Patrick T. Wallace

Expressions for IAU 2000 precession quantities

A new precession-nutation model for the Celestial Intermediate Pole (CIP) was adopted by the IAU in 2000 (Resolution B1.6). The model, designated IAU 2000A, includes a nutation series for a non-rigid Earth and corrections for the precession rates in longitude and obliquity. The model also specifies numerical values for the pole osets at J2000.0 between the mean equatorial frame and the Geocentric Celestial Reference System (GCRS). In this paper, we discuss precession models consistent with IAU 2000A precession-nutation (i.e. MHB 2000, provided by Mathews et al. 2002) and we provide a range of expressions that implement them. The final precession model, designated P03, is a possible replacement for the precession com- ponent of IAU 2000A, oering improved dynamical consistency and a better basis for future improvement. As a preliminary step, we present our expressions for the currently used precession quantities A;A; zA, in agreement with the MHB corrections to the precession rates, that appear in the IERS Conventions 2000. We then discuss a more sophisticated method for improving the precession model of the equator in order that it be compliant with the IAU 2000A model. In contrast to the first method, which is based on corrections to the t terms of the developments for the precession quantities in longitude and obliquity, this method also uses corrections to their higher degree terms. It is essential that this be used in conjunction with an improved model for the ecliptic precession, which is expected, given the known discrepancies in the IAU 1976 expressions, to contribute in a significant way to these higher degree terms. With this aim in view, we have developed new expressions for the motion of the ecliptic with respect to the fixed ecliptic using the developments from Simon et al. (1994) and Williams (1994) and with improved constants fitted to the most recent numerical planetary ephemerides. We have then used these new expressions for the ecliptic together with the MHB corrections to precession rates to solve the precession equations for providing new solution for the precession of the equator that is dynamically consistent and compliant with IAU 2000. A number of perturbing eects have first been removed from the MHB estimates in order to get the physical quantities needed in the equations as integration constants. The equations have then been solved in a similar way to Lieske et al. (1977) and Williams (1994), based on similar theoretical expressions for the contributions to precession rates, revised by using MHB values. Once improved expressions have been obtained for the precession of the ecliptic and the equator, we discuss the most suitable precession quantities to be considered in order to be based on the minimum number of variables and to be the best adapted to the most recent models and observations. Finally we provide developments for these quantities, denoted the P03 solution, including a revised Sidereal Time expression.

Considerations concerning the non-rigid Earth nutation theory.

This paper presents the reflections of the Working Group of which the tasks were to examine the non-rigid Earth nutation theory. To this aim, six different levels have been identified: Level 1 concerns the input model (giving profiles of the Earths density and theological properties) for the calculation of the Earths transfer function of Level 2; Level 2 concerns the integration inside the Earth in order to obtain the Earths transfer function for the nutations at different frequencies; Level 3 concerns the rigid Earth nutations; Level 4 examines the convolution (products in the frequency domain) between the Earths nutation transfer function obtained in Level 2, and the rigid Earth nutation (obtained in Level 3). This is for an Earth without ocean and atmosphere; Level 5 concerns the effects of the atmosphere and the oceans on the precession, obliquity rate, and nutations; Level 6 concerns the comparison with the VLBI observations, of the theoretical results obtained in Level 4, corrected for the effects obtained in Level 5.Each level is discussed at the state of the art of the developments.

Evaluation of the ALMA Prototype Antennas

ABSTRACT The ALMA (Atacama Large Millimeter Array) North American and European prototype antennas have been evaluated by a variety of measurement systems to quantify the major performance specifications. Near‐field holography was used to set the reflector surfaces to 17 μm rms. Pointing and fast‐switching performance was determined with an optical telescope and by millimeter‐wavelength radiometry, yielding 2 \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage[OT2,OT1]{fontenc} \newcommand\cyr{ \renewcommand\rmdefault{wncyr} \renewcommand\sfdefault{wncyss} \renewcommand\encodingdefault{OT2} \normalfont \selectfont} \DeclareTextFontCommand{\textcyr}{\cyr} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \landscape

Improvement of the IAU 2000 precession model

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Expressions for the Celestial Intermediate Pole and Celestial Ephemeris Origin consistent with the IAU 2000A precession-nutation model

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Learning from 25 years of the extensible N-Dimensional Data Format ☆

The IAU 2000 precession consists of the IAU 1976 ecliptic precession (Lieske et al. 1977, AA the model is recalled in Tables 3−5. Due to the strong dependence of the precession expressions on the precession rates and of the precession in longitude (or equivalently the celestial CIP X coordinate) on the J2 rate model, we also provide a parameterized P04 solution for these quantities as functions of those parameters. The expressions include the quantities to be used in both the equinox-based and CIO-based (i.e. referred to the Celestial Intermediate Origin) transformations.

