Time ‐ From Earth Rotation to Atomic Physics
... The Earth's rotation is generally decelerating, a state that is caused by the tidal friction related to the gravitational pull of the Moon and, to a lesser extent, the Sun [12,13]. Another process significantly influencing secular changes of the Earth's rotation is the melting and freezing of polar ice caps and the corresponding change of water volumes on continents and in the world ocean. ...
... Then, the Earth's rotation should decelerate before CTGE and accelerate after it. This totally contradicts the results of this review and corresponds to the widely accepted conception that rotation of Earth and other planets is primarily related to the causes from the initial stages of the solar system formation [12,13]. ...
... Then, the Earth's rotation should decelerate before CTGE and accelerate after it. This totally contradicts the results of this review and corresponds to the widely accepted conception that rotation of Earth and other planets is primarily related to the causes from the initial stages of the solar system formation [12,13]. Figure 12. Distance from the Sun (in average) and rotation period of major planets in the solar system (based on data from [47]). ...
This study reviews the Meso–Cenozoic tectonic paleo-reconstructions for the East Asian and western North American continental margins, focusing on strike-slip tectonics. It follows previous studies by the present and other authors, which investigated the Cretaceous turn of geological evolution (CTGE). They largely studied significant changes in the Earth’s mineralization, magmatism and climate. The present study focuses on significant changes related to the Earth’s rotation velocity. This question is significant not only for fundamental science, but also for applied geology, because CTGE is marked by abundant ore and energetic resources. The results show domination of sinistral shearing on the NE-oriented Asian margin during the pre-early Cretaceous time that turned to significant development of dextral movements in the mid Cretaceous–Cenozoic time. On the NW-oriented American margin, significant development of sinistral movements in the pre-early Cretaceous time turned to domination of dextral shearing during late Cretaceous and Cenozoic. These tectonic changes indicate the transition of the Earth’s rotation from the accelerating towards decelerating regime after CTGE (135–120 Ma). This change may be caused by the transition of the Earth’ mass to, and then, away from the polar regions, the processes being related to melting and freezing of the ice caps.
... Obviously, polar motion is one of the key parameters of ERP, which is defined as the motion of the Celestial Intermediate Pole (CIP) relative to the Earth's surface. It is composed of a collection of motions covering a range from secular to sub-daily time scales [50]. The polar motion series consists of three significant components: long-term trend, Chandler wobble, and annual wobble. ...
... The large-scale secular deformation of Earth causes longterm drift of the polar motion [51]. The Chandler wobble refers to the motion of the CIP over the Earth's surface, which is caused by the rotation axis not being aligned with the inertia axis [50], and is an excited resonance of the Earth's rotation over a period of about 14 months [52]. The annual wobble is another important component of the polar motion and current findings confirm that it consists of two components, retrograde, and prograde wobble [53,54]. ...
The Earth rotation parameters (ERPs), including polar motion (PMX and PMY) and universal time (UT1-UTC), play a central role in functions such as monitoring the Earth’s rotation and high-precision navigation and positioning. Variations in ERPs reflect not only the overall state of movement of the Earth, but also the interactions among the atmosphere, ocean, and land on the spatial and temporal scales. In this paper, we estimated ERP series based on very long baseline interferometry (VLBI) observations between 2011–2020. The results show that the average root mean square errors (RMSEs) are 0.187 mas for PMX, 0.205 mas for PMY, and 0.022 ms for UT1-UTC. Furthermore, to explore the high-frequency variations in more detail, we analyzed the polar motion time series spectrum based on fast Fourier transform (FFT), and our findings show that the Chandler motion was approximately 426 days and that the annual motion was about 360 days. In addition, the results also validate the presence of a weaker retrograde oscillation with an amplitude of about 3.5 mas. This paper proposes a hybrid prediction model that combines convolutional neural network (CNN) and long short-term memory (LSTM) neural network: the CNN–LSTM model. The advantages can be attributed to the CNN’s ability to extract and optimize features related to polar motion series, and the LSTM’s ability to make medium- to long-term predictions based on historical time series. Compared with Bulletin A, the prediction accuracies of PMX and PMY are improved by 42% and 13%, respectively. Notably, the hybrid CNN–LSTM model can effectively improve the accuracy of medium- and long-term polar motion prediction.
... As Guinot (1972), Vondrák and Ron (2005) rule out a variable or a double Chandler period and present instead several mechanisms to explain the great Chandler wobble change 1923-1940. McCarthy and Seidelmann (20093) write that the amplitude of the Chandler motion is ''known to be variable, but of the order of 150 mas" and that ''annual PM is a stable prograde motion with an amplitude of about 90 mas". McCarthy and Seidelmann (2009, Chapter 4) also describe the known variations of Earth rotation, in particular the variations of the ''clock" Earth ...
... The sharp bend in mean PM, which is assigned to the year 2000 by Wahr et al. (2015) will be discussed in Section 5.1. Seitz and Mü ller (2016) quote similar orders of magnitude for PM as McCarthy and Seidelmann (2009), also pointing out that the Chandler amplitude is subject to strong variations in time. The review article is in essence based on Seitz and Schmidt (2005), who applied a dynamic Earth system model and wavelet techniques to the IERS C01 series. ...
Polar motion (PM) series from various observation methods and sources are analyzed using one and the same simple analysis tool. The maximum time resolution of the Earth Rotation Parameter (ERP) series considered here is one day, which leaves out ERP series with sub-daily time resolution. A longer spacing between subsequent epochs is permissible, a variable spacing between epochs like in the VLBI (Very Long Baseline Interferometry) series as well. The shortest length of the PM time series analyzed, based on GNSS (Global Navigation Satellite Systems), is 26+ years, the longest one, the IERS C01 series, 173+ years.
