On a global expansion of the disturbing function in the planar elliptic restricted three-body problem

Starting with a simple Taylor-based expansion of the inverse of the distance between two bodies, we are able to obtain a series expansion of the disturbing function of the three-body problem (planar elliptic case) which is valid for all points of the phase space outside the immediate vicinity of the collision points. In particular, the expansion is valid for very high values of the eccentricity of the perturbed body. Furthermore, in the case of an interior mean-motion resonant configuration, the above-mentioned expression is easily averaged with respect to the synodic period, yielding once again a global expansion of (R) valid for very high eccentricities.Comparisons between these results and the numerically computed exact function are presented for various resonances and values of the eccentricity. Maximum errors are determined in each case and their origin is established. Lastly, we discuss the applicability of the present expansion to practical problems.     

Coordinate gauge conditions in theN-body equations of motion in the first-order post-Newtonian approximation of general relativity

The explicit forms of the metric as well as the equations of motion in the first-order post-Newtonian approximation are worked out under several gauge conditions. It is noted that the so-called EIH (Einstein, Infeld, and Hoffman) equation of motion for an assembly ofN finite mass points mutually interacting via gravitation is identically obtained under three different gauge conditions, namely the harmonic gauge, Chandrasekhar gauge and a composite Chandrasekhar gauge used by Misneret al. (1970), even though the solutions for the metric are found to be all different. In one case the metric has a component apparently diverging, but finally generates regular affine connections so that the equations of motions become free from any singularity. By use of the Chandrasekhar gauge and his formulation, the second-order contribution to the acceleration of planets in the limit of test particle motion around the Sun has been calculated, the inclusion of which in the EIH set of the equations of motion would extend the relative accuracy of computing the total acceleration of any planet to better than one part in 10¹⁷.     

Wavelet Spectrum Analysis Of Eit/Soho Images

The extreme ultraviolet imaging telescope (EIT) of SOHO offers a unique record of the solar atmosphere for its sampling in temperature, field of view, resolution, duration, and cadence. To investigate globally and locally its topology and evolution during the solar cycle, we consider a multi-scale approach, and more precisely we use the wavelet spectrum. We present three results among the applications of such a procedure. First, we estimate the typical dimension of the supergranules as seen in the 30.4 nm passband, and we show that the evolution of the characteristic network scale is almost in phase with the solar cycle. Second, we build pertinent time series that give the evolution of the signal energy present in the corona at different scales. We propose a method that detects eruptions and post-flaring activity in EUV image sequences. Third, we introduce a new way to extract active regions in EIT images, with perspectives in, e.g., long-term irradiance analysis.     

2060 Chiron back to a minimum of brightness

The results of photometric observations of comet/asteroid 2060 Chiron at the Observatório do Pico dos Dias (Brazil-OPD) and the Observatoire de Haute-Provence (France-OHP) during 1994 and 1995 are presented. The analysis of the data shows a decrease of 2060 Chiron brightness from its peak values of 1988–1991. The absolute magnitude, H_v, varies from a maximum of 6.6 in February 1994 up to a minimum of 6.8 in June 1995. Therefore 2060 Chiron is back to a minimum of activity close to that of 1983–1985. The slope parameter G is found to be G = 0.71 ± 0.15. It is suggested that the H-G magnitude system, generally adopted to present 2060 Chiron brightness, is not the most appropriate due to the cometary activity of this object.     

Cygnus A

Cygnus A was the first hyper-active galaxy discovered, and it remains by far the closest of the ultra-luminous radio galaxies. As such, Cygnus A has played a fundamental role in the study of virtually all aspects of extreme activity in galaxies. We present a review of jet theory for powering the double-lobed radio emitting structures in powerful radio galaxies, followed by a review of observations of Cygnus A in the radio, optical, and X-ray relevant to testing various aspects of jet theory. Issues addressed include: jet structure from pc- to kpc-scales, jet stability, confinement, composition, and velocity, the double shock structure for the jet terminus and the origin of multiple radio hotspots, the nature of the filamentary structure in the radio lobes, and the hydrodynamic evolution of the radio lobes within a dense cluster atmosphere, including an analysis of pressure balance between the various gaseous components. Also discussed are relativistic particle acceleration and loss mechanisms in Cygnus A, as well as magnetic field strengths and geometries both within the radio source, and in the intracluster medium. We subsequently review the classification, cluster membership, and the emission components of the Cygnus A galaxy. The origin of the activity is discussed. Concentrating on the nuclear regions of the galaxy, we review the evidence for an obscured QSO, also given the constraints on the orientation of the radio source axis with respect to the sky plane. We present an overview of models of central engines in AGN and observations of Cygnus A which may be relevant to testing such models. We conclude with a brief section concerning the question of whether Cygnus A is representative of powerful high redshift radio galaxies. Received October 10, 1995     

Long-Term Changes of Polar Activity of the Sun

We discuss long-time changes of polar activity of the Sun using the new observational data sets in the optical range during 1872–2001. A study of the secular and cycle variations of the magnetic activity at the high-latitude regions is the main goal that includes polar magnetic field reversals during 1872–2001 and secular changes of the duration of polar activity cycles. The secular increase of the area of polar zones during the minimum activity in the last 120 years and as consequence a decrease of coronal temperature of the Sun in the high-latitude zones during the last 50 years. Correlation between the polar cycles of Caii-K bright points with the Wolf sunspot numbers cycles, W(t), and the 22-year polar magnetic cycles of Caii-K bright points at the high latitudes during 1905–1995 is discussed.     

