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EN
The article describes in an accessible, conceptual way various types of relativistic effects, which are an important part of modern chemical education, practically absent in textbooks, however allowing for a better understanding of the properties of chemical elements and their compounds. This description was preceded by a concise non-relativistic characterization of electrons in multi-electron atoms, in terms of radial probability densities, in order to explain the dependence of electron energies on the principal (n) and orbital (l) quantum numbers. The results of recent quantum chemical calculations are discussed, which show the improved energy sequence of ns and (n-1)d orbitals in transition elements and explain the electron configurations of both neutral atoms and cations of the 3d and 4d block elements. The description of the relativistic effects begins with early Dirac concept of spin-orbit coupling as causing the splitting of the degenerate p, d and f orbitals for two sets of spinors. The role of this splitting in the stability of the respective oxidation states of the cations is discussed. Another important type of relativistic effects, confirmed only in the 1970s, operates in atoms of high nuclear charge (starting from 6. period) in which electrons move at a speed close to the speed of light. The resulting relativistic increase in the mass of the moving electron causes the stabilization of s and p orbitals, and destabilization of d and f orbitals. Representative examples of the influence of all relativistic effects on the properties of elements and their compounds are given (including mercury liquidity or the color of gold). In particular, relativistic effects specific for blocks 5d, 6p, 4f, 5f, 6d, and 7p were discussed. The possibilities of predicting further expansion of the periodic table with elements up to the atomic number of about 170 are outlined, based on taking into account both the relativistic effects for electrons and the stability of superheavy atomic nuclei. The article is addressed to chemists of all branches of this discipline.
EN
We present a summary of research carried out in 2019–2022 in Poland in the area of general theory and methodology in geodesy. The study contains a description of original contributions by authors affiliated with Polish scientific institutions. It forms part of the national report presented at the 28th General Assembly of the International Union of Geodesy and Geophysics (IUGG) taking place on 11-20 July 2023 in Berlin, Germany. The Polish authors developed their research in the following thematic areas: robust estimation and its applications, prediction problems, cartographic projections, datum transformation problems and geometric geodesy algorithms, optimization and design of geodetic networks, geodetic time series analysis, relativistic effects in GNSS (Global Navigation Satellite System) and precise orbit determination of GNSS satellites. Much has been done on the subject of estimating the reliability of existing algorithms, but also improving them or studying relativistic effects. These studies are a continuation of work carried out over the years, but also they point to new developments in both surveying and geodesy.We hope that the general theory and methodology will continue to be so enthusiastically developed by Polish authors because although it is not an official pillar of geodesy, it is widely applicable to all three pillars of geodesy.
EN
The effect of the geodetic rotation (which includes two relativistic effects: geodetic precession and geodetic nutation) is the most significant relativistic effect in the rotation of the celestial bodies. For the first time in this research, this relativistic effect is determined in the rotation of dwarf planets (Ceres, Pluto, and Charon) and asteroids (Pallas, Vesta, Lutetia, Europa, Ida, Eros, Davida, Gaspra, Steins, and Itokawa) in the Solar System with known values of their rotation parameters. Calculations of the values of their geodetic rotation are made by a method for studying any bodies in the Solar System with a long-term ephemeris. Values of geodetic precession and geodetic nutation for all these celestial bodies were calculated in ecliptic Euler angles relative to their proper coordinate systems and in their rotational elements relative to the fixed equator of the Earth and the vernal equinox (at the epoch J2000.0). The obtained analytical values of the geodetic rotation for the celestial bodies can be used to numerically investigate their rotation in the relativistic approximation, and also used to estimate the influence of relativistic effects on the orbital–rotational dynamics for the bodies of exoplanetary systems.
EN
The effect of the geodetic precession is the most significant relativistic effect in the rotation of celestial bodies. In this article, the new geodetic precession values for the Sun, the Moon, and the Solar System planets have been improved over the previous version by using more accurate rotational element values. For the first time, the relativistic effect of the geodetic precession for some planetary satellites (J1-J4, S1-S6, S8-S18, U1-U15, N1, and N3-N8) with known quantities of the rotational elements was studied in this research. The calculations of the values of this relativistic effect were carried out by the method for studying any bodies of the Solar System with long-time ephemeris. As a result, the values of the geodetic precession were first determined for the Sun, planets in their rotational elements, and for the planetary satellites in the Euler angles relative to their proper coordinate systems and in their rotational elements. In this study, with respect to the previous version, additional and corrected values of the relativistic influence of Martian satellites (M1 and M2) on Mars were calculated. The largest values of the geodetic rotation of bodies in the Solar System were found in Jovian satellite system. Further, in decreasing order, these values were found in the satellite systems of Saturn, Neptune, Uranus, and Mars, for Mercury, for Venus, for the Moon, for the Earth, for Mars, for Jupiter, for Saturn, for Uranus, for Neptune, and for the Sun. First of all, these are the inner satellites of Jupiter: Metis (J16), Adrastea (J15), Amalthea (J5), and Thebe (J14) and the satellites of Saturn: Pan (S18), Atlas (S15), Prometheus (S16), Pandora (S17), Epimetheus (S11), Janus (S10), and Mimas (S1), whose values of geodetic precession are comparable to the values of their precession. The obtained numerical values for the geodetic precession for the Sun, all the Solar System planets, and their satellites (E1, M1, M2, J1-J5, J14-J16, S1-S6, S8–S18, U1-U15, N1, and N3-N8) can be used to numerically study their rotation in the relativistic approximation and can also be used to estimate the influence of relativistic effects on the orbital-rotational dynamics of bodies of exoplanetary systems.
