Peter Brosche

Tidal friction and the earth's rotation

Historical Background and Introduction.- References.- Pre-Telescopic Astronomical Observations.- 1. Introduction.- 2. Historical Development.- 3. Inter-Relation of Parameters.- 4. Recent Investigations.- 5. Remarks on the Selection of Suitable Observations.- 6. Observations of Total and Near-Total Solar Eclipses.- 7. Method of Analysis.- 8. Geophysical Discussion.- 9. Conclusions.- References.- Tidal Deceleration of the Earths Rotation Deduced from Astronomical bservations in the Period A.D. 1600 to the Present.- 1. Introduction and Principle of Method.- 2. Moons Orbital Angular Deceleration.- 2.1 Deceleration with Respect to Dynamical Time.- 2.2 Deceleration with Respect to Atomic Time.- 3. Tidal Deceleration of Earths Rotation.- 4. Conclusions.- References.- Determination of the Rotation of the Earth (at Present).- 1. Introduction.- 1.1 Preview.- 2. General Features of the Rotation of the Earth.- 2.1 Variation in the Earths Rate of Rotation.- 2.2 Polar Motion.- 3. Equatorial System.- 4. Astronomic Longitude and Latitude.- 5. Time Scales.- 5.1 Astronomic Time.- 5.2 Atomic Time.- 6. Methods and Instruments of Observation.- 6.1 Optical Instruments.- 6.2 Doppler Satellite Measurements.- 7. Data Analysis Centers.- 8. Results on the Rotation of the Earth.- References.- Effect of Tidal Friction on the Lunar Orbit and the Rotation of Earth and Its Determination by Laser Ranging.- 1. Introduction.- 2. The Physical Problem.- 3. The Laser Technique and Its Application.- 4. Determination of the Lunar Acceleration.- 5. Comparisons and Difficulties of Interpretation.- References.- Appendix A: Comments on the Perturbed Mean Motion 52 ppendix B: Reality of the Venus Effect 53 ides of the Solid Earth from Gravimetric Measurements.- 1. Introduction.- 2. Basic Concepts.- 3. The Tidal Potential.- 4. Determination of LOVE numbers from Gravimetric Data.- 5. Instrumentation.- 6. Actual Problems.- 7. Recent Results.- 8. Future Activities.- References.- Tidal Friction in the Solid Earth: Loading Tides Versus Body Tides.- 1. Introduction.- 2. Dissipated Tidal Energy in the Solid Earth.- 2.1 Theory of Dissipation in a Heterogeneous Incompressible Earth.- 2.2 Dissipation of Body Tide Energy.- 2.3 Dissipation of Loading Tide Energy.- 3. Global Tidal Q and Tidal Phase Shifts.- 3.1 Loading Tide Q Versus Body Tide Q.- 3.2 Numerical Results for the Body Tide.- 3.3 Theoretical Relationship between Tidal Bulge Angles, Body Tide Phase Shifts, and the Global Body Tide Q.- 3.4 Some More Numerical Examples.- 3.5 Numerical Results for the Loading Tides.- 4. Conclusions.- References.- Tidal Dissipation in the Oceans.- References.- The Influence of Solid Earth Deformations on Semidiurnal and iurnal Oceanic Tides.- 1. Introduction.- 2. Considering Tidal Loading and Ocean Self-Attraction in.- Ocean-Tide Models.- 2.1 Tidal Integrodifferential Equations and the Energy-Equation Belonging to Them.- 2.2 Properties of Different Ocean-Tide Models.- 3. Generalization of the 4 -Primitive-Equations Model.- 3.1 The Finite-Difference Scheme.- 3.2 Oceanic Tides on a Nonrotating Earth.- 4. The Computed Global M2-Tide.- 5. The Computed Global K1-Tide.- 6. Conclusions.- Glossary of Symbols.- References.- The Numerical Computation of Tidal Friction for Present and ncient Oceans.- 1. Introduction.- 2. Computation of Tidal Friction by Hydrodynamic-Numerical.- Models.- 2.1 Basic Equations.- 2.2 Analytic Considerations.- 2.3 Hydrodynamic-Numerical Models.- 3. A Numerical Model for the Present Ocean.- 3.1 Requirements.- 3.2 Balance of Angular Momentum.- 4. Numerical Model for Ancient Oceans.- 4.1 Necessity of Such a Model.- 4.2 Bathymetry.- 4.3 Application to the Permian Ocean.- 4.4 Verification.- 5. Further Activities.- References.- The Earths Palaeorotation.- 1. The Coral Data.- 2. The Bivalve Data.- 3. Stromatolite Data.- 4. Combined Data 1.- References.- Periodic Growth Features in Fossil Organisms and the Lenght of the ay and Month.- 1. Introduction.- 2. Biological Considerations.- 2.1 Growth Increments in Corals.- 2.2 Growth Increments in Bivalves.- 2.3 Growth Increments in Stromatolites.- 2.4 Biological Clocks.- 3. The Data.- 3.1 Recording the Data.- 3.2 The Published Data.- 4. Implications of the Growth Increment Data.- 5. Conclusions.- References.- Geological and Geophysical Evidence Relating to Continental rowth and Dynamics and the Hydrosphere in Precambrian Times: Review and Analysis.- 1. Introduction.- 2. The Hydrosphere.- 3. The Continental Crust.- 4. Precambrian Dynamics of the Continental Crust.- 5. Palaeomagnetic Analysis of Precambrian Crustal Movements.- 5.1 Gondwanaland-Late Precambrian and Lower Palaeozoic.- 5.2 Laurentian Shield-Upper Proterozoic.- 5.3 African Shield-Upper Proterozoic.- 5.4 Laurentian Shield-Middle-Lower Proterozoic.- 5.5 Africa-Middle-Lower Proterozoic.- 5.6 Australia-2600-1100 my.- 5.7 Baltic-Ukrainian Shield-2000-1200 my.- 6. Palaeomagnetic Correlations Between the Proterozoic Shields.- 7. Proterozoic Supercontinent.- 8. Age of the Earth-Moon System.- 9. Stromatolite Evidence for Precambrian Tidal Parameters.- 10. Sedimentologic Evidence for Precambrian Tidal Parameters.- 11. The Tidal Couple and Changes in the Earths Rotation in Precambrian Times.- References.- Concluding Remarks.