Following the tradition, PM is decomposed into a mean motion, i.e., the motion of the center of the PM curve on the surface of the Earth, a prograde Chandler motion with a nominal period of 432.25 days, and a prograde annual motion with a nominal period of 365.25 days. In our analysis, Secular PM is not assumed as linear, but as piecewise linear and continuous. The defining parameters of the periodic parts of polar motion are not assumed as constant either, but as piecewise linear and continuous functions of time as well. All parameters of the PM model based on one particular ERP series are determined in one and the same linear least squares estimation. Parameters of the same type may be purely deterministic or filtered (smoothed) by constraining the second time differences of the parameters (the second time derivative of the parameter functions) of the same kind.
The key results achieved by applying our method to a wide variety of ERP series are visualized and discussed. They include: (a) the description of a sharp bend of mean PM around 1996, (b) strong evidence for a multi-component model for Chandler motion with periods separated by few days, similar to that proposed by Chandler (1901), (c) a reconstruction of mean PM from 1846 to present taking into account the composite nature of the series, and (d) a prediction of Chandler motion for the next decades.
A sharp bend of mean PM was found around 1995/96, along the meridian at about 70° West to the meridian at about 12–15° West. All PM curves analyzed show a mean motion in this new direction after 1995/95. Smaller excursions w.r.t.d this mean exist, with periods <10 years. A periodic variation with a period of about 180 years was observed in the Chandler signal of PM with an amplitude of more than 200 mas. The variation may be explained approximately by a composite nature of Chandler motion, similar to the model already proposed by Chandler (1901). This simple model was generalized using a Fourier series separated in period by few days. This alternative model of Chandler motion is used to predict the Chandler part of PM, with an amplitude close to zero currently, to reach values of the order of 100 mas around 2028–2030.
... The length of the solar year has undergone various estimations and interpretations. The pursuit to understand the precise length of the solar year has been a fascinating and captivating journey spanning millennia, marked by countless observations, calculations, revisions, and constant refinements and updates (Meeus and Savoie, 1992;McCarthy, 2009;Richards, 2013). From the ancient Egyptians' and Babylonians' simple observations of celestial patterns to the highly sophisticated calculations of modern astronomers, each era has contributed to refining our understanding and evolving knowledge of this fundamental unit of time. ...
There is a strong belief that Allah Almighty could reveal His existence by encoding the laws of nature and their fundamental constants in the Quran with impeccable precision. However, the mathematical frameworks and patterns embedded within the Quranic text to reveal scientific laws and constants may contain minor deviations in numerical values to empower personal exploration, accommodate diverse interpretations, and strengthen faith. This theory is based on the fact that the Quran is the word of Allah Almighty. Consequently, one would anticipate finding evidence suggesting a divine origin. Many scholars and researchers have suggested that this evidence can be found in the mathematical structure of the Quran through patterns, numerical codes, and other mathematical features within the text that are too complex to be simply attributed to human authorship. Therefore, it is believed that the Quran contains within its structure a mathematical encoding of all physical laws and constants. Verses like 20.98, which state, "He encompasses all things in knowledge," are quoted as evidence. According to this perspective, the Quran is assumed to incorporate mathematical miracles, indicating a potential correspondence between its text and the underlying order of the universe. This theory reveals many mathematical frameworks illustrating how the Quran embeds scientific knowledge. These include the identification of frequent occurrences of the golden ratio within the Quranic text and the manifestation of the golden ratio in the human body, alongside the determination of key celestial parameters such as the length of the solar year. Furthermore, this theory uncovers a numerical link between the Quran and fundamental scientific constants, notably the universal gravitational constant, the speed of light, and the Planck constant. Moreover, this theory utilizes numerical analysis to offer a compelling rationale for why the numbers 28 and 114 are used to represent the total number of Arabic letters and chapters in the Quran, respectively. Finally, this theory highlights the Quran's remarkable mathematical architecture, offering indisputable evidence of its divine composition. We behold a mathematical marvel of cosmic scale, a phenomenon defying human intelligence. Indeed, the Quranis a product of a super intelligence exceeding our comprehension.
... Geophys. Geod., 68 (2024) meridian at 0 longitude, and y, along the meridian at 90° west longitude (Gross, 2015;McCarthy and Seidelmann, 2018). Long-term drift, Chandler oscillation, and annual oscillation are the three main significant components of polar motion parameters (Guo and Han, 2009;King and Watson, 2014;Schuh et al., 2001). ...
As one of the main components of the Earth orientation parameters, short-term prediction of the geodetic polar motion series is crucial in the field of deep-space exploration, high-precision positioning, and timing services, which require high real-time performance. Additionally, its middle- and long-term prediction is equally important in climate forecasting and geodynamics research. In this study, we propose the combined BiLSTM+ARIMA model, which is based on bidirectional long- and short-term memory (BiLSTM) and autoregression integrated moving average (ARIMA). First, ensemble empirical mode decomposition (EEMD) is performed as a filter to decompose the polar motion time series to obtain low- and high-frequency signals. The EOP14 C04 time series provided by International Earth Rotation and Reference Systems Service and decomposed by EEMD includes low-frequency signals like the long-term trend, decadal oscillation, Chandler wobble, and prograde annual wobble, along with shorter-period high-frequency signals. Second, low- and high-frequency signals are predicted using BiLSTM and ARIMA models, respectively. Finally, the low- and high-frequency signal forecast components are reconstructed to obtain geodetic polar motion predictions. In middle- and long-term polar motion prediction, the results show that the proposed model can improve the prediction accuracy by up to 42% and 17%, respectively. This demonstrated that the BiLSTM+ARIMA model can effectively improve the accuracy of polar motion prediction.
... Most of the times the stars in the sky were the only reliable reference to determine our position [9]. However, such navigation method is fully dependent from the stars or the sun, which can only be seen during the day, or in a clear night sky, not to mentioned the fact that our perception of the stars change duo to the Earth rotation [10]. To answer such questions several instruments were created, like the Geographical Representation Systems, that map the entire world with a relative good precision or physical tools that helped solving possible errors in the calculation of the position. ...
