55908 26209 1341 1935 9555 39057 ­ 55959 1927 10000 67886 28261 955 1956 11218 42410 Ti m e interval 1911­1979 1964­1977 1971­1980 1970­1980 1911­1980 1717­1980 1961­1986 ­ 1972­1980 1717­1986 1911­1995 1964­1993 1971­1994 1970­1995 1911­1995 ­ 1961­1995 1971­1982 1970­1995 1961­1995 1911­1996 1964­1993 1971­1995 1969­1996 1911­1996

1700 - 2020

DE403 (1995) DE404 EPM98 (1998)

­1410 - 3000 ­3000 - 3000 1886 - 2006

ICRF

DE403

DE405 (1997) DE406

1600 - 2200 ­3000 - 3000

ICRF

57

(from Soffel & Langhans 2013)
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Definition and description of precession-nutation

!"#$%#!&'($)*&*#+$(,-./0(12&"34 5 @2'23*#&'(5+'2 ; 5

The celestial displacement of the CIP

; ?%'#!*#%(!+'2 5"2%233#+$ B9CD12&" !2"#+67((80(999(12&"3 :

8<=80>

32A# &$$)&'($)*&*#+$

Precession of the Earth's equator and precession of the ecliptic

CIP equator: plane perpendicular to the CIP axis has a precession-nutation motion Ecliptic: plane perpendicular to the mean orbital angular momentum vector of the Earth-Moon barycenter in the BCRS has a secular motion (called « precession of the
ecliptic »)

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Precession-nutation equations for a rigid Earth in the celestial reference system
(1) The equinox-based precession-nutation equations
variables: the Euler angles between the equinox and ecliptic of epoch and the ITRS L, M, N: Torque components in the true equator and equinox (CIP,1) Woolard (1953), Bretagnon et al.(1997) F2, G2, H2: 2d order terms (axially symmetric Earth)

(2) The CIO-based precession-nutation equations
variables: the GCRS CIP coordinates L, M, N: Torque components in the celestial intermediate system (CIP, ) (Capitaine et al. 2006) F'', G'': 2d order terms (axially symmetric Earth)

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Polynomial approximations for precession parameters
Almost all precession models are expressed in terms of polynomial developments of all the various precession parameters, which are intended for high-accuracy applications over a time span of a few centuries. In fact, the osculating elements of the Earth-Moon barycenter (EMB) orbit are quasi-periodic functions of the time that can be expressed in the form of Poisson series whose arguments are linear combinations of the mean planetary longitudes (see next slide). The precession of the ecliptic can be defined as the secularly-moving ecliptic pole (i.e. mean EMB orbital angular momentum vector) in a fixed ecliptic frame. The IAU 2006 motion of the shorter ones a ecliptic motion precession of the ecliptic was computed as the part of the ecliptic covering periods longer than 300 centuries, while re presumed to be included in the periodic component of the (VSOP87 + fit to DE406).

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IAU 2006 expressions for precession
(Capitaine et al. 2003) mas mas/cy mas/cy
2

mas/cy3

mas/cy

4

mas/cy5

ecliptic equator
(equinox based quantities)

equator
(CIO based quantities)

A1 x sin

, A1, X1, Y1 : equator rates

Polynomial coefficients for all the precession angles in Hilton et al. (2006)
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Long term expressions for the precession of the ecliptic (Vondrak et al. 2011)

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Equinox: Concepts and definitions

·

equinox: either of the two points at which the ecliptic intersects the celestial equator; also the time at which the Sun passes through either of these intersection points; i.e., when the apparent longitude of the Sun is 0° or 180°. When required, the equinox can be designated by the ephemeris of the Earth from which it is obtained (e.g. vernal equinox of DE 405). By 2100 the equinox will have moved 1.4° from the ICRS meridian, due to the precession of the equinoxes. dynamical mean equinox: the ascending node of the ecliptic on the mean equator. The mean equinox of epoch corresponds to the definition of the ecliptic in its "inertial" sense. It differs by 93.66 mas from the "rotational dynamical mean equinox of J2000.0", which was intended to coincide with the FK5 equinox. *: definitions from the IAU 2006 NFA Glossary, http://syrte.obspm.fr/iauWGnfa/ Mixing BCRS and GCRS should be avoided
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·

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The role of the ecliptic in the modern context
· No ecliptic is needed for the realization of the ICRS · The time-dependent ecliptic is no more needed as reference for the astronomical coordinates · The modern numerical barycentric ephemerides are referred to the ICRF · The modern description of precession-nutation of the equator is the motion of the CIP in the GCRS without reference to the ecliptic . · Numerical integration of precession-nutation does not use an ecliptic · Several semi-analytical Earth's rotation models use the concept of a time dependent ecliptic as a practical intermediate plane. · Precession distinguishes the precession of the ecliptic from the precession of the equator.

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Definition of the ecliptic in GR ?

· In relativity, it is necessary to carefully distinguish between barycentric and geocentric quantities, so the calculation of a moving ecliptic presents a serious problem when it is used in the GCRS. · Due to the loss of the importance of the ecliptic, the definition of the time-dependent ecliptic in GR is not required · If this can convention BCRS by equinox J2 be useful, for continuity to traditional approach, to define a al BCRS fixed ecliptic frame as realized by rotating the a constant rotation according to some mean ecliptic an 000.

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