Globular cluster orbits based on Hipparcos proper motions

Abstract We present and analyse space motions and orbits for a sample of 15 galactic globular clusters. The absolute proper motions of these clusters have been determined with respect to reference stars of the new Hipparcos system. Orbital integrations in two model potentials for the Galaxy are considered. The sample shows a mean rotation near 40 km s−1 in the sense of rotation of the galactic disk. Six clusters are however found to be in retrograde motion. Velocity dispersions are around 104 km s−1 in the direction of rotation, near 116 km s−1 in latitudinal direction and near 127 km s−1 in radial direction. The orbits of the clusters preferentially have small axial angular momenta and high eccentricities, the median of the orbital eccentricities being 0.62. From the spatial extent of the orbits we conclude that the Galaxy must have a massive halo with a radius of at least 30 kpc. The space density distribution of our sample of clusters system, except for distances less than 4 kpc from the galactic center. space density distribution of the total globular cluster system, except for distances less than 4 kpc from the galactic center. The largest apogalactic distances in the sample reach out to 65 kpc. The orbits provide evidence that the more metal-rich clusters are concentrated towards the galactic center. The clusters with significant retrograde motion have metal abundances between − 1.5 and − 2.0 and hence appear to be relatively homogeneous in chemical composition. The small subgroup of ‘young halo’ clusters within our sample is orbiting with a net retrograde rotation of −9 km s−1. A general relation between orbital eccentricity and metal-abundance does not show up in the sample. The observed radii of the clusters are found to be in a well-defined relation to the tidal limits imposed by orbital motion in the galactic field. It is shown that the cluster radii are however not uniquely determined by the perigalactic distances, but involve at least also the geometry of the orbit.