The research of the brain has led to many questions, with most of them still not having a definitive answer. One of those questions is about how the brain acts when we navigate a new space. Inside the Temporal Lobe's Hippocampal structure, specific types of neurons and neuronal structures are responsible to identify spatial elements. To recognize spaces, these cells require data, which is obtained from the subject's senses. It is important to understand how these features are captured, processed, encoded and how the Hippocampus, and its neighboring elements, use the information to help in the navigation and mapping of a place. A specific type of neurons seems to support an animals location and spatial mapping, on other areas of research, discrete global grid systems are used to increase the independence of the autonomous vehicles, allowing the indexing of assets across the globe by partitioning the earth into grids that take into account the heterogeneity of the scales of the associated geospatial data. In this context, the main objective of this chapter is to make an analysis about the biological and technical aspects of navigation by establishing a bridge between the Hippocampus and Simultaneous Localization and Mapping (SLAM) methods.
... Thus, astronomical, nautical, and air almanacs are designed for astronomical observations and astronomy, navigation of ships, and airplanes, respectively. Calendars are designed to follow the solar and/or the lunar periods, with some relations to the vernal equinox for religious purposes (McCarthy and Seidelmann, 2018). ...
... The present-day increase rate of lunar semi-major axis is 3.808 ± 0.019 cm/year (Williams et al., 2014) and present-day EMD (in terms of semi-major axis of the lunar orbit) is 384,402 km (Murphy, 2013). LOD is precisely measured using very long baseline interferometry and other methods (McCarthy and Seidelmann, 2018); present-day LOD of 23.9345 h (86,164 sidereal seconds) is defined by the present-day Earth mean angular velocity of ϕ 0 = 7.2921150(1) × 10 − 5 rad/s at J2000 (Supplementary Material). EMD and LOD remain poorly known for most of the geological past. ...
The theoretical prediction of Earth-Moon dynamics in deep geologic time is hampered by limited knowledge of Earth's past tidal dissipation and dynamical ellipticity. Cyclostratigraphy can, however, provide valuable information on the geologic evolution of the Earth-Moon dynamical parameters. Here we investigate Eocene cyclostratigraphy to estimate Earth's precession rate (p), Earth-Moon distance (EMD) and length-of-day (LOD). Two highly-resolved deep sea records are selected from the Atlantic Ocean, with ages centered on 42.5 Ma (40.9–44.3 Ma; IODP Site U1410) and 54.95 Ma (54.1–55.8 Ma; ODP Site 1262). The sedimentary sequences at these sites recorded Milankovitch forcing signals with prominent precession index (Site 1262) and obliquity (Site U1410) frequencies and their amplitude modulations. At Site U1410, amplitude modulation of the main obliquity cycle was tuned to the Earth's 173-kyr orbital inclination (s3-s6) metronome, and at Site 1262, the dominant precession index amplitude modulation to the 405-kyr orbital eccentricity (g2-g5) metronome. This enabled estimation of Earth's precession rate p of 51.486 ± 0.064 arcsec/yr and 51.546 ± 0.168 arcsec/yr for 42.5 Ma and 54.95 Ma, respectively. These p estimates indicate EMD values of 383.710 ± 0.090 × 10³ km and 382.625 ± 0.265 × 10³ km, and LOD values of 23.679 ± 0.0115 h and 23.667 ± 0.039 h for 42.5 Ma and 54.95 Ma, respectively. These estimates deviate from theoretical predictions based on back calculation assuming present-day tidal dissipation. In particular, a significant discrepancy between the model and observations (cyclostratigraphy) occurs at 54.95 Ma (Site 1262) suggesting contributions from other effects on Earth's rotation, including changes in tidal dissipation and/or Earth's dynamical ellipticity related to mantle convection and the early Eocene global warming.
... More details about calendars and history were provided (Grun, 1979.). Based on the orbital motions of the solar system, time was introduced (McCarthy & Seidelmann, 2009). Astronimical algorithms are necessary to check the accuracy of calendars (Verkhovsky, 2011;Meeus, 1999). ...
The study aimed to develop a relationship between Gregorian calendar dates in AD and Julian calendar dates in AD which is shown as algorithms. It also solved ordinal numbers of dates and dates of ordinal numbers that are in AD with the use of algorithms. Dates of ordinal numbers were also solved using algorithms. Algorithms for converting a Julian calendar date into the Gregorian calendar date and vice versa were derived; conversions for the two calendars were derived. The study used applied Mathematics using derivation of Algorithms in answer to the objectives. There were sample problems to check the accuracy of the algorithms; the algorithms are correct. Six algorithms were established.
Some commentators admit that there is constant conflict between science and theology. The reason they put forward is that metaphysical concepts cannot be linked with empirical sciences. Despite such a theoretical background, many commentators claim that the Western Medieval period has no scientific significance. If their claims are true, science and scientific research should have completely stagnated after the Greek period, and the renaissance of science should have come again with the Copernican revolution. Are these reviews true? Or a myth? The fact that there are some problematic conditions here is evident from the works related to the investigations of the Middle Ages. Therefore, through this article, I attempt to explain the form of medieval scientific thought. It can identify the relationship between medieval theology and scientific thought, as well as the collapse of science due to theology. A more recent period of human thought spans almost 17 centuries, spanning almost the period of medieval scientific thought. Therefore, instead of investigating the above objectives in detail, it is important to focus on important milestones. As this study should be conducted within the framework summarized above, what was the contribution of medieval theological thought to the advancement of science? Is that scientific thinking acceptable? Are the criticisms presented in this regard acceptable? It can be explored through research questions, etc.