Instrument development to search for biomarkers on mars: Terrestrial acidophile, iron-powered chemolithoautotrophic communities as model systems

Recent findings by the MER rover opportunity confirming the presence of iron minerals that can only be formed in the presence of water emphasize the study of analogous environments to Mars on Earth. The study of chemolithoautotrophic communities living in acidic iron-rich habitats is highly relevant in order to identify Mars analog environment-specific biomarkers. Iron oxidizing bacteria like Leptospirillum ferrooxidans and Acidithiobacillus ferrooxidans have ways of life for which it is feasible to identify a past or present hypothetical niche on Mars. We have developed a strategy for biomarker identification based on: (i) search for biosignatures on acid and metal-rich environments; (ii) development of an immunosensor microarray; and (iii) integration into an instrument for autonomous and remote operation. The instrument that we have built, called Signs Of LIfe Detector (SOLID), is capable of processing a variety of samples for the detection of specific biomarkers. Antibodies against several bacterial strains have been developed and tested in a microarray biosensor on SOLID. Tests with field samples have been successfully performed, allowing the detection of L. ferrooxidans, A. ferrooxidans present in sediment samples.     

Geochemistry of metabauxites in the Bergsträsser Odenwald (Mid German Crystalline Rise) and palaeoenvironmental implications

Summary Pre- to early Variscan metamorphosed volcano-sedimentary series of the western (Bergstr?sser) Odenwald have been intruded by Variscan calc-alkaline magmatites with plate margin affinities. Within the NE-SW trending metabasic and metapelitic series, intercalations of anomalously aluminous- and iron-rich compositions representing former bauxites are distinguishable. Geochemical data indicate that the Al-, Fe-rich rocks are the metamorphic equivalents of a former bauxitic-ferralitic weathering profile, now comprising spinel fels (top) with relics of pisolitic structures, corundum-chlorite fels, corundum-cordierite-plagioclase gneiss, sillimanite-cordierite-plagioclase gneiss, cordierite-plagioclase gneiss and kinzigite (base) displaying a decrease of weathering in the order as listed. The evolution of such terrestrial sediments is related to specific climatic, environmental, and physico-chemical conditions similar to those of the present-day tropical to subtropical humid regions with high seasonal rains and intensive drainage. Comparison with palaeomagnetic and palaeoclimatic data indicate that the Odenwald metabauxites originally formed during the Lower to Mid-Devonian. Our results imply that, during this geological time span, parts of the precursors of the Mid-German Crystalline Rise not only transversed low latitudes but also were exposed to terrestrial weathering.

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Zusammenfassung Die Geochemie der Metabauxite im Bergstr?sser Odenwald (Mitteldeutsche Kristallinschwelle) und ihre Bedeutung für das Pal?omilieu Im westlichen (Bergstr?sser) Odenwald intrudierten variszische Plattenrand-Kalkalkali-Magmatite in pr?- bis früh-variszische, ehemalige vulkano-sediment?re Serien. Innerhalb der heute NE-SW streichenden Metabasit- und Metapelitzüge treten lokal Al-Fe-reiche Einschaltungen auf, die strukturell und geochemisch als metamorphe ?quivalente eines ehemaligen bauxitisch-ferralitischen Verwitterungsprofils klassifiziert werden k?nnen. Sie umfassen Spinellfelse mit erhaltenen, ehemaligen zonierten Pisolithen, Korund-Chloritfelse, Korund-Cordierit-Plagioklasgneise, Sillimanit-Cordierit-Plagioklasgneise, Cordierit-Plagioklasgneise und Kinzigite. Bauxite k?nnen als terrestrische Bildungen nur unter speziellen klimatischen und physiko-chemischen Bedingungen entstehen. Pal?omagnetische und pal?oklimatische Daten legen die Bildung der ehemaligen Bauxite im unteren bis mittleren Devon nahe. Daraus folgt, da? w?hrend dieser geologischen Zeitspanne die Vorl?ufer der mitteldeutschen Kristallinschwelle bei der Norddrift nicht nur ?quatorn?he passierten, sondern auch partiell ungest?rte, terrestrische, tropisch-subtropische Verwitterungsprozesse abliefen.

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Received June 10, 1999; revised version accepted October 30, 2000