Influence du champ magnétique terrestre sur le mouvement d'un satellite autour de son centre de gravité

Résumé On étudie l'effet du champ magnétique terrestre sur le mouvement d'un satellite autour de son centre de gravité. Le satellite possède une symétrie dynamique et un moment magnétique propre dirigé suivant l'un des axes principaux d'inertie; le champ magnétique terrestre est assimilé au champ d'un dipôle dont les pôles coïncident avec les pôles terrestres. On néglige les perturbations de la trajectoire du satellite qui est supposée circulaire. La position du satellite par rapport à son centre de gravité est repérée dans un système d'axes lié au plan de l'orbite et le mouvement est décrit à l'aide des angles d'Euler , , . La symétrie sphérique et le choix du moment magnétique sur l'un des axes d'inertie permettent d'éliminer l'angle .La solution pour et peut se développer en séries de puissance d'un petit paramètre . Les séries convergent pour ||<1.Lorsque le moment magnétique est faible on la rotation du satellite rapide, est faible. Les développements sont calculés effectivement jusqu'à ².La comparaison des résultats avec l'intégration numérique du système d'équations différentielles est satisfaisante.

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The effect of the Earth's magnetic field on the motion of a satellite around its centre of mass is investigated. The satellite is assumed to be dynamically symmetric and to be magnetized in the same direction as that of a principal axis. The Earth's magnetic field is assumed to be a dipole field whose poles coincide with the rotation poles of the Earth. The satellite's orbit is circular and perturbations are neglected. The position of the satellite with respect to its centre of mass is given with respect to a coordinate system fixed in the orbital plane and the motion is described by Euler's angles , , . The spherical symmetry and the coincidence of the magnetic moment with a principal axis allow one to eliminate the angle .The solution for and , can be expanded in power series for small parameter .The series converge for <1. is small for a small magnetic moment or a high angular velocity of the rotating satellite. The terms of the expansion of the series are calculated up to ².The comparison of the results with those obtained by numerical integration of the differential equation is satisfactory.

     

Динамические равновесные плазменные конфигуации и физика магнитосферы

, 1-, 2- 3- . , .     

Internal temperature of isothermal neutron star core matter

Two new equations of state obtained for matter constituting isothermal neutron star core by using isentropic nature of matter for the equalities =₂ and =₃ (where 's are usual adiabatic exponents) have been utilised to discuss the internal temperature of core. The temperature of matter has been obtained asT=T _a(P+E)/. Variation ofT/T _a(t) with energy density has been discussed for these new equations of state and some standard equations of state for nuclear matter.     

Observations of chromospheric lines from OSO-8

The line profiles of L, Ca ii K and Mg iik were measured with the spectrometer of the Laboratoire de Physique Stellaire et Planétaire on board of OSO-8. The results of these measurements are presented.Mitteilungen aus dem Kiepenheuer-Institut Nr. 181.     

Contribution à l'étude du spectre solaire de l'hydrogène

R'esumé Les raies et le rayonnement continu de l'hydrogène sont calculés, dans le cas solaire, en tenant compte des écarts à l'équilibre thermodynamique local.La comparaison des résultats, interprétés par la théorie de la formation des raies de Jefferies et Thomas, avec les observations donne des renseignements sur le modèle de l'atmosphère solaire.L'énergie émise par Ly dépend très fortement de la densité électronique. Seuls les modèles á palier de température dans la haute chromosphère donnent un profil de Ly à dépression centrale.La raie H, qui est contrôlée essentiellement pour les photoionisations dépend surtout du modèle de photosphère; toutefois les modèles de chromosphère à fortes température et densité électroniques ont une influence sur le profil de H.

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Summary The continuous and line spectrum of hydrogen emitted by the sun is computed, taking deviations of local thermal equilibrium into account. The theory of line formation as given by Jefferies and Thomas has been applied to the computations; a comparison of these results with the observations gives information on the solar atmospheric model.The energy emitted by Lyman has been computed for a two- and three-level atom: it appears to increase slightly with the number of levels. The energies, computed with the HAO model and the model of Coates, are larger than the observed values. The core of the Lyman profile is determined by collisions; the peaks are formed at a height where the electron temperature is about 20 000 °K; the energy depends very strongly on the electron density of the model.It is shown that the profile of Lyman only shows a central self reversal if the model of the high chromosphere has a temperature plateau.An interpretation of the observed distance of the peaks of the Lyman and Lyman line profiles is possible; it can also be shown why the distance of the Lyman peaks to the line centre is always of the order of 0.2 Å.The residual central intensity of H increases slightly with the number of atomic levels; the value computed with a five level atom, with the HAO chromospheric model, and the Utrecht photospheric model (1964) does not differ very much from the observed value: it is slightly smaller than the observed value and the computed profile is narrower than the observed profile.In the case of the HAO model the source function of H is dominated by the photo-ionization terms; nevertheless, the collision terms are not much smaller than the photo-ionization terms; the residual central intensity of H computed with a chromospheric model similar to the interspicular model of Athay and Thomas but assuming a higher electron temperature and density is larger than the observed value.

