Determination of secular terms in general planetary theory

A method to calculate secular terms of the two parts of the planetary disturbing function— when it is expressed in terms of the true anomalies or the eccentric anomalies instead of the mean anomalies - is described. Also an alternative method is outlined.     

Fourier analysis of the light curves of eclipsing variables,XV

A new general expression for the theoretical momentsA _2m of the light curves of eclipsing systems has been presented in the form of infinite series expansion. In this expansion, the terms have been given as the product of two different polynomials which satisfy certain three-term recursion formulae, and the coefficients diminish rapidly with increasing number of terms. Thus, the numerical values of the theoretical momentsA _2m can be generated recursively up to four significant figures for any given set of eclipse elements. This can be utilized to solve the eclipse elements in two ways: (i) with an indirect method (for the procedures see Paper XIV, Kopal and Demircan, 1978), (ii) with a direct method as minimization to the observational momentsA _2m (area fitting). The procedures given in Paper XIV for obtaining the elements of any eclipsing system consisting of spherical stars have been automated by making use of the new expression for the momentsA _2m of the light curves. The theoretical functionsf ₀,f ₂,f ₄,f ₆,g ₂ andg ₄ which are the functions ofa andc ₀, have been used to solve the eclipse elements from the observed photometric data. The closed-form expressions for the functionsf ₂,f ₄ andf ₆ have also been derived (Section 3) in terms of Kopal'sI-integrals.The automated methods for obtaining the eclipse elements from one minimum alone have been tested on the light curves of YZ (21) Cassiopeiae under the spherical model assumptions. The results of these applications will be given in Section 5 which follows a brief introduction to the procedure we followed.     

Expansion of the planetary mutual distance raised to any negative power by the method of symbolic differential operators

We present a literal approach to evaluate ^–s necessary for the construction of high order planetary theories. This approach is valid to be applied on very large scale digital computers with standard Poisson series programs, for high order and high degree planetary theories. We apply the method of symbolic differential operators for single variable functions, and the binomial theorem expansions, for the evaluation of ^–s . We utilize Laplace coefficients and its derivatives to carry out the development, without dealing with Newcomb operators or Hansen's coefficients.     

On the elimination of the critical term in a general first-order Uranus-Neptune theory

A solution of the Uranus-Neptune planetary canonical equations of motion through the Von Zeipel technique is presented. A unique determinging function which depends upon mixed canonical variables, reduces the 12 critical terms of the Hamiltonian to the set of its secular terms. The Poincaré canonical variables are used. We refer to a common fixed plane, and apply the Jacobi-Radau set of origins. In our expansion we neglected terms of power higher than the fourth with respect to the eccentricities and sines of the inclinations.     

The expansion of negative powers of mutual distance between two planets

In this part we obtain the expression for ^–s by the application of Smart's method, which involves Taylor's theorem for functions of several variables. We neglected terms of power higher than the fourth with respect to eccentricities and tangents of inclinations.     

The elimination of the critical terms of a first order Uranus-Neptune theory through Hori's method

An outline for the elimination of the critical terms of a first order Uranus-Neptune theory is presented with a stress on the application of Hori's procedure to the problem.     

First-order secular planetary theory up to fourth power in eccentricities and inclinations

We construct a first-order secular general planetary theory, using the Jacobi-Radau set of origins, referring to common fixed plane and in terms of Poincaré canonical variables. We neglect powers higher than the fourth with respect to the eccentricities and sines of inclinations.     

A Detached Binary System V505 Persei

The UBV photometry of a detached F-type eclipsing binary V505 Persei is presented. The light curve solution by a simple spherical model combined with the radial velocity data from two high resolution spectra by Marschall et al. (1990) reveals that the system is formed with two identical component stars of M 1.2 M in the main sequence close to ZAMS in evolution. They should have about solar metallicity (z 0.017). The isochrones with solar metallicity by Van denBerg (1985) yield an age of about (2.2± 0.5) × 10⁹ yr for the system. The distance of the system should be about 60 pc.     

A new approach to the structural features of the Aegean Sea: Cellular neural network

In this study, structural features in the Aegean Sea were investigated by application of Cellular Neural Network (CNN) and Cross-Correlation methods to the gravity anomaly map. CNN is a stochastic image processing technique, which is based on template optimization using neighbourhood relationships of pixels, and probabilistic properties of two-Dimensional (2-D) input data. The performance of CNN can be evaluated by various interesting real applications in geophysics such as edge detection, data enhancement and separation of regional/residual potential anomaly maps. In this study, CNN is used in edge detection of geological bodies closer to the surface, which are masked by other structures with various depths and dimensions. CNN was first tested for (prismatic) synthetic examples and satisfactory results were obtained. Subsequently, CNN/Cross-Correlation maps and bathymetric features were evaluated together to obtain a new structural map for most of the Aegean Sea. In our structural map, the locations of the faults and basins are generally in accordance with the previous maps from restricted areas based on seismic data. In the southern and southeastern parts of the Aegean Sea, E–W trending faults cut NE–SW trending basins and faults, similar to on-shore Western Anatolia. Also, in the western, central and northern parts of the Aegean Sea, all of these structures are truncated by NE-trending faults.     

An investigation of seismicity for western Anatolia

In order to investigate the seismicity of western Anatolia limited with the coordinates of 36°–40° N, 26°–32° E, Gutenberg–Richter magnitude–frequency relation, seismic risk and recurrence period have been computed. The data belonging to both the historical period before 1900 (I₀ ≥ 5.0 corresponding to M_S ≥ 4.4) and the instrumental period until the end of 2006 (M_S ≥ 4.0) has been used in the analysis. The study area has been divided into 13 sub-regions due to certain seismotectonic characteristics, plate tectonic models and geology of the region. All the computations have been performed for these sub-regions, separately. According to the results, a and b values in the computed magnitude–frequency relations are in the intervals 3.19±0.17 – 5.15±0.52 and 0.42±0.05 – 0.66±0.07, respectively. The highest b values have been determined for sub-regions 3 and 12 (Demirci-Gediz and Gökova Gulf-Mu?la-Gölhisar). The lowest b values have also been determined for sub-regions 1 and 9 (Bal?kesir and Bodrum-?stanköy). Finally, seismic risk and recurrence period computations from a and b values have shown as expected that sub-regions 1 and 9 which have the lowest b values and the highest risks and the shortest-recurrence periods.