Secular tidal changes in lunar orbit and Earth rotation

Small tidal forces in the Earth–Moon system cause detectable changes in the orbit. Tidal energy dissipation causes secular rates in the lunar mean motion n, semimajor axis a, and eccentricity e. Terrestrial dissipation causes most of the tidal change in n and a, but lunar dissipation decreases eccentricity rate. Terrestrial tidal dissipation also slows the rotation of the Earth and increases obliquity. A tidal acceleration model is used for integration of the lunar orbit. Analysis of lunar laser ranging (LLR) data provides two or three terrestrial and two lunar dissipation parameters. Additional parameters come from geophysical knowledge of terrestrial tides. When those parameters are converted to secular rates for orbit elements, one obtains dn/dt = \(-25.97\pm 0.05 ''/\)cent\(^{2}\), da/dt = 38.30 ± 0.08 mm/year, and di/dt = ?0.5 ± 0.1 \(\upmu \)as/year. Solving for two terrestrial time delays and an extra de/dt from unspecified causes gives \(\sim \) \(3\times 10^{-12}\)/year for the latter; solving for three LLR tidal time delays without the extra de/dt gives a larger phase lag of the N2 tide so that total de/dt = \((1.50 \pm 0.10)\times 10^{-11}\)/year. For total dn/dt, there is \(\le \)1 % difference between geophysical models of average tidal dissipation in oceans and solid Earth and LLR results, and most of that difference comes from diurnal tides. The geophysical model predicts that tidal deceleration of Earth rotation is \(-1316 ''\)/cent\(^{2}\) or 87.5 s/cent\(^{2}\) for UT1-AT, a 2.395 ms/cent increase in the length of day, and an obliquity rate of 9 \(\upmu \)as/year. For evolution during past times of slow recession, the eccentricity rate can be negative.     

Line-of-Sight Anisotropies in the Cosmic Dawn and Epoch of Reionization 21-cm Power Spectrum

The line-of-sight direction in the redshifted 21-cm signal coming from the cosmic dawn and the epoch of reionization is quite unique in many ways compared to any other cosmological signal. Different unique effects, such as the evolution history of the signal, non-linear peculiar velocities of the matter etc. will imprint their signature along the line-of-sight axis of the observed signal. One of the major goals of the future SKA-LOW radio interferometer is to observe the cosmic dawn and the epoch of reionization through this 21-cm signal. It is thus important to understand how these various effects affect the signal for its actual detection and proper interpretation. For more than one and half decades, various groups in India have been actively trying to understand and quantify the different line-of-sight effects that are present in this signal through analytical models and simulations. In many ways the importance of this sub-field under 21-cm cosmology have been identified, highlighted and pushed forward by the Indian community. In this article, we briefly describe their contribution and implication of these effects in the context of the future surveys of the cosmic dawn and the epoch of reionization that will be conducted by the SKA-LOW.     

Splendid isolation: local uniqueness of the centered co-circular relative equilibria in the <Emphasis Type="Italic">N</Emphasis>-body problem

We study the neighborhood of the equal mass regular polygon relative equilibria in the N-body probem, and show that this relative equilibirum is isolated among the co-circular configurations (in which each point lies on a common circle) for which the center of mass is located at the center of the common circle. It is also isolated in the sense that a sufficiently small mass cannot be added to the common circle to form a \(N+1\)-body relative equilibrium. These results provide strong evidence for a conjecture that the equal mass regular polygon is the only co-circular relative equilibrium with its center of mass located at the center of the common circle.     