     

Lois exponentielles de distance pour les systèmes de satellites

Résumé Une formulation exponentielle de la loi empirique de Titus-Bode a été proposée par Basano et Hugues. Ces auteurs introduisent l'hypothèse de trois planètes manquantes ou trous. Toutes les planètes obéissent à la relation a _n = ⁿ qui donne les demi-grands axes a des planètes pour des valeurs entières de n.Nous proposons une nouvelle méthode qui permet de retrouver la relation de Basano et Hugues pour le système solaire. Nous appliquons cette méthode aux systèmes de satellites de Jupiter, Saturne et Uranus en introduisant des trous pour combler les lacunes dans les séquences de satellites. Nous en tirons trois relations exponentielles de distance, analogues à la relation de Basano et Hugues. Nous constatons que les coefficients sont semblables pour les systèmes solaire, jovien et uranien alors que le coefficient du système de Saturne vaut approximativement la racine carrée des trois autres .Nous expliquons cet espacement exponentiel grâce à un modèle simple d'une nébuleuse gazeuse initiale soumise à de petites perturbations qui engendrent des oscillations dans la distribution de densité. Les minima de la densité perturbée sont donnés par les zéros des fonctions de Bessel décrivant la propagation de la perturbation. Les positions des maxima correspondent aux sites d'accrétion.Tous les trous introduits dans les parties intérieures des systèmes de satellites sont comblés par les anneaux et petits satellites. Dans le système d'Uranus, il reste deux trous vacants qui pourraient être occupés par des petits satellites non encore découverts.

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Exponential distance laws for satellite systems

A revised Titius-Bode law for the Solar system was proposed by Basano and Hugues, by introducing three missing planets. This law can be written a _n = ⁿ (with = 0.2853 AU and = 1.5226), which gives the distances a _n of the nth planet for successive integers n.We propose a new method to find this Basano-Hugues law for the Solar system. Based upon the comparison of the ratios of successive distances, this method can be applied to the satellite systems of the three giants planets Jupiter, Saturn and Uranus by introducing missing satellites to fill the gaps in satellites sequences. We find three exponential distance relations, similar to that of Basano-Hugues. We note that the coefficients for the Solar, Jovian and Uranian systems are almost equal while the Saturnian system's coefficient is nearly the square root of that of the three others.We explain that exponential spacing by a simple model of an initial gaseous nebula subject to small perturbations generating oscillations in the density distribution. The minima of the perturbed density are given by the zeros of Bessel functions describing the perturbation propagation. The maxima positions correspond to accretion sites.All the empty places in the inside parts of satellite systems are occupied by rings and small satellites. In the Uranian system, there are two empty places which could be filled by new undiscovered small satellites.

     

Equation de Szebehely et principes variationnels

Resume On montre l'équivalence entre l'équation de Szebehely du problème inverse et un problème variationnel déduit du principe de Maupertuis.

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Szebehely's equation and principle variations

We show that the inverse problem Szebehely's equations is equivalent to a multiple variation problem deduced from the principle of Maupertuis.

     

Quelques effets de l'interaction des centres actifs solaires

Résumé Il existe une certaine symétrie dans l'évolution des Centres Actifs (C.A.) simples nés à l'est (_p) ou à l'ouest (_f) d'un centre ancien.Dans l'un et l'autre cas, les taches directement exposées à la polarité inverse du C.A. ancien deviennent les taches de plus grande surface du groupe: tache de tête T_t des _p, tache de queue T_q des _f.Dans le même temps leur mouvement propre tend à les rapprocher du centre ancien. Les déplacements en longitude sont supérieurs, en valeur absolue, aux déplacements moyens des taches homologues d'un C.A. isolé. Les différences ainsi mesurées sont les mêmes pour les T_t ou les T_q et égales à environ 1°.5 en 3 jours pour les groupes de l'échantillon choisi, les déplacements mesurés étant en moyenne de l'ordre de 3°.

