International Astronomical Union
Standards Of Fundamental Astronomy
SOFA Tools for Earth Attitude
Software version 10
Document revision 1.4
http://www.iausofa.org/
2014 March 21
MEMBERS OF THE IAU SOFA BOARD
John Bangert United States Naval Observatory
Wim Brouw University of Groningen
Mark Calabretta Australia Telescope National Facility
Anne-Marie Gontier Paris Observatory
Catherine Hohenkerk Her Majesty’s Nautical Almanac Office
Wen-Jing Jin Shanghai Observatory
Zinovy Malkin Inst. Appl. Astron., St Petersburg
Dennis McCarthy United States Naval Observatory
Jeffrey Percival University of Wisconsin
Patrick Wallace Rutherford Appleton Laboratory
c
Copyright 2007-9 International Astronomical Union. All
Rights Reserved. Reproduction, adaptation, or translation
without prior written permission is prohibited, except as al-
lowed under the copyright laws.
CONTENTS iii
Contents
1 INTRODUCTION 1
1.1 The SOFA software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Quick start . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 CELESTIAL COORDINATES 3
2.1 Stellar directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Precession-nutation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.3 Evolution of celestial reference systems . . . . . . . . . . . . . . . . . . . . . . . . 4
2.4 The IAU 2000 changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.5 Frame bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.6 CIO and TIO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.7 Equation of the origins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.8 Equinox versus CIO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.9 The celestial to terrestrial transformation . . . . . . . . . . . . . . . . . . . . . . 9
3 SOFA EARTH ATTITUDE MODELS 10
3.1 Classical precession . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2 Classical nutation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.3 The CIP X, Y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.4 The CIO locator, s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.5 Polar motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.6 Earth rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.7 Fundamental arguments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.8 Supporting routines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4 CURRENT MODELS 15
4.1 Canonical basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.2 SOFA routines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
5 EXAMPLES 17
5.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
5.2 IAU 1976/1980/1982/1994, equinox based . . . . . . . . . . . . . . . . . . . . . . 20
5.3 IAU 2000A, CIO based, using classical angles . . . . . . . . . . . . . . . . . . . . 21
5.4 IAU 2000A, equinox based, using classical angles . . . . . . . . . . . . . . . . . . 23
5.5 IAU 2006/2000A, CIO based, using classical angles . . . . . . . . . . . . . . . . . 24
5.6 IAU 2006/2000A, CIO based, using X, Y series . . . . . . . . . . . . . . . . . . . 26
6 FURTHER READING 27
APPENDIX
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1
1 INTRODUCTION
1.1 The SOFA software
SOFA stands for Standards Of Fundamental Astronomy. The SOFA software is a collection of
Fortran 77 and C subroutines that implement official IAU algorithms for fundamental-astronomy
computations. At the present time the SOFA subprograms comprise 131 “astronomy” routines
supported by 55 “vector/matrix” routines.
The basic documentation for the SOFA collection is terse, consisting of (i) detailed preamble
comments in the individual routines and (ii) classified and alphabetic lists of subroutine calls. For
an important subset of the SOFA routines, namely those concerned with the Earth’s orientation
and rotation, the present paper supplements the basic documentation with descriptive material
and cookbook examples.
1.2 Quick start
Expert readers may wish to start with Examples, Section 5. Anyone already familiar with the
elementary concepts can safely omit the introductory material in Section 2. Those interested
in only the latest models can also omit Section 3, which has a large historical component, and
start with Current Models, Section 4.
1.3 Abbreviations
BCRS Barycentric Celestial Reference System
CIO Celestial Intermediate Origin
CIP Celestial Intermediate Pole
CIRS Celestial Intermediate Reference System
EE equation of the equinoxes
EMB Earth-Moon barycenter
EO equation of the origins
FK4 fourth fundamental catalog
FK5 fifth fundamental catalog
GCRS Geocentric Celestial Reference System
GMST Greenwich mean sidereal time
GST Greenwich (apparent) sidereal time
IAU International Astronomical Union
ICRS International Celestial Reference System
IERS International Earth rotation and reference systems service
ITRS International Terrestrial Reference System
J2000.0 2000 January 1.5 (in some specified time scale)
NPB nutation, precession and frame bias
SOFA Standards of Fundamental Astronomy
ST sidereal time
