Broad search for unstable resonant orbits in the planar circular restricted three-body problem

Unstable resonant orbits in the circular restricted three-body problem have increasingly been used for trajectory design using optimization and invariant manifold techniques. In this study, several methods for computing these unstable resonant orbits are explored including grid searches, flyby maps, and continuation. Families of orbits are computed focusing on orbits with multiple loops near the secondary in the Jupiter–Europa system, and their characteristics are explored. Different parameters such as period and stability are examined for each set of resonant orbits, and the continuation of several specific orbits is explored in more detail.     

Über die Verteilung der aus Gezeitenbeobachtungen bestimmten gravimetrischen Faktoren in Europa

auamaumuu am, n u a¶rt;u nuu n ¶rt;a ₂, ₂, ₁ u ₁ (u. 1–4). na ¶rt;a ¶rt;am au ¶rt;um au an¶rt;u mu naam. a n¶rt;aam unam nu nuu nna m uu u u mmu mam ¶rt; uu u a a mau n.

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Vorgetragen am 2. Internationalen Symposium Geodäsie und Physik der Erde, Potsdam, Mai 1973.     

Non-Linear Theory and Power-Law Models for Information Integration and Mineral Resources Quantitative Assessments

Singular physical or chemical processes may result in anomalous amounts of energy release or mass accumulation that, generally, are confined to narrow intervals in space or time. Singularity is a property of different types of non-linear natural processes including cloud formation, rainfall, hurricanes, flooding, landslides, earthquakes, wildfires, and mineralization. The end products of these non-linear processes can be modeled as fractals or multifractals. Hydrothermal processes in the Earth’s crust can result in ore deposits characterized by high concentrations of metals with fractal or multifractal properties. Here we show that the non-linear properties of the end products of singular mineralization processes can be applied for prediction of undiscovered mineral deposits and for quantitative mineral resource assessment, whether for mineral exploration or for regional, national and global planning for mineral resource utilization. In addition to the general theory and framework for the non-linear mineral resources assessment, this paper focuses on several power-law models proposed for characterizing non-linear properties of mineralization and for geoinformation extraction and integration. The theories, methods, and computer system discussed in this paper were validated using a case study dealing with hydrothermal Au mineral potential in southern Nova Scotia, Canada.     

Errors and correction of precipitation measurements in China

In order to discover the range of various errors in Chinese precipitation measurements and seek a correction method, 30 precipitation evaluation stations were set up countrywide before 1993. All the stations are reference stations in China. To seek a correction method for wind-induced error, a precipitation correction instrument called the ＂horizontal precipitation gauge＂ was devised beforehand. Field intercomparison observations regarding 29,000 precipitation events have been conducted using one pit gauge, two elevated operational gauges and one horizontal gauge at the above 30 stations. The range of precipitation measurement errors in China is obtained by analysis of intercomparison measurement results. The distribution of random errors and systematic errors in precipitation measurements are studied in this paper. A correction method, especially for wind-induced errors, is developed. The results prove that a correlation of power function exists between the precipitation amount caught by the horizontal gauge and the absolute difference of observations implemented by the operational gauge and pit gauge. The correlation coefficient is 0.99. For operational observations, precipitation correction can be carried out only by parallel observation with a horizontal precipitation gauge. The precipitation accuracy after correction approaches that of the pit gauge. The correction method developed is simple and feasible.     

Surface and groundwater quality characterization of Deoria District,Ganga Plain,India

A water quality investigation was carried out in the Deoria district, Ganga plain, to assess the suitability of surface and groundwaters for domestic, agricultural, and industrial purposes. As much as 50 representative samples from river and groundwater were collected from various stations to monitor the water chemistry of various ions, comprising Ca²⁺, Mg²⁺, Na⁺, K⁺, HCO₃ ⁻, SO₄ ²⁻, NO₃ ⁻, Cl⁻, F⁻, and trace metals, such as Fe, Cu, Mn, Zn, Cd, and Pb. The results showed that electrical conductance (EC), total dissolved solids (TDS), HCO₃ ⁻, Mg²⁺, Na⁺, and total hardness (TH) are above the maximum desirable limit, and apart from Fe and Mn all other trace metals are within the maximum permissible limit for drinking water. The calculated values for sodium absorption ratio (SAR), salinity, residual sodium carbonate (RSC), and permeability index (PI) indicate well to permissible use of water for irrigation. High values of Na%, RSC, and Mg-hazard (MH) at some stations restrict its use for agricultural purpose. Anthropogenic activities affect the spatial variation of water quality. Economic and social developments of the study area is closely associated with the characteristics of the hydrological network.     