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Following the study of anomalies in spot groups correlated to the existence of an older active center (A.C.) in the same region, we compared the evolution of 50 A.C. of simple magnetic configuration or .We associated the growth and the proper motion of their spots to the absence or the presence of an A.C. in the vicinity, and in that eventuality to the relative disposition of the two A.C. in presence.We find that a group situated to the west of an older one evolves to the type _f and shows an eastward motion of the following spot greater than in the case of an isolated group.Symmetrically, the evolution to _p of a group situated to the east of the original formation is associated with a westward motion of the leading spot greater than in the case of an undisturbed group.The difference between those displacements and the average ones corresponding to an isolated A.C. is the same in both cases and is equal to about 1°.5 in three days for the groups of the sample chosen.

     

Is a Power-Law Form of the Correlation Gamma Function Sufficient to State that a Distribution Has Fractal Properties?

This investigation indicates an ambiguity in interpreting the results of applying the apparatus of the correlation gamma function [(r) and ^*(r)] to analyze the spatial distribution of objects from some sample. The presence of a linear section in the dependences of log() on log(r) and of log(^*) on log(r) proves to be insufficient to state that the distribution has fractal properties (self-similarity). It is shown that a change in the geometrical boundaries of the sample may influence the form of the dependences of log() on log(r) and of log(^*) on log(r).     

Isothermal neutron star cores

By considering the relativistic expression for isothermal NS cores,T·e ^/2 = constant, we have shown that some of the standard equations of state, when applied to NS cores, correspond to constancy of some adiabatic exponents. It has been shown that the equation of state,P=KE, corresponds to ₁ = to ₂ = ₃ 1 +K and the equation of state, dP/dE=K, corresponds to ₃ 1 +K. The conditions under which different equations of state represent isothermal cores have been obtained: For isothermal NS, the local temperatureT, can be expressed in terms of pressureP, energy densityE, and rest mass density . For example: (a)P =KE :T = constant × (E/); (b)P=KE :T = constant × (P/); (c) dP/dE =K :T ^K ; (d) = ₂ :T = constant × (P/E); and (e) = ₃ :T = constant × (P/)^1/2. Equation of state corresponding to = ₂ is obtained as:P=E/ln(K/E) and the equation corresponding to = ₃ comes out as:E=P ln(K/P). Core-envelope models can be developed for these two cases. When core equation corresponding to = ₂ or = ₃ is used in the core, we can ensure the continuity of dP/dE at the core-envelope boundary, along with the continuity ofP, E, , and . The parameters of isothermal NS cores corresponding to the cases = ₂ and = ₃, have been obtained. The maximum mass of these NS cores comes out to be 2.7 .     

Non-restricted double-averaged three body problem in Hill's case

A limiting case of the problem of three bodies (m ₀,m ₁,m ₂) is considered. The distance between the bodiesm ₀ andm ₁ is assumed to be much less than that between their barycenter and the bodym ₂ so that one may use Hill's approximation for the potential of interaction between the bodiesm ₁ andm ₂. In the absence of resonant relations the potential, double-averaged by the mean longitudes ofm ₁ andm ₂, describes the secular evolution of the orbits in the first approximation of the perturbation theory.As Harrington has shown, this problem is integrable. In the present paper a qualitative investigation of the evolution of the orbits and comparison with the analogous case in the restricted problem are carried out.The set of initial data is found, for which a collision between the bodiesm ₀ andm ₁ takes place.The region of the parameters of the problem is determined, for which plane retrograde motion is unstable.In a special example the results of approximate analysis are compared with those of numerical integration of the exact equations of the three body problem.

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m ₀,m ₁,m ₂. , m ₀ m ₁. m ₂, m ₁ m ₂ m ₁ m ₂ . , . . , m ₀ m ₁. , . .

     

Carbon suboxide and the genetic code

Carbon suboxide (C₃O₂) polymers formed in the primitive atmosphere would have produced an organic compound soup of high concentration on the Earth. Various vestiges of C₃O₂ are found in the present genetic scheme, which might suggest that the living system had formed from the polymer soup.     

Étude photométrique des structures fines de la pénombre d'une tache solaire

Resumé L'analyse microphotométrique des structures fines de la pénombre d'une tache solaire, photographiée en lumiére blanche au Pic du Midi avec une résolution de l'ordre de 0'.3, permet d'en donner, à 15280, l'image suivante: elle est constituée d'un fond sombre (espaces interfilamentaires) de brillance I/I _d = 0.6 à peu près uniforme, avec un léger gradient radial, sur lequel se détachent des grains brillants alignés en filaments, de brillance moyenne I/I _b = 0.95, de largeur moyenne 0'.36 (270 km) et qui recouvrent 43% de sa surface.