Comparison between high precision precession models for the ecliptic and the equator

Expressions for the position of the Celestial Intermediate Pole (CIP) and the Celestial Ephemeris Origin (CEO) in the Geocentric Celestial Reference System (GCRS) have been computed using the IAU 2000A precession-nutation ? .T hese expressions are for use in the new transformation between the GCRS and the International Terrestrial Reference System (ITRS) which is recommended by IAU Resolution B1.8. Various comparisons and numerical checks have been performed between the classical and the new transformations based on the IAU 2000A precession-nutation. These comparisons revealed necessary improvements to be applied to the classical form of the transformation in order to achieve the required level of accuracy. Once these improvements are applied, the consistency between the positions of the CIP in the GCRS corresponding to the classical and the new transformations is at a level of a few microarcseconds after one century. This work has demonstrated that the new method, in addition to providing an explicit separation between precession-nutation of the equator from Earth rotation, is more simple, compact and direct than the classical one, achieving accuracies at the level of a few microarcseconds with greatly reduced scope for accidental misuse. The resulting expressions for X, Y and s have been included in the IERS Conventions 2000. References for the numerical expressions are provided in Appendix C.

New precession expressions, valid for long time intervals

The extensible N-Dimensional Data Format (NDF) was designed and developed in the late 1980s to provide a data model suitable for use in a variety of astronomy data processing applications supported by the UK Starlink Project. Starlink applications were used extensively, primarily in the UK astronomical community, and form the basis of a number of advanced data reduction pipelines today. This paper provides an overview of the historical drivers for the development of NDF and the lessons learned from using a defined hierarchical data model for many years in data reduction software, data pipelines and in data acquisition systems.

Atmospheric Refractive Electromagnetic Wave Bending and Propagation Delay

Three independent high precision solutions for precession were published in 2003 that provide expressions consistent with the IAU 2000A precession-nutation model (Mathews et al. 2002) and offer a possible replacement for the precession component of IAU 2000A, with improved dynamical consistency and a better basis for future improvement. Each is based upon an improved model for the precession of the ecliptic and, with respect to the IAU 1976 precession, they all provide higher- degree terms in the polynomials for the precession angles of the equator. This paper compares the expressions for the basic parameters of the above solutions for precession both of the ecliptic and the equator and investigates the possible physical and computational reasons for their differences. This leads to a realistic evaluation of the accuracy of the solutions and provides estimated deficiencies in them. These studies have identified expressions for the ecliptic precession quantities that are accurate to about 0.05 mas/cy over a two-millennium interval centered on J2000 instead of the few mas/cy accuracy of the current IAU model. They have also provided the theoretical and experimental basis for future improvements in the precession of the equator.

Proposed terminology in fundamental astronomy based on IAU 2000 resolutions

Context. The present IAU model of precession, like its predecessors, is given as a set of polynomial approximations of various precession parameters intended for high-accuracy applications over a limited time span. Earlier comparisons with numerical integrations have shown that this model is valid only for a few centuries around the basic epoch, J2000.0, while for more distant epochs it rapidly diverges from the numerical solution. In our preceding studies we also obtained preliminary developments for the precessional contribution to the motion of the equator: coordinates X,Y of the precessing pole and precession parameters ψA ,ω A, suitable for use over long time intervals. Aims. The goal of the present paper is to obtain upgraded developments for various sets of precession angles that would fit modern observations near J2000.0 and at the same time fit numerical integration of the motions of solar system bodies on scales of several thousand centuries. Methods. We used the IAU 2006 solutions to represent the precession of the ecliptic and of the equator close to J2000.0 and, for more distant epochs, a numerical integration using the Mercury 6 package and solutions by Laskar et al. (1993, A&A, 270, 522) with upgraded initial conditions and constants to represent the ecliptic, and general precession and obliquity, respectively. From them, different precession parameters were calculated in the interval ±200 millennia from J2000.0, and analytical expressions are found that provide a good fit for the whole interval. Results. Series for the various precessional parameters, comprising a cubic polynomial plus from 8 to 14 periodic terms, are derived that allow precession to be computed with an accuracy comparable to IAU 2006 around the central epoch J2000.0, a few arcseconds throughout the historical period, and a few tenths of a degree at the ends of the ±200 millennia time span. Computer algorithms are provided that compute the ecliptic and mean equator poles and the precession matrix. Precession models are designed for two different phenomena: the precession of the ecliptic due to planetary perturbations and the precession of the equator due to the luni-solar and planetary torques on the oblate Earth. In both cases, precession represents the secular part of the motion. The term “secular” will be used throughout the paper to designate quasi periodic motions with very long periods. The motion of the Celestial Intermediate Pole (CIP), or equivalently of the equator of the CIP, with respect to the Geocentric Celestial Reference System (GCRS), is composed of precession and nutation, which are differentiated by a convention. Here we define the precession of the equator as that part of the motion of the equator that covers periods longer than 100 centuries, while terms of shorter periods are presumed to be