Jan Vondrak

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.

New precession expressions, valid for long time intervals

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

Earth Orientation Parameters — Combination of Results Obtained by Different Techniques

The recently developed method of ‘combined smoothing’ is shortly introduced and its main philosophy presented. The method is tested with simulated data in order to demonstrate that the method is capable of removing both long-term and stepwise systematic errors in time derivatives of certain Earth Orientation Parameters measured by satellite methods.

Common 22-year cycles of Earth rotation and solar activity

Astronomical Institute, Academy of Sciences of Czech RepublicBoˇcn´i II, 141 31 Prague, Czech Republicemail: vondrak@ig.cas.cz, ron@ig.cas.czAbstract.The 22-year oscillations of the Earth rotation due to several geophysical processesin the core-mantle system, oceans, atmosphere and geomagnetic field are excited mainly by 22-year cycles of the solar activity. These geophysical processes produce their own oscillations ofthe Earth rotation with different periods around 22 years. The direct and indirect influence ofthe solar activity on 22-year cycles of the Earth rotation are separated from the core effects andcorresponding amplitudes are estimated by means of two approaches. The first, direct approachuses extended time series of Wolf’s numbers with22-year cycles, determined by sign alternationof even sunspot cycles. A linear regression between 22-year cycles of UT1 and solar activityis determined and this regression model is used to calculate the UT1 response to the 22-yearcycles of the solar activity. The second, indirect approach uses 22-year oscillation of the mean sealevel, caused by water evaporation due to variations of the total solar irradiance. The influenceof the mean sea level variations on the Earth rotation is calculated by means of an empiricalmodel of global water redistribution. The core-mantle effects on the 22-year UT1 variations aredetermined by excluding the UT1 response to the solar activity and core angular momentumdue to the geomagnetic field variations, according to the solutions from the Special Bureau oftheCore(SBC).Keywords.Sun: activity, sunspots, solar-terrestrial relations, time

Precession-Nutation Estimates from Optical Astrometry 1899.7–1992.0 and Comparison with VLBI Results

Abstract : The most recent solution of Earth Orientation Parameters (EOP) from the observations made by optical astrometry from 1899.7 to 1992.0 at 33 observatories is used to estimate the corrections of the present International Astronomical Union (IAU) model of precession-nutation. Since the resolution of the solution is about 5 days, only the terms with periods of 14 days and longer are considered. The results are compared with Very Long Baseline Interferometry-based corrections of the standard precession-nutation model, and the differences are discussed.

New solution of Earth Orientation Parameters in 20th century

We present a new solution of Earth Orientation Parameters, based on optical astrometry and catalog EOC-4.

Commission 19: Rotation of the Earth

The activities in scientific research related to Commission 19 are mostly developed in the different institutions that have sent their reports here enclosed, in the different meetings that have been organized in related themes, and in the WGs of the Division 1. An important additional activity has been developed in the frame of precession and nutation. This research has been initiated by the Descartes Prize received by the Nutation Consortium in 2003. 1. Terms of Reference of Commission 19 The OC has prepared the following charter: Commission 19 of the International Astronomical Union (IAU) is a part of the IAU Division I. The Commission is created to fulfill a specific scientific goals related to the Earth rotation, Earth orientation, and related reference frames. The objectives of Commission 19 are: (a) Encourage and develop cooperation and collaboration in observation and theoret- ical studies of Earth orientation (the motions of the pole in the terrestrial and celestial reference systems and the rotation about the pole). (b) Serve the astronomical community by linking it to the officialorganizations pro- viding the International Terrestrial and Celestial Reference Systems/Frames (ITRS and ITRF) and Earth orientation parameters: International Association of Geodesy (IAG), International Earth Rotation and Reference System Service (IERS), International VLBI Service for Geodesy and Astrometry (IVS), International GPS Service (IGS), Interna- tional Laser Ranging Service (ILRS), International DORIS Service (IDS). (c) Develop methods for improving the accuracy and understanding of Earth orienta- tion and related reference systems/frames. (d) Ensure agreement and continuity of the reference frames used for Earth orientation with other astronomical reference frames and their densification. (e) Provide means of comparing observational and analysis methods and results to ensure accuracy of data and models. The organization of Commission 19 is the following. The Commission consists of its members and consultants, and is chaired by the President. To coordinate its activity, the Commission forms the Organizing Committee (OC) (see above for its composition). The Organizing Committee includes ex-officiomembers (the past Commission President and representatives from the IAG, IERS, IVS, IGS, ILRS, and IDS) and members at large. Each IAU member who is interested in the participation in the Commission activity may be a member of the Commission. No election procedure for a membership is established; only recommendation from the Commission 19 OC is needed.

History of Monitoring Earth Orientation, and Re-analyses of Old Data

The history of monitoring Earth orientation goes back to the end of nineteenth century, when polar motion was discovered. Description of international efforts in organizing coordinated observations to determine Earth’s orientation is presented. The services, such as International Latitude Service (ILS), Bureau International de l’Heure (BIH), International Polar Motion Service (IPMS) and, finally, International Earth Rotation and Reference Systems Service (IERS), are described, as well as the observational techniques used by them. Each improvement of the techniques and their accuracies led to new discoveries and corresponding improvements of the theory of Earth’s rotation. From the very beginning of these efforts, classical astrometric observations were used for almost one century. Later on, as more precise modern data obtained by space geodesy appeared, new and more accurate theories of precession-nutation became necessary. Finally, to explain the differences between the observations and theory, more and more data from other sources (mainly of geophysical origin) became necessary to be considered. These data and their effects are also shortly commented. Here we concentrate on optical astrometry that dominated throughout the twentieth century; namely we present some important re-analyses of these observations. Special attention is devoted to the re-analyses done in 1998–2012 at the Astronomical Institute, Czech Academy of Sciences. Data covering 1899.7–1992.0 were used to derive Earth orientation parameters and to improve star positions and proper motions in the Hipparcos celestial reference frame.

DIVISION I: FUNDAMENTAL ASTRONOMY

The goal of the division is to address the scientific issues that were developed at the 2009 IAU General Assembly in Rio de Janeiro. These are: • Astronomical constants —Gaussian gravitational constant, Astronomical Unit, GM Sun , geodesic precession-nutation • Astronomical software • Solar System Ephemerides —Pulsar research —Comparison of dynamical reference frames • Future Optical Reference Frame • Future Radio Reference Frame • Exoplanets —Detection —Dynamics • Predictions of Earth orientation • Units of measurements for astronomical quantities in relativistic context • Astronomical units in the relativistic framework • Time-dependent ecliptic in the GCRS • Asteroid masses • Review of space missions • Detection of gravitational waves • VLBI on the Moon • Real time electronic access to UT1-UTC In pursuit of these goals Division I members have made significant scientific and organizational progress, and are organizing a Joint Discussion on Space-Time Reference Systems for Future Research at the 2012 IAU General Assembly. The details of Division activities and references are provided in the individual Commission and Working Group reports in this volume. A comprehensive list of references related to the work of the Division is available at the IAU Division I website at http://maia.usno.navy.mil/iaudiv1/ .

Long-periodic precession parametrization

We discuss aspects of long-periodic precession parametrization.