Zur Bahnberechnung von Geostationären Satelliten

Zusammenfassung Mittels kanonischer Resonanztheorie wird eine Störungsrechnung erster Ordnung für die Bahn eines geostationären Satelliten durchgeführt. Die von der Erdabplattung, der Elliptizität des Erdäquators, sowie von Sonne und Mond herrührenden Störungen werden berücksichtigt. Die durch den Einfluss der verschiedenen Störeffekte modifizierte Resonanzfrequenz wird bestimmt.

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A first order perturbation theory for a geostationary satellite is presented. The perturbations caused by the oblateness of the Earth, the ellipticity of the Earth equator and the gravitational influence of Sun and Moon are considered. The resonance frequency which is slightly modified by these perturbations is determined.

     

Homographic motions of a Newtonian system of point masses

A complete classification is established of the possible types of homographic motions of a Newtonian system of point masses interacting through two-body forces which are arbitrary functions of their mutual separations. Several types of motion are included which had not been considered previously, but not all possible rigid body motions; thus it is not possible to build up rigid body dynamics from point dynamics by means of static two-body forces. All general results hold even if many-body forces are considered, which are functions of all separations. In an Appendix, the problem of homographic motions of a relativistic system of interacting point masses is outlined. For a particular form of relativistic interactions, the existence of several types of such motions is established.

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Zusammenfassung Für ein Newtonsches System von Punktmassen mit Zweikörperkräften, die willkürliche Funktionen der Abstände sind, wird eine vollständige Klassifikation aller möglichen Ähnlichkeitsbewegungen gegeben. Sie schliesst mehrere Typen von Bewegungen ein, die bisher nicht in Betracht gezogen wurden, enthält aber nicht alle möglichen Starrkörperbewegungen; daher ist es nicht möglich, die Starrkörperdynamik von der Punktdynamik mit statischen Zweikörperkräften her aufzubauen. Alle allgemeinen Ergebnisse gelten selbst wenn Vielkörperkräfte in Betracht gezogen werden, die Funktionen aller Abstände sind. In einem Anhang wird das Problem der Ähnlichkeitsbewegungen eines relativistischen Systems von Punktmassen skizziert. Für eine besondere Form der relativistischen Wechselwirkung wird die Existenz mehrerer Typen solcher Bewegungen bewiesen.

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Sommaire On établit une classification complète des types possibles des mouvements homographiques pour un système Newtonien de masses ponctuelles avec des forces entre paires de particules qui sont des fonctions arbitraires de leur distance mutuelle. Plusieurs types de mouvements sont inclus qui n'ont pas été considérés auparavant, sans toutefois inclure tous les mouvements possibles d'un corps solide; donc il n'est pas possible de construire la dynamique du corps solide en partant de la dynamique des points avec des forces statiques entre pairess de particles. Tous les résultats généraux restent valables même avec des forces généralisées dependant de toutes les distances. Dans un Appendice, on donne une prësentation générale du problème des mouvements homographiques pour un système relativiste de masses ponctuelles. L'existence de plusieurs types de tels mouvements est établie pour une forme particulère des interactions relativistes.

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Research supported in part by the National Science Foundation.     

Modulation of ion acoustic waves

The multiple scales perturbation theory is applied to a system of dispersive waves including plasma waves (ion-acoustic waves). Assuming the amplitudes of waves are slowly varying function of space and time, we find that long-time slow modulation of the complex amplitude can be described by the non-linear Schrödinger equation. This result agrees with that obtained by Shimizu and Ichikawa using the reductive perturbation theory, and agrees exactly with the nonrelativistic limit of the nonlinear Schrödinger equation obtained by Nejoh using the stretching method.     

Nonlinear disturbances in self-gravitating media

Using a multiple time-scale method, the weakly nonlinear waves on a self-gravitating incompressible fluid column are investigated. The analysis reveals that near the wavenumberk=k _c , the amplitude modulation of a standing wave can be described by the nonlinear Schrödinger equation with the roles of time and space variables interchanged. The nonlinear cutoff wavenumber, which depends sensitively on initial conditions, can then be derived from the nonlinear Schrödinger equation so obtained. The finite amplitude standing wave is stable against modulation.     