The equations of relative motion in the orbital reference frame

The analysis of relative motion of two spacecraft in Earth-bound orbits is usually carried out on the basis of simplifying assumptions. In particular, the reference spacecraft is assumed to follow a circular orbit, in which case the equations of relative motion are governed by the well-known Hill–Clohessy–Wiltshire equations. Circular motion is not, however, a solution when the Earth’s flattening is accounted for, except for equatorial orbits, where in any case the acceleration term is not Newtonian. Several attempts have been made to account for the \(J_2\) effects, either by ingeniously taking advantage of their differential effects, or by cleverly introducing ad-hoc terms in the equations of motion on the basis of geometrical analysis of the \(J_2\) perturbing effects. Analysis of relative motion about an unperturbed elliptical orbit is the next step in complexity. Relative motion about a \(J_2\)-perturbed elliptic reference trajectory is clearly a challenging problem, which has received little attention. All these problems are based on either the Hill–Clohessy–Wiltshire equations for circular reference motion, or the de Vries/Tschauner–Hempel equations for elliptical reference motion, which are both approximate versions of the exact equations of relative motion. The main difference between the exact and approximate forms of these equations consists in the expression for the angular velocity and the angular acceleration of the rotating reference frame with respect to an inertial reference frame. The rotating reference frame is invariably taken as the local orbital frame, i.e., the RTN frame generated by the radial, the transverse, and the normal directions along the primary spacecraft orbit. Some authors have tried to account for the non-constant nature of the angular velocity vector, but have limited their correction to a mean motion value consistent with the \(J_2\) perturbation terms. However, the angular velocity vector is also affected in direction, which causes precession of the node and the argument of perigee, i.e., of the entire orbital plane. Here we provide a derivation of the exact equations of relative motion by expressing the angular velocity of the RTN frame in terms of the state vector of the reference spacecraft. As such, these equations are completely general, in the sense that the orbit of the reference spacecraft need only be known through its ephemeris, and therefore subject to any force field whatever. It is also shown that these equations reduce to either the Hill–Clohessy–Wiltshire, or the Tschauner–Hempel equations, depending on the level of approximation. The explicit form of the equations of relative motion with respect to a \(J_2\)-perturbed reference orbit is also introduced.     

Uncertainty propagation in orbital mechanics via tensor decomposition

Uncertainty forecasting in orbital mechanics is an essential but difficult task, primarily because the underlying Fokker–Planck equation (FPE) is defined on a relatively high dimensional (6-D) state–space and is driven by the nonlinear perturbed Keplerian dynamics. In addition, an enormously large solution domain is required for numerical solution of this FPE (e.g. encompassing the entire orbit in the \(x-y-z\) subspace), of which the state probability density function (pdf) occupies a tiny fraction at any given time. This coupling of large size, high dimensionality and nonlinearity makes for a formidable computational task, and has caused the FPE for orbital uncertainty propagation to remain an unsolved problem. To the best of the authors’ knowledge, this paper presents the first successful direct solution of the FPE for perturbed Keplerian mechanics. To tackle the dimensionality issue, the time-varying state pdf is approximated in the CANDECOMP/PARAFAC decomposition tensor form where all the six spatial dimensions as well as the time dimension are separated from one other. The pdf approximation for all times is obtained simultaneously via the alternating least squares algorithm. Chebyshev spectral differentiation is employed for discretization on account of its spectral (“super-fast”) convergence rate. To facilitate the tensor decomposition and control the solution domain size, system dynamics is expressed using spherical coordinates in a noninertial reference frame. Numerical results obtained on a regular personal computer are compared with Monte Carlo simulations.     

Single-binary star separation by ultraviolet color index diagrams

Detection of a composite flux in photometry can serve as an indication of a photometrically unresolved binarity and can contribute to the parameterization of the components of binary systems. A main goal of the present study is to develop a method of automatic photometric detection of binaries, based on multi-color photometry, theoretical stellar spectral energy distributions and general understanding of binary evolution. In particular, we consider an ultraviolet photometry where, in combination with optical and infrared photometry, interstellar reddening can be easier distinguished from temperature reddening.     

Sixty Years in Solar Physics

I recount my career in solar physics beginning at Ondřejov Observatory in 1948 and ending with my ∼30 year stay at the Laboratory of Space Research in Utrecht.     

Integrated stratigraphy and 40Ar/39Ar chronology of the early to middle Miocene Upper Freshwater Molasse in western Bavaria (Germany)