The article is devoted to the scientific and theoretical substantiation of the problem of defining the Great Baryon Pump of the Earth (GBP of the Earth) as a natural prototype of the "tree of life" and an object of environmental law that is integrated with the natural human environment. It is indicated that the authors of the article had previously investigated the issue of the relationship between the "right [of man] to the tree of life" and the biological rights of man, simultaneously touching on another important humanitarian and at the same time civilizational and legal issue - the identification of the so-called "GBP of the Earth" as material and natural prototype of the biblical metaphorical way of "tree of life". However, an even more important issue in the context of this study, which precedes this issue, is the qualification of the Earth's natural environment as an ecological object that is integrated with the natural habitat of man (his natural environment). It is proven that, according to the data of geological sciences, the GBP of the Earth in the process of rotation of the Earth on its axis, transforms the tangential acceleration (the component of acceleration directed along the tangent to the trajectory of the material point, which characterizes the change in the velocity module. – author) into radial (normal) acceleration, which explains the formation of vortex tracks on the lithosphere and pushing the Moon into a higher orbit relative to the Earth. Extrapolating its dynamics to 4.0 billion years ago - in the early eons of our planet, taking into account objective scientific data on the transformation of substances in the system of geospheres, it can be assumed that the GBP of the Earth was able to transform inanimate matter into living matter. This became a more significant and revolutionary factor, which was directed to the formation of an actor (acting subject) for the beginning of biological evolution and created the conditions for the emergence of man on Earth. In turn, the need to study the functions of the Earth's natural resources in the environmental discourse and its qualification as an object of law is a natural stage in the development of the system of ecological, noospheric law, and in the future - anthropic law as a metasystem of the natural law of our universe. Therefore, it is stated that the existence GBP of the Earth is inextricably linked with the concept of the anthropic properties of the space of our Universe in the light of the Poincaré-Perelman theorem, according to which "any single-connected closed three-dimensional manifold without an edge is a homeomorphic (continuous reversible transformation of space. – author) of the three-dimensional sphere". This theorem indicates the integrity, continuity and unbreakability of the space of our Universe from the moment of the socalled "Big Bang" (or another event similar to it) onwards: the formation of our Galaxy, the Solar System, the Earth-Moon system, the emergence of living matter, the beginning of biological evolution, the formation of Earth Man and the formation of the noosphere. On the other hand – in a functional bioecological context, the GBP of the Earth can be considered not only as an Eozoic (life-creating) object, but also as an actor that controls the continental cycle – continental drift, which is associated with the formation of the single continent of Pangea and its subsequent disintegration to separate continents. It is characteristic that in the process of geographical discoveries and human development of the global natural environment (environment), this led to the emergence of a modern picture of the world and the formation of a "topological two-circuit – shell-nuclear informational and legal structure of the noosphere". These events of the border of the XV-XVI centuries and the development of the colonial system determined the vector of the next evolution of the geopolitical landscape – its legal structuring, which, in accordance with the Legal Triad (order – rules – law) and the doctrine "rule based international order", was embodied in the picture of the modern world order. Currently, the world structure that has emerged can be imagined as a complex global-regional legal system, in the regulatory field of which there is a process of deep integration of international public law and municipal law. In turn, this has formed stable trends that indicate the active development of value ideas about biological human rights, as well as their implementation on a global scale. It is stated that the strategic goals, the achievement of which is important for the biologization of law, cannot be achieved without the identification of the Earth's natural reserve as a prototype of the "tree of life" object, and the qualification of the Earth's natural reserve as an Eozoic object that is integrated with the surrounding natural environment man (his natural environment). In addition, the resolution of the natural-law conflict that has arisen is absolutely necessary for the development of the system of international environmental law, the formation of the system of noospheric law, as well as the improvement of IL-forecasting methods in the process of strengthening the trends of global constitutionalism, noospherism and the development of the institute of biological human rights in the world civilizational legal system.
While the physical reality of time may always be one of nature’s mysteries, modern science has provided some clues. We explore the association of time with the second law of thermodynamics, which stipulates that the degree of randomness, termed entropy, must always increase. But time as known by Newton and others has given way to new understandings brought about by twentieth century physics from the Theories of Relativity and Quantum Mechanics, and the need to make them mutually consistent. At the level of everyday experience however, humanity responds to the rhythm set about by the Earth’s rotation. Early timescales were based on the Earth’s rotation as well as its orbit. The Earth’s rotation was discovered to be variable on all scales, and slowing down in the long run. As civilization advanced, improvements in time transfer allowed time to be determined globally rather than locally, and the exploration of outer space required the creation of timescales that fully incorporate relativity. The need for synchronization across national borders was satisfied by Coordinated Universal Time (UTC), which is generated by the International Bureau of Weights and Measures (BIPM).
The 15 yr pulsar timing data set collected by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) shows positive evidence for the presence of a low-frequency gravitational-wave (GW) background. In this paper, we investigate potential cosmological interpretations of this signal, specifically cosmic inflation, scalar-induced GWs, first-order phase transitions, cosmic strings, and domain walls. We find that, with the exception of stable cosmic strings of field theory origin, all these models can reproduce the observed signal. When compared to the standard interpretation in terms of inspiraling supermassive black hole binaries (SMBHBs), many cosmological models seem to provide a better fit resulting in Bayes factors in the range from 10 to 100. However, these results strongly depend on modeling assumptions about the cosmic SMBHB population and, at this stage, should not be regarded as evidence for new physics. Furthermore, we identify excluded parameter regions where the predicted GW signal from cosmological sources significantly exceeds the NANOGrav signal. These parameter constraints are independent of the origin of the NANOGrav signal and illustrate how pulsar timing data provide a new way to constrain the parameter space of these models. Finally, we search for deterministic signals produced by models of ultralight dark matter (ULDM) and dark matter substructures in the Milky Way. We find no evidence for either of these signals and thus report updated constraints on these models. In the case of ULDM, these constraints outperform torsion balance and atomic clock constraints for ULDM coupled to electrons, muons, or gluons.