Constants of motion of geodesics equations. Examples

Particular examples of constants of motion associated with non-Noetherian symmetries are found for pp-waves, Gödel cosmological solution and Kimura metric. Examples of symmetries for these cases are also obtained.     

Force-free fields in the vicinity of a Reissner-Nordstrøm black hole

The behavioyr of a force-free field has been studied in a Reissner-Nordström metric. An expansion in tensor harmonics of even-odd parity reduced the radial equations in a differential equation of the Sturm-Liouville system which was solved asymptotically in a conveniently defined space coordinate. Further, it has been possible to regularize the singular behaviour of the Reissner-Nordström metric at the event horizon and the modified metric to be given explicitly.     

Weathering of Fe-bearing minerals under Martian conditions, investigated by Mössbauer spectroscopy

The surface of Mars is covered by weathered material. Mars' rusty red colour in particular is commonly ascribed to ferric iron-bearing minerals. The planet's surface is generally iron rich. Mössbauer spectroscopy is a powerful tool for quantitative mineralogical analysis of Fe-bearing minerals. Consequently, the miniaturized Mössbauer spectrometer MIMOS II is part of the payload of NASA's twin Mars Exploration Rovers “Spirit” and “Opportunity”, and ESA's ill-fated Mars Express lander “Beagle 2”. Both Mars Exploration Rovers are currently conducting successful surface operations on Mars. In this paper, we give a brief insight into mission operations with respect to the reconstruction of local weathering scenarios at the landing sites, which in turn will help to illuminate the climatic history of the planet. Mössbauer spectra obtained in preparation of the mission from the SNC meteorites Nakhla, Dar al Gani 476, and Sayh al Uhaymir, show weathering and other alteration features. Preliminary results of laboratory weathering experiments on Fe-bearing minerals (olivine and pyroxene) show the importance of analysing individual minerals to understand weathering of more complex mineral assemblages like, e.g., basalt.     

Exact solution of a radiative transfer problem by the Laplace Transform and Wiener-Hopf Technique

In this paper the authors have extended Bayin's (1978) work to the case of charged fluid spheres. These solutions are matched at the boundary with the Reissner-Nordström solution.     

On the stability parameters of periodic solutions

The stability parametersa, b, c, d of plane symmetric periodic solutions of non-integrable dynamical systems of two degrees of freedom are obtained in terms of their initial states of motion and elements of their variational matrics. Explicit formulae are given in the cases of the Störmer problem and the restricted problem of three bodies.     

On diurnal variations of the solar rotation rate as derived from sunspot tracings

The heliographic positions of more than 100 sunspots were accurately measured several times a day from 1974 until 1979 by means of the computer-controlled tracing method described by Schröter and Wöhl (1975). A striking degree of constancy of the solar rotation rate (about 0.15% or 3 m s^–1) is found, when east-west proper motion components of each individual stable sunspot is considered. However, large differences of the rotation rate are observed (up to 7% or 130 m s^–1) when comparing different sunspots. We found no significant correlation of these fluctuations with characteristics of the sunspots (age, evolution, etc.).Mitteilungen aus dem Kiepenheuer-Institut Nr. 191.     

Self-modulation of pulsar radiation in strongly magnetized electron-positron plasmas

A nonlinear Schrödinger equation is obtained for linearly polarized electromagnetic waves propagating across the ambient magnetic field in an electron-positron plasma. The nonlinearities arising from wave intensity induced particle mass modulation, as well as harmonic generation are incorporated. Modulational instability and localization of pulsar radiation are investigated.     

Strömgren and Hβ photometry of OB stars in Serpens

Strömgren and H photometry of 25 stars in the field of Serpens are presented. The excesses, the absolute magnitude and the temperatures of the stars are obtained. The masses and the ages are also estimated.     

