The critical inclination problem — 30 years of progress

The critical inclination problem in artificial satellite theory, first discovered 30 years ago, has aroused great interest and provoked much discussion and controversy in the intervening years. It was this problem which essentially provided the seed corn for the development of the theory of the Ideal Resonance Problem (IRP). The latter theory provides good first-approximation solutions to a number of important resonance problems in celestial mechanics. It is not applicable, however, to certain other interesting resonant systems within the solar system. For these resonances a new fundamental mathematical model of resonance, in the spirit of the IRP, has recently been formulated and successfully applied.This paper reviews the history of the critical inclination problem and highlights the controversies it has generated over the years. The Problem's strong connection with the IRP is outlined with both thenormal andabnormal forms featuring. Finally, with reference to the critical inclination problem, the essential properties of the newer fundamental model are described and compared with the IRP. A strong correspondence is established between recent independent investigations of a variety of resonance problems and earlier work of Andoyer.     

Secular resonances: New results

We integrated numerically, in the frame of the four body problem Sun-Jupiter-Saturn-asteroid the orbit of the asteroid 1974 MA, an Earth-crosser, which is located in a region where three resonances overlap: the two secular resonances ₅ and ₁₆ and the mean motion resonance 5/1. The numerical integration yields a qualitative orbital evolution of this particular region.     

On Goudas' surfaces in the magnetic-binary problem

The containment property Goudas' surfaces has been studied in this paper. Physical implications of this property a consequently discussed. A general relationship is obtained, which connects the sizes of those surfaces, the magnetic moments of two stars and their mean motion.     

High pressure experimental calibration of the olivine-orthopyroxene-spinel oxygen geobarometer: implications for the oxidation state of the upper mantle

Synthetic spinel harzburgite and lherzolite assemblages were equilibrated between 1040 and 1300° C and 0.3 to 2.7 GPa, under controlled oxygen fugacity (f _{O 2}). f _{O 2} was buffered with conventional and open double-capsule techniques, using the Fe−FeO, WC-WO₂-C, Ni−NiO, and Fe₃O₄−Fe₂O₃ buffers, and graphite, olivine, and PdAg alloys as sample containers. Experiments were carried out in a piston-cylinder apparatus under fluid-excess conditions. Within the P-T-X range of the experiments, the redox ratio Fe³⁺/ΣFe in spinel is a linear function of f _{O 2} (0.02 at IW, 0.1 at WCO, 0.25 at NNO, and 0.75 at MH). It is independent of temperature at given Δlog(f _{O 2}), but decreases slightly with increasing Cr content in spinel. The Fe³⁺/ΣFe ratio falls with increasing pressure at given Δlog(f _{O 2}), consistent with a pressure correction based on partial molar volume data. At a specific temperature, degree of melting and bulk composition, the Cr/(Cr+Al) ratio of a spinel rises with increasing f _{O 2}. A linear least-squares fit to the experimental data gives the semi-empirical oxygen barometer in terms of divergence from the fayalite-magnetite-quartz (FMQ) buffer:

Littoral '92

Reports

Littoral '92     

Periodic Hartree-Fock study of minerals: Tetracoordinated silica polymorphs

Periodic Hartree-Fock STO-3G calculations have been performed on several tetracoordinated silica polymorphs: low and high quartz, low and idealized high cristobalite and prototype tridymite. The optimized structural parameters are in overall good agreement with experimental data. In the particular case of -quartz, the SiO₄ tetrahedra are found to be irregular. The optimized values of the two different SiO bond lengths are respectively 1.608 Å and 1.613 Å. The potential energy versus tilt angle curves suggest a picture of the high temperature phases in terms of delocalized oxygen atoms which is consistent with a disordered structure. Finally, the bonding in silica polymorphs is discussed from electron density maps and Mulliken population analysis.     

The structural state of the former lower continental crust in Calabria (S. Italy)

In the Northern Serre (S. Italy), a continuous section through a former lower continental crust is exposed (Schenk 1984, 1985). These granulite facies rocks have not been penetratively deformed during their uplift to higher crustal levels. Therefore, they allow to study the structural state of the lower continental crust. Most rockforming minerals, among them ortho- and clinopyroxene and cordierite, show recrystallization structures. Quarz basal subgrain boundaries are developed in lower levels of the lower crust and disappear toward higher levels. In addition to dimensional orientations of the rockforming minerals, the preferred crystallographic orientations of plagioclases, cordierite, amphibole, pyroxenes and, rarely, quartz reflect the strain orientation of the prograde high-T deformation. During this deformation, the stretching direction was constant NNE-SSW throughout the exposed lower crustal section. Shear indicators are rare. This points to the fact that deformation has been homogeneous and coaxial flattening. There is only a small variation in orientation and strength of textures throughout the exposed lower crust. Therefore, neighbouring layers of different composition rather than different deformation might serve as seismic reflectors in the former lower crust.