The present article describes the design and development of a universal device for precise and accurate distribution of time or frequency signal, i.e., one pulse per second (PPS) or 10 MHz and 5 MHz sinusoidal signal generated from an atomic clock or ensemble of atomic clocks. The frequency distribution unit provides four identical outputs of excellent stability along with suppression of all high harmonics by more than 50 dB with respect to the fundamental frequency. For time (PPS) distribution, all four outputs also provide very much similar signal as the input with excellent stability. The rising time of the output pulses is very much similar to the input pulse and stays within 3 ns.
The accuracy of timing across a seismic network is important for locating earthquakes as well as studies that use phase‐arrival information (e.g., tomography). The Global Seismographic Network (GSN) was designed with the goal of having reported timing be better than 10 ms. In this work, we provide a brief overview of how timing is kept across the GSN and discuss how clock‐quality metrics are embedded in Standard for Exchange of Earthquake Data records. Specifically, blockette 1001 contains the timing‐quality field, which can be used to identify time periods when poor clock quality could compromise timing accuracy. To verify the timing across the GSN, we compare cross‐correlation lags between collocated sensors from 1 January 2000 to 1 January 2020. We find that the mean error is less than 10 ms, with much of the difference likely coming from the method or uncertainty in the phase response of the instruments. This indicates that timing across the GSN is potentially better than 10 ms. We conclude that unless clock quality is compromised (as indicated in blockette 1001), GSN data’s timing accuracy should be suitable for most current seismological applications that require 10 ms accuracy. To assist users, the GSN network operators have implemented a “gsn_timing” metric available via the Incorporated Research Institutions for Seismology Data Management Center that helps users identify data with substandard timing accuracy (the 10 ms design goal of the GSN).
Science and engineering mathematical formulas are based on proportionality, principle of superposition, and dimensional homogeneity. This chapter reviews the development of the concept of dimensions and shows how to use them in the study of physical phenomena described by mathematical equations. By studying this chapter, you will learn why and how the concept of physical dimensions have been invented and expanded, and the method of expressing the relation among physical quantities by mathematical equations. The expansion of the dimensional concept to cover the mathematical equation is the dimensional homogeneity, of which its need and use will be covered in this chapter. There are seven accepted basic dimensional quantities in engineering and science: Length [L], Mass [M], Time [T], Electric Current [I], Temperature [Θ], Amount of Substance [N], Luminous [J]. Every other physical quantity is a derived quantity whose dimension is a multiplication of the basic dimensional quantity. The classical static dimensional analysis determines the powers of the involved parameters, variables, and constants contributing in a physical equation.
Genel Görelilik teorisinin bir sonucu olarak, kütleçkimsel alanlar gözlemci zaman akışını etkilemektedir. Zaman akışının aynı hıza sahip olduğu yüzeyler, Newton potansiyeli ile tariflenen eşpotansiyel yüzey kavramı ile aynı yüzeyleri tarif etmektedir. Eşpotansiyel yüzeyler klasik anlamda uzun yıllardır gravite ve yükseklik ölçmelerine bağlı olarak belirleniyordu.
Yükseklik belirleme için kullanılan geleneksel yöntemler bütünsel açıdan bakıldığında ölçme sonuçlarını etkileyebilecek önemli hata kaynakları barındırmaktadır. Bunlardan biri nokta üzerindeki potansiyel değerlerin doğrudan ölçülememesi nedeni ile yükseklik taşınması ile artan derecelerde hata birikmesidir. Ortalama deniz seviyeleri farklı olarak belirlenen karasal kütleler arasındaki yükseklik entegrasyonunun zorluğu da ayrı bir sorun oluşturmaktadır. Gözlemlerin yatay düzlemde gerçekleşmesi ve arazi zorlukları nedeniyle engebeli arazilerde işgücü, ekipman gücü ve yol uzunluğunun artması ile klasik yöntemlerde büyük zorluklar yaşanabilmektedir. Bu ciddi olumsuzlukları aşabilmek açısından, son yıllarda uydu teknolojileri önde gelen çözümlerden birisi olarak kullanılmaktadır. Fakat son 10 yıldır, temelleri 20. yüzyılın ikinci yarısına dayanan bir yöntem olan kronometrik nivelman, doğrulukları artan saatler ve ağ teknolojilerinin kullanıldığı test gözlemleri sonucunda önemli sonuçlar ortaya koymaya başlamıştır.
Zaman bilgisi atomik saat teknolojilerindeki gelişmeler ile birlikte atomik frekans standardında optik spektrumda yüksek frekansta gözlemler yapılarak artan ölçüde doğruluklarla belirlenebilmektedir. Bugüne kadar kullanılan mikrodalga atom saatlerinin daha düşük düzeydeki doğruluk ve kararlılıklarına karşı 100 kat daha iyileştirilmiş olan optik atomik saatler yükseklik belirlenmesinde yeni bir yöntem olarak kronometrik nivelman yönteminin önünü açmaktadır. Ayrıca fiber iletim teknolojileri ile birlikte optik atomik saat karşılaştırmaları 10−19 mertebelerinde bir hassasiyetle yapılabilmektedir. Yerçekimi ivmesi g≈10 m/s2 ve c≈ 300 000 000 m/s olmak üzere; 1 santimetrelik yükseklik değişimlerinde Δ𝑣𝑣≈10−18 frekans kayması oranı elde edilebilmektedir. Böylece optik atomik saatlerin 1 santimetrelik yükseklik farklarını belirleyebilecek hassasiyette olduğu söylenebilir.