Die Gezeiten des Meeres und die Rotation der Erde

SummaryThe problem of tidal friction as a cause of the secular deceleration of earth rotation was higherto approached on the basis of estimating the kinetic energy dissipated by bottom friction. It would appear however, that in any analysis of the influence of oceanic tides on earth rotation the varying directions of the torques due to tidal streams and acting on the solid earth, must be taken into account. As examples for this, the torques due to tidal friction are calculated for the North Sea and for the 10°-world ocean, applying hydrodynamical-numerical methods. The results show that earth rotation is not retarded at all points of the world ocean, but that tidal areas exist exerting either decelerating or accelerating forces.

The Antarctic circumpolar current and its influence on the Earth's rotation

At least in case of semidiurnal tides, theirmotions “contain” most of their relative angular momentum. There are other periodic currents in the ocean with cycles of months to years which may influence the Earths rotation within such time scales. These currents are mainly due to seasonal or climatic variations of the wind stress and the water mass distribution in the oceans. The main question is: how much of the oceanic angular momentum is temporarily stored within the oceans and what is the time scale of the transfer to the solid Earth. As an example, we have estimated the phase and the amplitude of the angular momentum which is stored in the Antarctic Circumpolar Current. Its phase resembles the one of the whole observed semiannual discrepancy in the angular momentum budget of the solid Earth plus the atmosphere; the amplitudes are comparable.

Instantaneous and average tidal radii of globular clusters

Abstract The main aim of this paper is an extension of the heuristic concept of the tidal radii of globular clusters to the case of very non-circular orbits, i.e. with large differences between the peri- and apogalactic distances. We had found earlier that perigalactic tidal radii do clearly not represent the observed limiting photometric radii. For 16 globular clusters with orbits based on absolute proper motions we derived instantaneous tidal radii along the orbit. We computed four kind of averages of the instantaneous values. The comparison between average tidal radii and observed limiting radii relies on the ratios between the two, since the equations for the theoretical values may need the inclusion of an additional constant factor. In case that the said ratios do not depend on the shape of the orbits, we consider the underlying method of averaging as satisfying. In a quantitative approximation, this non-dependence can be assumed for all methods within 3σ-limits; but one method stands out in that it fulfils it within 1σ. This method or way consists in forming the reciprocal squares of the instantaneous tidal radii and their mean along the orbit.

Restströme, Gezeitenstromellipsen und Bodenreibung

Unter der Annahme, das sich die Gezeitenstromungen exakt als Summe eines relativ kleinen Reststroms und einer Gezeitenstromellipse darstellen lassen, wird die durch die Bodenreibung auf die feste Erde wirkende mittlere Kraftkomponente in einer speziellen Richtung explizit angegeben. Im Falle der Ost-West-Richtung folgt daraus das mittlere Drehmoment um die Rotationsachse der Erde.

COMMISSION 41 WORKING GROUP on ASTRONOMY AND WORLD HERITAGE

What follows is a short report on the Business Meeting of the Astronomy and World Heritage Working Group held on Thursday August 6, 2009. This was the first formal Business Meeting of the Working Group since its formation following the signing of the Memorandum of Understanding between the IAU and UNESCO on Astronomy and World Heritage in October 2008.

Astronomy in and around Prague

H 01 Astronomy in medieval Prague H 02 News in the Identification of Tycho Brahes Handwritings H 03 Keplers Astrology and the Wallensteins Horoscopes H 04 Kepler and the Star of Bethlehem H 05 Augenschein and Finsternisse – the language of the women astronomer Maria Cunitia (1604?–1664) H 06 Christoph Scheiners Investigations of the Physiological Optics of the Eye H 07 Kepler, Horrocks and the Transit of Venus in 1639 H 08 Astronomy and “Musaeum Mathematicum” at Prague Clementinum College H 09 Josef Petzval (1807–1891) and the Early Development of Astrophotography H 10 Petzval Astrograph of Tartu Observatory H 11 Christian Doppler (1803–1853) and the Impact of the Doppler Effect in Astronomy H 12 The Phenomenon of Doppler in Modern Science H 13 Czech and German Astronomers at the Prague University I. German Part of the Prague Universitas Carolo-Ferdinandea (1882–1920) II. Deutsche Universitat in Prag (1920–1939) and Deutsche Karls-Universitat in Prag (1939–1945) H 14 Keplers Astrology and the Wallenstein Horoscopes