A detailed integrated stratigraphic study (biostratigraphy and magnetostratigraphy) was carried out on five sections from the western part of the Bavarian Upper Freshwater Molasse of the North Alpine Foreland Basin (NAFB), greatly improving the chronostratigraphy of these sediments. The sections belong to the lithostratigraphic units Limnische Untere Serie (UL) and Fluviatile Untere Serie (UF) and contain 19 (mostly new) small-mammal bearing levels, significantly refining the local biostratigraphy. Radiometric ages obtained from glass shards from tuff horizons are used together with the biostratigraphic information for constructing and confirming the magnetostratigraphic correlation of the studied sections to the Astronomical Tuned Time Scale (ANTS04; Lourens et al. in Geologic Time Scale 2004, Cambridge University Press, 2004). This correlation implies that the UL lithostratigraphic unit corresponds to the latest Ottnangian and the Early Karpatian, whereas the UF corresponds to the Karpatian and the Early Badenian. This indicates that the Brackish- to Freshwater Molasse transition already occurred during the late Ottnangian. The pre-Riesian hiatus occurred in the latest Karpatian and lower Early Badenian in Eastern Bavaria and Bohemia and in the Late Karpatian and earliest Badenian in Western Bavaria. The geochemical and Ar–Ar data of volcanic ashes suggest that highly evolved silicic magmas from a single volcano or volcanic center, characterized by a uniform Nd isotopic composition, erupted repetitively over the course of at least 1.6 Myr. Three phases of eruptive activity were identified at 16.1 ± 0.2 Ma (Zahling-2), 15.6 ± 0.4 Ma (Krumbad), and 14.5 ± 0.2 Ma (Heilsberg, Hegau). The correlation of the local biostratigraphic zonation to the ANTS04 enables further the characterization of both the Ottnangian–Karpatian and Karpatian–Badenian boundaries in the NAFB by small-mammal biostratigraphy. According to these results the Ottnangian–Karpatian boundary is contemporaneous with the first appearance datum of Megacricetodon bavaricus (in the size of the type population) and the first common occurrence of Keramidomys thaleri, whereas Ligerimys florancei, Melissiodon dominans and Prodeinotherium aff. bavaricum have been already disappeared during the late Ottnangian. The Karpatian–Badenian boundary is characterized by a significant size increase of the large Megacricetodon lineage and possibly a (re-)immigration of Prodeinotherium bavaricum.     

Complex system approach to interpretation of monitoring time series: two case histories from NW Bohemia

Ever wider implementation of information technologies is flooding us by monitoring data. To an efficient risk management, those data have to be processed and assessed in the same rate as they are recorded and transported. Paper demonstrates some methods dealing with intrinsic, nonlinear dynamics of slope system for computerized safety assessment of monitoring time series, their modeling and early warning launching. Analysis and modeling of phase changes – i.e. specific transient states between different developmental stages of dynamics of unstable slope systems, enabled to fix new types of precursors for rock fall warning and to enhance time prediction of rock fall occurrence. Mathematically well based, novel numerical and topological methods from the toolbox of complex system theory were successfully implemented to that challenge. Their pattern-recognition ability, i.e., diagnostic sensitivity, and more realistic results of modeling of time series relevant patterns have reached beyond ranges of regularly used—both the idea- and the data-driven—methods. Moreover, results yielded by phase space analyses are in good agreement with the ones by numerical fractal analyses. Obtained results have strengthened the primary, mainly theoretically based hypothesis; the dynamics of an unstable rock slope has to be considered as behavior of nonlinear, dissipative, non-equilibrium, self-organizing complex system. Correspondingly to the theoretical assumptions, two qualitatively different types of slope system dynamics—near to equilibrium and far from equilibrium states, were identified. All field monitoring data used originated in practice of highly automated, integrated IT system of monitoring assessment, and management of rock fall hazard at sandstone rock walls in the NW Bohemia.     

Isolation of protoplasts from <Emphasis Type="Italic">undaria pinnatifida</Emphasis> by alginate lyase digestion

The aim of this study is to isolate protoplasts from Undaria pinnatifida. Protoplasts of the alga were isolated enzymatically by using alginate lyase, which was prepared by fermenting culture of a strain Vibrio sp. 510. Monofacterial method was applied for optimizing digestion condition. The optimum condition for protoplast preparation is enzymatic digestion at 28°C for 2h using alginate lyase at the concentration of 213.36 U (8 mL) every 0.5g fresh thalline with NaCl 50 and at the shaking speed of 150 r min⁻¹ during digestion. The protoplast yield can reach 2.62±0.09 million per 0.5 g fresh leave under the optimum condition. The enzyme activity is inhibited by Ca²⁺ and slightly enhanced by Fe²⁺ and Mn²⁺ at concentrations of 0.05, 0.08 and 0.10 mol L⁻¹.