Latitude variations of photospheric activity areas with particular reference to solar faculae

Detailed studies of the development of photospheric activity centres for two solar cycles show that Spörer's Law holds in a very similar form to that applying to sunspots for the faculae which inhabit the sunspot zones. Similar differences between the two solar hemispheres can arise, and it seems to be confirmed that the average latitude of faculae tends to be a few degrees poleward of that of sunspots throughout a given cycle. It is shown that the normal averaging process involved in deriving Spörer's Law obscures a detail which is revealed in a breakdown into the variations within successive narrow latitude strips. These show the existence within a cycle of three separate maxima of activity occurring at different epochs and with different preferred latitudes. The main properties of these maxima are discussed.Now at NOAA, Environmental Data Service, NGSTDC, Boulder, Colo. 80302, U.S.A.     

Relativistic Langmuir solitons-applications to pulsars

The non-linear Schrödinger equation, describing the non-linear Langmuir waves in a relativistic Vlasov plasma in a strong magnetic field, is derived. In the relativistic limit,KT>mc ², this equation gives envelope solitons which are discussed from a point of view of their applications to pulsars.     

Axial perturbations of Wyman's solution

Wyman's solution is the most general solution to the static spherically-symmetric Einstein massless scalar field equations. It is shown that it has no axial perturbation in which the scalar field is incremented, except in the case where the initial scalar field and the cross-metric increments are negligible. The one dimensional Schrödinger equation which governs axial metrix perturbations is produced.     

Periodic three body orbits in the case of small third mass

Near a symmetric periodic orbit of the plane circular or elliptic restricted probelm, the conditions for a symmetric periodic orbit of the plane general three body problem are reduced, under a natural nondegeneracy condition, to the vanishing of a single real valued function. The implicit function theorem and Hörmander's generalized Morse's lemma are then used to analyze the set of zeros of this function.     

Navigationsformel zu A. Busemanns Variationsproblem der Raumfahrt

Die Indikatrix des Variationsproblems wird außer durch die Störungsdifferentialgleichung für die große Halbachse und die Exzentrizität durch einen Zusammenhang zwischen der Richtung des Impulsausstoßes und der exzentrischen Anomalie gegeben. Die Hamilton-Gleichungen einer Extremalen reduzieren sich dann auf eine Navigationsgleichung. Die restlichen Störungsgleichungen für die Perihellänge und die mittlere Länge der Epoche geben schließlich den sparsamsten zeitlichen Ablauf des Raketenausstoßes.

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Presented at the Conference on Celestial Mechanics, Oberwolfach, Germany, August 17–23, 1969.

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Die Untersuchung wurde durch einen Forschungsauftrag der Deutschen Forschungsgemeinschaft gefördert. Meine Mitarbeiter waren Frau Dr. Hildebrandt (bis 1968) und Fräulein Christel Schäfer.     

Proof of a conjecture of E. Strömgren

The conjecture of Strömgren according to which, in the restricted problem, a class of doubly asymptotic orbits are limit members of families of periodic orbits is examined in the more general framework of analytic Hamiltonian system with two degrees of freedom. Sufficient conditions for the conjecture to become a theorem are established. Theses conditions amount to a transversality condition for the doubly asymptotic orbits and are likely to be verified in the cases considered in the literature of numerical explorations of the restricted problem.     

uvbyβ Electrophotometry of the components of trapezium multiple star systems

The results of electrophotometric observations of the 19 components of six Trapezium multiple star systems with primary stars of class M are presented. The Strömgren spectral intervals are determined. Of the 19 components, 18 belong to interval 3 ("late group").Translated fromAstrofizika, Vol. 39, No. 3, pp. 407–410, July–September, 1996.     

Did Eötvös torsion experiment detect Cartan's contortion?

In a previous paper (Mészáros, 1984) the author proposed to describe Cartan's contortion by a spin-2 field twin. The behaviour of these fields is highly similar to gravity; contortion should determine a new interaction. In order to explain some geophysical data and the results of the old Eötvös experiment, Fischbachet al. (1986) proposed the existence of a fifth force. It is shown that the identity of contortion and of this fifth force cannot be excluded.