Assessment of rock slope stability by probabilistic-based Slope Stability Probability Classification method along highway cut slopes in Adilcevaz-Bitlis (Turkey)

Rock slope stability is of great concern along highway routes as stability problems on cut slopes may cause fatal events as well as loss of property. In rock slope engineering, stability evaluations are commonly performed by means of analytical or numerical analyses, principally considering the factor of safety concept. As a matter of fact, the probabilistic assessment of slope stability is progressively getting popularity due to difficulties in assigning the most appropriate values to design parameters in analytical or numerical methods. Additionally, the effect of heterogeneities in rock masses and discontinuities on the analysis results is minimized through the probabilistic concept. In this study, slope stability of high and steep sedimentary rock cut slopes along a state highway in Adilcevaz-Bitlis (Turkey) was evaluated on the basis of probabilistic approach using the Slope Stability Probability Classification (SSPC) system. The probabilistic assessment indicates major slope stability problems because of discontinuity controlled and discontinuity orientation independent mass movements. Almost all studied cut slopes suffer from orientation-independent stability problems with very low stability probabilities. Additionally, the probability of planar and toppling failures is significantly high with respect to the SSPC system. The stability problems along the investigated rock slopes were also verified by field reconnaissance. Remedial measures such as slope re-design and reinforcement at the studied locations should be taken to prevent hazardous events along the highway. On the other hand, the probabilistic approach may be a useful tool during rock slope engineering to overcome numerous uncertainties when probabilistic and analytic results are compared.     

On the convective instability of finitely conducting viscous model chromosphere

The convective stability of a simple model chromosphere, consisting of protons, electrons and hydrogen atoms in the ground state, has been studied in the presence of a vertically upward uniform magnetic field to include the effects of FLR, Hall-currents, finite conductivity and ionization. The ionization in the chromosphere is collisional and the recombination is radiative. It is found that the Schwarzchild criterion should necessarily be satisfied for the stability together with the condition thatv > 2v ₀, where is kinematic viscosity andv ₀ is gyroviscosity. Some special cases have also been investigated.     

Misconceptions about the Hubble recession law

Almost all astronomers now believe that the Hubble recession law was directly inferred from astronomical observations. It turns out that this common belief is completely false. Those models advocating the idea of an expanding universe are ill-founded on observational grounds. This means that the Hubble recession law is really a working hypothesis. One alternative to the Hubble recession law is the tired-light hypothesis originally proposed by Zwicky (Proc. Nat. Acad. Sci. 15:773, 1929). This hypothesis leads to a universe that is an eternal cosmos continually evolving without beginning or end. Such a universe exists in a dynamical state of virial equilibrium. Observational studies of the redshift-magnitude relation for Type Ia supernovae in distant galaxies might provide the best observational test for a tired-light cosmology. The present study shows that the model Hubble diagram for a tired-light cosmology gives good agreement with the supernovae data for redshifts in the range 0<z<2. This observational test of a static cosmology shows that the real universe is not necessarily undergoing expansion nor acceleration. An erratum to this article can be found at     

Nature of the small main belt Asteroid 3169 Ostro

We present a set of rotational lightcurve measurements of the small main belt Asteroid 3169 Ostro. Our observations reveal an unambiguous, double-peaked rotational lightcurve with a peak-to-peak variation up to 1.2±0.05 mag and a synodic period of 6.509±0.001 h. From the large flux variation and the overall shape of the lightcurves, we suggest that 3169 Ostro could be a tightly bound binary or a contact binary, similar to the Trojan Asteroid 624 Hektor. A shape model of this system is proposed on the assumption that 3169 Ostro is a Roche binary described by a pair of homogeneous elongated bodies, with a size ratio of 0.87, in hydrostatic equilibrium and in circular synchronous motion around each other. The direction of the spin axis is determined modulo 180° by its J2000 ecliptic coordinates λ₀=50±10°, β₀=±54±5°. The binary interpretation and the pole solution adequately fit the earlier photometric observations made in 1986 and 1988. However, additional supporting lightcurves are highly desirable especially in the next mutual events occurrence of 2008 and 2009 in order to remove the pole ambiguity and to confirm unambiguously the binary nature of 3169 Ostro.