Bu kapsamda, bu tez çalışmasında atom saatleri arasında yapılan frekans karşılaştırmaları neticesinde kütle-çekimsel Doppler etkisi ile ortaya çıkan farktan yararlanılarak potansiyel farkların belirlenmesi konusundaki teorik temellere, yöntemin genel çerçevesine ve güncel atomik saat test ağlarına değinilmektedir.
Bu bağlamda kronometrik nivelman yönteminin teorik temelleri ve güncel çalışmalar incelenmekte, uluslararası yükseklik referans sistemine olabilecek katkıları, sistemin çalışma mekanizmaları ve geoit belirleme yöntemlerine katkıları tartışılmaktadır.
The tendency of capitalist modernity to impose predictable, homogenous and linear representations of time for economic productivity has made it increasingly difficult, if not impossible, to effectively respond to catastrophic environmental changes that are emergent, sudden, non-linear and unpredictable. A confusion between the actions and consequences of environmental change, and socialized representations of time and space within which humans must respond to such changes, not only paralyses possible solutions within fixed imaginaries but is also out of synch with the perpetual coming-into-being of socionature entanglements. The multiple temporalities coordinating interactions of humans and non-human natures are instead fetishized and made governable, commensurable and reproducible through the mechanistic intervals of the clock. We argue that the desire for transformative system change can be found in temporal desynchronizations to clock Time (capital T) and that political strategies to responding to socio-ecological crises reside in alter-temporalities (lower t time) of emergent socionature relations. Through an example of the desynchronized temporalities of tinawon rice production, we show how alter-temporalities emerge to reclaim cultural and food sovereignty from the otherwise flattening effects of modernity. We highlight the futuring potentials of such temporalities and their implication within ongoing debates between ecomodernists and those advocating limits to growth. Given that continuing to act in the Time of capital evidently fails to bring about system change and even aids in perpetuating our crises, we claim that responding in time (lower t) is itself a political act in raising the possibility for more convivial and life-affirming futures.
In 1969, the 50th anniversary of the IAU was marked at two Symposia, in Basel and Brussels. It was a modest way to celebrate, but astronomer’s minds may have been elsewhere. The 1960s were among the most exciting decades in astronomical history.
The 1970s and 1980s are a somewhat ambiguous period for the IAU, characterised by consolidation while waiting for the next great step. Astronomy kept expanding, mainly driven by instrument development. The succession of discoveries of the 1960s, based on the opening of the electromagnetic spectrum, was followed by more detailed and systematic observations in all wavelength ranges. Space-borne instruments became standard parts of the astronomical toolkit. Planetary missions brought the solar system into close view. A range of 4-metre class optical telescopes was opened, which became the workhorses for astronomy in the next decades. At the same time, planning and preparations for a new generation of 8–10-metre size telescopes were started, spearheaded by the experimental 4.5-m Multiple Mirror Telescope.
We study the ground state energy of an atom interacting with an oscillating optical field with electric dipole and quadrupole coupling. Under the rotating wave approximation, we derive the effective atomic Hamiltonians of the dipole/quadrupole coupling term within the perturbation theory up to the second order. Based on the effective Hamiltonians, we analyze the atomic ground-state energy corrections of these two processes in detail. As an application, we find that for alkali-like atoms, the energy correction from the quadrupole coupling is negligible small in comparison with that from the dipole coupling, which justifies the so-called dipole approximation used in literatures. Some special cases where the quadrupole interaction may have considerable energy corrections are also discussed. Our results would be beneficial for the study of atom–light interaction beyond dipole approximation.
We review experimental progress on optical atomic clocks and frequency transfer, and consider the prospects of using these technologies for geodetic measurements. Today, optical atomic frequency standards have reached relative frequency inaccuracies below 10-17, opening new fields of fundamental and applied research. The dependence of atomic frequencies on the gravitational potential makes atomic clocks ideal candidates for the search for deviations in the predictions of Einstein's general relativity, tests of modern unifying theories and the development of new gravity field sensors. In this review, we introduce the concepts of optical atomic clocks and present the status of international clock development and comparison. Besides further improvement in stability and accuracy of today's best clocks, a large effort is put into increasing the reliability and technological readiness for applications outside of specialized laboratories with compact, portable devices. With relative frequency uncertainties of 10-18, comparisons of optical frequency standards are foreseen to contribute together with satellite and terrestrial data to the precise determination of fundamental height reference systems in geodesy with a resolution at the cm-level. The long-term stability of atomic standards will deliver excellent long-term height references for geodetic measurements and for the modelling and understanding of our Earth.
Timekeeping, together with navigation, is one of the oldest missions of astronomy, originating long before the dawn of written history. The ancient and sacred task of timekeeping, linking the eternal with the everyday, stood at the origin of the Vatican Observatory. The history of timekeeping schemes throughout millennia has been a search for a balance between the practical and the symbolic. The current debate focuses on the Leap Second, a mechanism first applied in 1972. Atomic clocks, careful observations of distant quasars, etc. tell us that the Earth spins somewhat irregularly. The symbolic value of coupling civil timekeeping to the heavens is so strong, however, that the international community still requires the International Telecommunication Union to broadcast time signals following Earth’s rotation. In order to reconcile this symbolically significant requirement with the practicality of uniformly flowing atomic time, a leap second is added (or subtracted) from the otherwise perfectly regular sequence, so that every so often there is a minute with 61 (or 59) seconds. This system is currently under review, with a proposal on the table to abandon the leap second, decoupling civil timekeeping from astronomical phenomena. Social mechanisms involved in timekeeping can be studied by examining the historical evidence related to calenders. These lessons may provide a broader context for the leap-second debate and they may shed light on it. Calculated timekeeping does not actually agree with the heavens at any given moment, but this does not seem to jeopardize the general perception of its astronomical conformity since it is rightly perceived as a way of preserving it on average. The current proposal, however, clearly entails decoupling civil time from Earths rotation. If presented as a definitive solution, it would result in a direct and unprecedented breach with the principle of astronomical conformity. If presented as a temporary measure, to be applied until a better solution is found, it would preserve the principle of astronomical conformity because the latter fulfills its social function even when it is not observed perfectly considering that in the realm of symbolism what counts is the general perception, not the fact.