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Zusammenfassung In der nördlichen Serre (Süditalien) ist ein zusammenhängender Bereich einer ehemaligen kontinentalen Unterkruste aufgeschlossen (Schenk 1984, 1985). Diese granulitfaziellen Gesteine sind bei ihrem Aufstieg in höhere Krustenbereiche nicht durchgreifend überprägt worden. Deshalb läßt sich an ihnen noch der strukturelle Zustand der ehemaligen Unterkruste studieren. Außer in Feldspäten, Quarz und Amphibol tritt auch in Ortho- und Klinopyroxen und in Cordierit Rekristallisation auf. In tieferen Krustenniveaus sind im Quarz basisparallele Subkorngrenzen entwickelt, die in höheren Krustenbereichen nicht auftreten. Sowohl die Gestaltregelungen der gesteinsbildenden Minerale als auch die kristallographischen Plagioklas-, Cordierit-, Amphibol-, Pyroxen- und (seltener) Quarzregelungen spiegeln die Strain-orientierung der prograden hochtemperierten Deformation wider. Während dieser Deformation blieb die Streckung im gesamten Unterkrustenbereich konstant NNE-SSW orientiert. Scherindikatoren sind selten. Beides deutet darauf hin, daß die Deformation homogen und als koachsiale Plättung abgelaufen ist. Im gesamten aufgeschlossenen Unterkrustenbereich variieren weder Intensität noch Orientierung der kristallographischen und gestaltlichen Regelungen der gesteinsbildenden Minerale wesentlich. Deshalb sollten in der ehemaligen Unterkruste Lagen unterschiedlicher Deformation weniger als seismische Reflektoren in Frage kommen als Lagen unterschiedlicher Zusammensetzung.

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Résumé Le Massif de la Serre Septentrionale en Calabre (Sud de l'Italie) représente un tronçon d'une ancienne croûte continentale profonde (Schenk 1984, 1985). Les roches du faciès granulite qui le constituent n'ont pas subi de déformation penetrative lors de leur ascension dans les niveaux plus superficiels de la croûte. Leur étude permet donc de reconstruire les caractéristiques structurales de l'ancienne croûte profonde. Non seulement les feldspaths, le quartz et l'amphibole, mais encore l'orthopyroxène, le clinopyroxène et la cordiérite ont recristallisé. Dans les niveaux les plus profonds de la croûte on observe dans les cristaux de quartz des bordures de sous-grains parallèles à la base. Celles-ci n'apparaissent plus dans les niveaux plus superficiels. L'orientation des cristaux des minéraux constitutifs des roches, de même que l'orientation des réseaux cristallins du plagioclase, de la cordiérite, de l'amphibole, du pyroxène et (mais plus rarement) du quartz réflètent la direction de contrainte de la phase de déformation prograde de haute température. Pendant cette phase de déformation, la direction d'extension est demeurée NNE-SSW. Les témoins de cisaillement sont rares, ce qui montre que la déformation s'est effectuée de façon homogène, en relation avec un aplatissement coaxial. Les textures varient très peu en orientation comme en intensité dans toute la coupe de croûte profonde exposée. En conséquence, l'existence de réflecteurs sismiques devrait refléter des différences dans les compositions minéralogiques des roches plutôt que dans leurs caractéristiques structurales.

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African linkage of Precambrian Sri Lanka

New age and isotopic data show that the high-grade basement rocks of Sri Lanka were not linked to the Archaean granulite domain of southern India but experienced their main structural and metamorphic development during the Pan-African event some 950 to 550 Ma ago. This occurred when West Gondwana and East Gondwana collided to form one of the longest collisional structures in the Supercontinent — the Mozambique belt that extends from Mozambique to Ethiopia and Sudan. A major tectonic boundary, interpreted as a thrust zone, divides the Highland/Southwestern Complex in the central part of Sri Lanka from the Vijayan Complex in the E and SE. The former is interpreted to represent the remnant of a once extensive passive margin extending west, in a Gondwana reconstruction, via Madagasgar to Tanzania and Mozambique. The Vijayan Complex may have been part of a separate continental margin plutonic assemblage, and its collision with the Highland/ Southwestern Complex marks the final amalgamation of East and West Gondwana into a supercontinent some 550 Ma ago. The Sri Lankan granulites cannot be correlated with the distinctly older granulites of the Eastern Ghats belt of India, and this suggests that Sri Lanka was situated close to the SE coast of Madagascar in a Gondwana reconstruction.