EN
The most significant relativistic effects (the geodetic precession and the geodetic nutation, which consist of the effect of the geodetic rotation) in the rotation of Jupiter's inner satellites were investigated in this research. The calculations of the most essential secular and periodic terms of the geodetic rotation were carried out by the method for studying any bodies of the solar system with long-time ephemeris. As a result, for these Jupiter’s satellites, these terms of their geodetic rotation were first determined in the rotational elements with respect to the International Celestial Reference Frame (ICRF) equator and the equinox of the J2000.0 and in the Euler angles relative to their proper coordinate systems. The study shows that in the solar system there are objects with significant geodetic rotation, due primarily to their proximity to the central body, and not to its mass.
EN
Study of the trajectories of the motion of satellites remains an urgent task for modern science. This is especially true for GNSS systems and for satellites intended for Earth remote sensing. The basis of their operation is to accurately determine the position of the satellite, and the parameters of signal propagation. Considering the great distances and speeds of both satellites and the Earth in calculating these parameters, it is necessary to take into account the special and general theory of relativity. In the article formulas have been derived for calculating additional corrections for relativistic effects. A mathematical model for calculating the metric tensor was created. A sequence of correction was also proposed.
EN
Position determination of Global Navigation Satellite Systems (GNSS) depends on the stability and accuracy of the measured time. However, since satellite vehicles (SVs) travel at velocities significantly larger than the receivers and, more importantly, the electromagnetic impulses propagate through changing gravitational potentials, enormous errors stemming from relativity-based clock offsets would cause a position error of about 11 km to be accumulated after one day. Based on the premise of the constancy of light, two major relativistic effects are described: time dilation and gravitational-frequency shift. Following the individual interests of the author, formulas of both are scrupulously derived from general- and special-relativity theory principles; moreover, in the penultimate section, the equations are used to calculate the author’s own numerical values of the studied parameters for various GNSSs and one Land Navigation Satellite System (LNSS).
EN
Complexes of alkali atoms with ammonium have been studied using the Denity Functional Theory with nonlocal and quasi-relativistic corrections. The stable complexes were found for allalkali atom–ammonia complexes. The calculated interaction energies decrease as one progresses down the periodic table and are in range from –18.9 kcal/mol for lithium system up to –6.5 kcal/mol for the frans complex. Similar tendency is noted for the calculated values of charge transfer. The influence of calculated quasi-relativistic (QR) corrections on values of interaction energies is determined. The QR corrections have no effect on lithium complexes whereas reduce the binding energy from 0.1 kcal/mol for Na system up to 0.9 kcal/mol for Fr complex. The DFT calculated IR harmonic frequencies are compared with experimental values and discussed. The calculated vibrational freuencies of ammonia in complexes exhibit trends that for all systems they are parallel to the strength of the bind ing energies. For the H3N–Li complex the vibrational analysis was supported by an harmonic calculations at the MP2 level. It has been shown that there is a discrepancy between the experimental assignment and MP2 harmonic and an harmonic low frequency intermolecular modes.
PL
Efekty relatywistyczne stały się powodem rozróżnienia pomiędzy czasem własnym i czasem koordynatowym. Metryka Minkowskiego czasoprzestrzeni pozwala stwierdzić wydłużenie czasu w przemieszczających się układach inercjalnych. Geometria czasoprzestrzeni Riemanna indentyfikuje wpływ potencjału grawitacyjnego i dośrodkowego na bieg czasu oraz efekt Sagnaca. Przedyskutowano synchronizację koordynatową zegarów.
EN
Relativistic effects forced the introducing of differentiation between proper and coordinate time. Spacetime of Minkowski metric makes it possible to investigate time dilation in moving inertial frames. Riemann's geometry of spacetime identifies the influence of gravitational and centrifugal potentials on time as well as Sagnac effect. Coordinate synchronization of clocks is discussed.
PL
Opisano metodę otrzymywania istotnego dla telekomunikacji umownego uniwersalnego czasu międzynarodowego TAI, uniwersalnego czasu ziemskiego, rolę satelitarnych systemów nawigacyjnych do przesyłania wzorca czasu i perspektywy rozwoju miar czasu.
EN
The methods of the Coordinated Universal Time UTC and the Universal Earth Time UT1 calculations has been presented. The satellite navigation systems time delivery problems are noticed and the future development of these systems.
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