This article offers a short history of the transformation of time signals into a fundamental stability around which new communication infrastructures are built. These infrastructures include the Network Time Protocol, the Global Positioning System, and high-frequency trading. This article argues that “high-resolution time” can serve as a useful analytic framework for understanding the making and appropriation of contemporary temporal standards. Contemporary temporal infrastructures—the systems of time measurement and dissemination that subtend communication infrastructures—are based on the vibrations of caesium atoms, which act as fixed points. A focus on resolution aligns an analysis with the ways that time standards are, in practice, treated as both infrastructures and texts. High-resolution time, therefore, offers an understanding of time as a scalable resource built through contingent media practices.
The increased interest of the public in UTC and the leap second demands popular explanations on its background, practice, and future. This paper gives some hints on how to talk about this matter to different audiences and to journalists. It con-centrates on the following topics: (1) Background: Explaining the difference be-tween the slow increase of the length of day (LOD) with time on the one hand and the rather large frequency of leap seconds on the other hand. (2) Prospects: The future of the time system with and without leap seconds. (3) History: The end of the Earth as the most precise clock around 1935.
This paper was written to commemorate the 50th anniversary of the atomic redefinition of the second in the International System (SI) in 1967. It focuses on the work of individuals and organizations in the United States who made significant contributions to the redefinition of the SI second and helped to establish the era of atomic timekeeping.
Geodesy is the science of the measurement and mapping of the Earth’s surface, and in this context it is also the science that defines and realizes coordinates and associated coordinate systems. Geodesy thus is the foundation for all applications of global navigation satellite system (GNSS
). This chapter presents the reference systems needed to describe coordinates of points on the Earth’s surface or in near space and to relate coordinate systems among each other, as well as to some absolute system, visually, a celestial system. The topic is primarily one of geometry, but the geodynamics of the Earth as a rotating body in the solar system plays a fundamental role in defining and transforming coordinate systems. Therefore, also the fourth coordinate, time, is critical not only as the independent variable in the dynamical theories, but also as a parameter in modern geodetic measurement systems. Instead of expounding the theory of geodynamics and celestial mechanics, it is sufficient for the purpose of this chapter to describe the corresponding phenomena, textually, analytically and illustratively, in order to give a sense of the scope of the tasks involved in providing accurate coordinate reference systems not just to geodesists, but to all geoscientists.
The atmosphere strongly affects the Earth’s spin rotation in wide range of timescale from daily to annual. Its dominant
role in the seasonal perturbations of both the pole position and spinning rate of the Earth is once again confirmed by a
comparison of two recent data sets; i) the Earth orientation parameter and ii) the global atmospheric state. The atmospheric
semi-diurnal tide has been known to be a source of the Earth’s spin acceleration, and its magnitude is re-estimated by
using an enhanced formulation and an up-dated empirical atmospheric S2 tide model. During the last twenty years, an
unusual eastward drift of the Earth’s pole has been observed. The change in the Earth’s inertia tensor due to glacier mass
redistribution is directly assessed, and the recent eastward movement of the pole is ascribed to this change. Furthermore,
the associated changes in the length of day and UT1 are estimated.
Global navigation satellite systems (GNSS) are part of the most complex modern space systems humankind has created, and therefore their orbits, orbital parameters, and their two main terrestrial mappings are firstly described. Different frames of space-time reference systems are treated as part of such descriptions.
Communication systems engineering are important sections to allow for a GNSS precise fix positioning. All signal structures and data streams are treated for a clear understanding permitting the reader to see how ranging is obtained from space.
Theoretical and practical error budgets are considered to give the reader a perception of limitations during scientific and/or technical user campaigns or for simple common life enjoyment.
Commission 4 was among the first set of commissions formed within the IAU at its founding in 1919. (Commissions were originally called “Standing Committees.”) During its 96 years of service to the IAU and astronomical community in general, the commission has been fortunate to have been led by many distinguished scientists — see the list of presidents below.
This paper deals with the factors that influence the weight of an object near the Earth's surface. They are: (1) the Earth's gravitational force, (2) the centrifugal force due to the Earth's diurnal rotation, and (3) tidal forces due to the gravitational field of the Moon and Sun, and other solar system bodies to a lesser extent. Each of these three contributions is discussed and expressions are derived. The relationship between weight and gravitation is thus established in a direct and pedagogical manner readily understandable by undergraduate students. The analysis applies to the Newtonian limit of gravitation. The derivation is based on an experimental (or operational) definition of weight, and it is shown that it coincides with the Earth’s gravitational force modified by diurnal rotation around a polar axis and non-uniformity of external gravitational bodies (tidal term). Two examples illustrate and quantify these modifications, respectively the Eötvös effect and the oceanic tides; tidal forces due to differential gravitation on a spacecraft and an asteroid are also proposed as examples. Considerations about inertia are also given and some comments are made about a widespread, yet confusing, explanation of tides based on a centrifugal force. Finally, the expression of the potential energy of the tide-generating force is established rigorously in the appendix.
In 2008 a fragment of a time‐reckoning device was found at Vindolanda. This fragment has been interpreted as part of an anaphoric water clock. There are important differences between this fragment and other objects thought to come from anaphoric water clocks. This article seeks to reinterpret the fragment in terms of a broader array of Roman time‐reckoning tools than anaphoric water clocks and also in terms of the archaeological context of Vindolanda in which the fragment was found. The emphasis on cultural context in interpreting this fragment reveals much about the temporal consciousness of its possible users and maker.
