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.     

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:

The effect of bulk rock composition on the stability of amphibole in the upper mantle: Implications for solidus positions and mantle metasomatism

Summary The stability of pargasitic amphibole in the upper mantle is a function of water content and bulk rock composition, and under water-undersaturated conditions, the stability of amphibole controls the solidus position. Experiments in the system Tinaquillo peridotite +0.2% H₂O, a refractory peridotite under water-undersaturated conditions, show that amphibole is stable to 1030°C and 26 kb. In contrast, pargasitic amphibole is stable to 1150°C and 30 kb in Hawaiian pyrolite, a more fertile peridotite composition. This indicates that under water-undersaturated conditions, the most fertile part of a crystallizing mantle diapir with an inhomogeneous composition will solidify first while a more refractory component will contain an alkali-rich melt which will have the ability to metasomatize adjacent regions. The relative stabilities of amphibole in refractory and fertile bulk compositions may result in increasing rather than diminishing chemical contrasts in high temperature lherzolite, i.e. a process of metamorphic differentiation. Ti, Fe, Al and Na metasomatism can therefore be considered a normal occurrence associated with the upward migration and solidification of an H₂O-bearing mantle diapir.

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Der Einfluß der Gesamtgesteins-Zusammensetzung auf die Stabilität von Amphibol im oberen Mantel: Bedeutung für Solidus-Positionen und Mantel-Metasomatose

Zusammenfassung Die Stabilität pargasitischer Amphibole im oberen Mantel ist eine Funktion von Wassergehalt und Gesamtgesteins-Zusammensetzung. Unter wasser-untersättigten Bedingungen, kontrolliert die Stabilität von Amphibol die Solidus-Position. Experimente in dem System Tinaquillo Peridotit +0,2% H₂O, einem refraktären Peridotit unter wasser-untersättigten Bedingungen, zeigen daß Amphibol bis 1030°C und 26 Kb stabil ist. Im Gegensatz dazu ist pargasitische Hornblende in einem Hawaii-Pyrolit, von mehr fertiler Peridotit-Zuammensetzung, bis 1150°C und 30 Kb stabil. Das zeigt, daß bei wasser-untersättigten Bedingungen der am meisten produktive Teil eines kristallisierenden Mantel-Diapirs mit inhomogener Zusammensetzung sich zuerst verfestigen wird, während eine mehr refraktäre Komponente eine alkali-reiche Schmelze enthalten wird, die wiederum die Fähigkeit hat, umliegende Bereiche metasomatisch zu beeinflussen. Die relativen Stabilitäten von Amphibol in refraktären und fertilen Gesamtzusammensetzungen können dazu führen, daß die chemischen Gegensätze in Hochtemperaturlherzoliten eher zunehmen als abnehmen, d. h. ein Prozeß metamorpher Differentiation. Ti, Fe, Al und Na Metasomatose können deshalb als ein verbreiteter Vorgang, der mit der Aufwärtsbewegung und Verfestigung eines H₂O-führenden Mantel-Diapirs assoziiert ist, betrachtet werden.

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With 4 Figures     

Littoral '92

Reports

Littoral '92     

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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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.     

V792 Her=HD 155638: A totally eclipsing RS CVn binary

Photometry of HD 155638=V792 Her has been analyzed to determine the elements of this totally eclipsing RS CVn binary. The light variation outside eclipse was found to have a period of 27^d.07±0^d.07, which is slightly different from the 27^d.5384±0^d.0045 orbital period. Analysis of the eclipses was achieved by a modification of the Russell-Merrill technique. With the aid of radial velocity measures, absolute elements were obtained for the hot and cool stars, respectively;R _h=2.58R ,R _c=12.28R ,M _h=1.40M ,M _c=1.46M ,i=80^o.61 and velocity semi-amplitudesK _c=48.36 km s^–1±0.79 km s^–1, andK _h=50.50 km s^–1±0.33 km s^–1. The apparent magnitudes areV _h=9 ^m .73 andV _c=8 ^m .48. The distance to HD 155638 was estimated to be 310 parsecs.     

The maximum limit of the density variation parameter λ for a stable neutron star

A static spherically-symmetric model, based on an exact solution of Einstein's equation, gives the permissible matter density 2×10¹⁴ g cm^–3. If we use the change in the ratio of central density to the radiusr=a (i.e., central density per unit radius (₀/a), we call it radius density) minimum, we have estimated the upper limit of the density variation parameter () and minimum mass limit of a superdense star like a neutron star. This limit gives an idea of the domain where the neutron abundance with negligible number of electrons and protons (may be treated as pure neutrons) and equilibrium in neutrons begins.