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Zusammenfassung Neue Isotopen- und Altersdaten aus dem metamorphen Grundgebirge von Sri Lanka zeigen, daß dieses Gebiet nicht, wie vielfach vermutet, Teil des archaischen Granulitkomplexes von Südindien war, sondern seine strukturelle und metamorphe Entwicklung während der panafrikanischen Orogenèse zwischen ca. 950 Ma und ca. 550 Ma hatte. Diese Orogenèse ist das Resultat der Kollision zwischen West-Gondwana (Afrika und Südamerika) und Ost-Gondwana (Südindien, Australien und Antarktis) und führte zur Bildung eines der längsten Kollisionsgürtel des Superkontinentes, dem Mosambik-Gürtel, der sich von Mosambik bis nach Äthiopien und in den Sudan erstreckt. Der West- und Zentralteil Sri Lankas mit den Wanni und Highland/Southwestern Komplexen wird vom Vijayan Komplex im Osten und Südosten durch eine Überschiebungszone getrennt, die möglicherweise eine Sutur darstellt. Die Gesteine im Westen und in den Highlands werden als der Rest eines ehemals weiträumigen passiven Kontinentalrandes interpretiert, zu dem wohl auch die lithologisch ähnlichen Abfolgen der hochmetamorphen Gebiete in Mosambik, Tansania und Madagaskar gehörten. Der Vijayan Komplex war wohl Teil der separaten plutonischen Suite eines aktiven Kontinentalrandes, und seine Kollision mit dem Highland/ Southwestern Komplex markiert das endgültige Verschweißen von West- und Ost-Gondwana zu einem Superkontinent vor ca. 550 Ma. Die Granulite Sri Lankas können nicht mit den deutlich älteren Granuliten des Gürtels der Eastern Ghats in Südost Indien korreliert werden sondern ähneln eher den hochgradigen Gesteinen in Südost Madagaskar. Damit ist die Lage Sri Lankas nahe Madagaskar in einer Gondwana Rekonstruktion wahrscheinlicher als nahe der Südostküste Indiens.

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Résumé De nouvelles données isotopiques et géochronologiques montrent que les roches métamorphiques du socle du Sri Lanka ne constituent pas, comme on l'a souvent cru, une partie du complexe granulitique archéen de l'Inde méridionale, mais qu'elles ont vécu leur propre histoire tectono-métamorphique au cours de l'orogenèse panafricaine, entre 950 et 550 Ma. Cette orogenèse est le résultat de la collision entre le Gondwana occidental (Afrique et Amérique du Sud) et le Gondwana oriental (Inde du sud, Australie et Antarctique) et constitue une des plus grandes chaînes de collision du Supercontinent: la chaîne du Mozambique, qui s'étend du Mozambique jusqu'au Soudan et en Ethiopie. Un contact tectonique majeur, interprété comme un charriage, sépare le »Highland/South-western Complex« (partie centrale du Sri Lanka) du »Vijayan Complex« (partie est et sud-est). Le premier de ces complexes est interprété comme un reste d'une ancienne marge passive de grande étendue, à laquelle appartenaient aussi les séries lithologiquement analogues du domaine très métamorphique du Mozambique, de Tanzanie et de Madagascar. Le «Vijagan Complex« a pu être une partie d'un ensemble plutonique séparé de marge active; sa collision avec le »Highland/Southwestern Complex« marque la réunion finale en un super-continent il y a quelque 550 Ma, des Gondwanas oriental et occidental. Les granulites du Sri Lanka ne peuvent pas être corrélées avec celles de la chaîne des Eastern Ghats (Inde du sud-est) qui sont nettement plus anciennes; elles se rapprochent plutôt des roches très métamorphiques du sud-est de Madagascar. On en déduit que la position du Sri Lanka, dans une reconstruction du Gondwana, devait être plus proche de Madagascar que de la côte sud de l'Inde.

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Coulomb-trapped particles in the electromagnetic fields of an oblique magnetic rotator

An oblique, rotating magnetized sphere emits electromagnetic waves which, for large magnetization, can quickly accelerate charged particles to very high energies. A central, attractive Coulomb force can trap particles in the region beyond the light cylinder by balancing the accelerating influence of the radiation on the particles. We sample some of the particle orbits possible under these dynamical conditions. A general feature of these orbits is that non-interacting particles started with random initial conditions in the domain of attraction of these orbits will arrange themselves on a curve corotating with the axis of magnetization. Such particle configurations can be a source of pulsed radiation. In the idealized case of no interparticle interactions the spectral index for the radiation emitted by one frequently occurring configuration is found to be –2/3, for emission from radio to -ray frequencies. The dynamical conditions in this simple model closely match those prevalent in outer pulsar magnetospheres, making it possible that part of the radiation from pulsars is emitted by trapped plasma in the region beyond the light cylinder.     

Interpretation of the frequency distribution of isochrone ages of nearby F and G stars

The frequency distribution of isochrone ages of nearby F and G stars is used in a synthetic approach to the history of the star-formation rate (SFR). On the basis of stellar evolutionary sequences, age distributions are calculated for different assumptions on the SFR history. Models with a constant past SFR provide a good fit of the empirical age distributions, unless a feature at ages 4 Gyr. If real, a shoulder in the empirical frequency distribution of isochrone ages at 4–5 Gyr points toward an enhanced SFR during a more or less (1 to 6 Gyr) extended period which ceased with a peak about 4 Gyr ago. It is shown that models with such a nonmonotonous SFR history reproduce the empirical stellar age distribution and, moreover, the age-metallicity relation and the metallicity distribution of nearby stars. An era of enhanced star formation in this time interval is consistent with recently published interpretation of several age-dependent properties in different samples of nearby stars.