An architecture and main performance methods of a knowledge support system of ubiquitous time
computation based on relativity are proposed. As main results, modern time theories are described as certain
relations of term-nodes in a tree, and some space-time computation models in a large scale and time computation models in different time measurement systems (institutions) are programmed as interfaces for time computation in complex conditions such as time-anisotropic movement systems or gravity-anisotropic environments.
Iran is a developing country, and nowadays, a demand to establish a time transfer system can be sensed more than anytime. On the other hand, global positioning system (GPS) is one of the most efficient and accurate systems in precise time estimation and dissemination domain. This study aims to investigate the different accuracy limiting effects of a time transfer system in a geodetic point of view. For this purpose, a simulation study is performed in which pseudorange and carrier phase observations are simulated for some
GPS stations in Iran. The baselines for time transfer have been chosen in a way that the maximum effect of each bias source can be analyzed. Therefore, the results of this study can be used in order to design the absolute and relative locations of the GPS stations equipped with external atomic frequencies in Iran considering a specific application. As a result, the most prominent bias source is the site-specific troposphere parameters which produce a variation of more than 1 ns in the time transfer results. Other bias sources including bias in the coordinate components and orbital information have a considerable impact only for time keeping purposes. Additionally, the influence of noise of the carrier phase and pseudo-range observations is
analyzed. Variations of clock estimations between consecutive epochs up to 70 ps and day boundary discontinuities up to 0.6 ns, respectively, are the results of measurement errors. On the other hand, a time transfer between H-masers located at US Naval Observatory and National Resources Canada has been
conducted to pursue a standard and efficient algorithm to deal with the problem of day boundary jumps. The method of overlapping batches with 12 h coverage of each of the involved days is applied to overcome this problem. The results of this method show a considerable decrease in the magnitude of the day boundary jumps.
The algorithms for relativistic time transfer in the vicinity of the Earth and in the solar system are derived. The concepts of proper time and coordinate time are distinguished. The coordinate time elapsed during the transport of a clock and the propagation of an electromagnetic signal is analysed in three coordinate systems: an Earth-Centred Inertial (ECI) coordinate system, an Earth-Centred Earth-Fixed (ECEF) coordinate system and a barycentric coordinate system. The timescales of Geocentric Coordinate Time (TCG), Terrestrial Time (TT) and Barycentric Coordinate Time (TCB) are defined and their relationships are discussed. Some numerical examples are provided to illustrate the magnitudes of the effects.
By means of a simple mathematical model developed by the authors, the apparent
movement of the Sun can be studied for arbitrary latitudes. Using this model, it is easy to
gain insight into various phenomena, such as the passage of the seasons, dependences of
position and time of sunrise or sunset on a specific day of year, day duration for different
latitudes and seasons, and time dependence of the solar altitude reckoned from the
horizontal plane. We present simulations of the Sun path alongside animated data. We
show that the model adopted can also be used to explain the principle of a horizontal
sundial and to determine shadow areas. We give recommendations as regards
how to build energy-effective houses and how to optimize solar cell positions.
Astronomy has provided a means to mark the passage of time throughout history. One of the repeating phenomena that makes this possible is the Earth's rotation. The basic variability in its rotational speed, however, makes astronomical techniques unsuitable for timekeeping with the precision required for modern applications. Physical metrology from the first mechanical clocks to the most sophisticated atomic standards of today has assumed a growing role in timekeeping. Along with this progress in technology, more sophisticated concepts of timescales have appeared to take advantage of those improvements.
Before the invention of atomic clocks, the second was defined by dividing the period of an astronomical event into a shorter time interval. For example, the second was once defined by dividing the average period of one revolution of the Earth on its axis. The mean solar second was equal to 1/86,400 of the mean solar day. To create a more stable unit of time interval, the second was redefined in 1956 as 1/31,556,925.9747 of the tropical year 1900. The ephemeris second was indeed more stable than the mean solar second but was nearly impossible to use as a time reference and of little use to metrologists or engineers. In retrospect, it seems almost ridiculous that another astronomical definition of the second was accepted during a period when atomic clocks were already being built [1], [2]. A clean transition from the mean solar second to the atomic second would have made more sense. Doomed from the start, the ephemeris second would be easy to forget about except for one thing – it became the comparison reference for the atomic second.
Short-period high-amplitude pulsating stars of Population I ( Sct stars) and II (SX Phe variables) exist in the lower part of the classical (Cepheid) instability strip. Most of them have very simple pulsational behaviours, only one or two radial modes being excited. Nevertheless, BL Cam is a unique object among them, being an extreme metal-deficient field high-amplitude SX Phe variable with a large number of frequencies. Based on a frequency analysis, a pulsational interpretation was previously given. aims heading (mandatory) We attempt to interpret the long-term behaviour of the residuals that were not taken into account in the previous Observed-Calculated (O-C) short-term analyses. methods heading (mandatory) An investigation of the O-C times has been carried out, using a data set based on the previous published times of light maxima, largely enriched by those obtained during an intensive multisite photometric campaign of BL Cam lasting several months. results heading (mandatory) In addition to a positive (161 3) x 10 yr secular relative increase in the main pulsation period of BL Cam, we detected in the O-C data short- (144.2 d) and long-term ( 3400 d) variations, both incompatible with a scenario of stellar evolution. conclusions heading (mandatory) Interpreted as a light travel-time effect, the short-term O-C variation is indicative of a massive stellar component (0.46 to 1 M_{\sun}) with a short period orbit (144.2 d), within a distance of 0.7 AU from the primary. More observations are needed to confirm the long-term O-C variations: if they were also to be caused by a light travel-time effect, they could be interpreted in terms of a third component, in this case probably a brown dwarf star ( 0.03 \ M_{\sun}), orbiting in 3400 d at a distance of 4.5 AU from the primary. Comment: 7 pages, 5 figures, accepted for publication in A&A
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