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The microphotometric analysis of the fine structure of a sunspot penumbra, photographed in white light with the 38 cm refractor of the Pic du Midi Observatory with a resolution very close to 0'.3, allows to give from it, at 5280, the following picture: the penumbra appears to consist of bright grains, lined up in the form of filaments, with an average brightness I/I _b = 0.95 of average width 0.36 (270 km) and which cover 43% of its surface, showing up a dark background of brightness I/I _d = 0.6 nearly uniform.

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Ce travail a été en grande partie réalisé alors que l'auteur faisait un séjour à l'Universitäts Sternéwarte de Göttingen.     

Bidimensional spectroscopy of network bright points

We develop an automatic, computer controlled procedure to select and to analyze the Network Bright Points (NBPs) on solar images. These have been obtained at the Sac Peak Vacuum Tower Telescope by means of the Universal Birefringent Filter and Zeiss H filters, tuned, respectively, along the profiles of the H, Mg-b1, Na-D2, and H lines.A structure is identified as an NBP if at the wavelength H- 1.5 A its maximum intensity is greater than I + 3 and its area is greater than 1.5 arc sec² at I + 1.5, where I is the mean value and the standard deviation of the intensity distribution on the image. Each detected NBP is then searched and confirmed in all the remaining 31 images at different wavelengths.For each NBP several parameters are measured (position, area, mean and maximum contrast, Dopplergram velocity, compactness, and so on) and some identification constraints are applied.The statistical analysis of the various parameter distributions, for NBPs present within an active region and its surroundings, shows that two types of NBPs can be identified according to the value of their mean contrast C _min the H- 1.5 Å image (C _m 0.1 type I, C _m> 0.1 type II). The type I NBPs (all occurring on the boundaries of the supergranular network) appear to be much more frequent (180/26) than the type II ones.The size A of type I NBPs is less than 1.0 arc sec for H/H wings but of the order of 1.2 arc sec for Na-D2 and Mg-bl. The mean contrast C _m is around the value of 10% along the Na-D2 and Mg-bl profiles and of 20% along the H/H wings.The C _m - A scatter diagrams show, for the photospheric radiation (h < 100 km), a narrow range of variability for C _min correspondence with a wide range for A. For radiation orginated at higher levels (h > 200 km), the C _m- A scatter diagrams seem to indicate, even if with a large variance, that the highest C _m's tend to correspond to the highest A values.The mean Doppler shift is close to zero for Na-D2 and Mg-bl lines but negative (downward motion) for H and H lines.The type II NBPs tends to be preferentially located in the neighbourhood of small, compact sunspots and their detectability is almost constant through all the 4 studied line profiles. No conclusions can be derived on the mean size, contrast and Doppler shift values because their distributions are too dispersed. The only positive information is that its C _m- A scatter diagram, in H and H wings, indicates a wide range of variability for C _m in correspondence with very narrow range of variability for A.     

The distribution of the angular momenta of galaxies

Since the average relation between the angular momentaP and the massesM of galaxies can be represented by a power lawPM , we can define a relative angular momentum =P/M (or a constant timeP/M ). For a random motion picture within protogalaxies, should follow a Maxwellian distribution and consequently the dispersion of log should be 0.210.For the reasonable range of ( to 2), the limited sample of galaxies with known dynamical parameters gives between and 1 times the Maxwellian value. For the plausible special case =2 the reciprocal of the maximum rotational velocityv _m is already a measure of and the larger sample ofv _m-values not only yields the Maxwellian but, moreover, shows the shape of the distribution.

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PM , =constP/M . , (lg )=0.210. 7/42, . =2 v _m- .

     

Some comments on the photographic subtraction method of determining chromospheric velocities

The photographic subtraction formula expressing the Doppler signal in terms of line-of-sight velocity is rederived and the conditions governing its validity are carefully stated. By appealing to the observed profiles of individual bright and dark mottles it is shown that, in the case of H observations of the quiet chromosphere, two essential conditions are violated.An analysis based on Beckers' (1964) theoretical mottle profiles shows that, assuming the correctness of his model, the photographic subtraction method correctly maps regions of zero velocity and, provided the original photographs are taken sufficiently far from the centre of H, gives the correct signs of any line-of-sight velocities present. However, at H ± 0.25 Å the method gives inconsistent signs. Moreover, at all wavelengths in the line the magnitude of the Doppler signal depends not only on velocity but also on the source function S, optical thickness t ₀, and line broadening parameter ₀. Accordingly, there is no one-to-one correspondence between velocity and the Doppler signal since S, in particular, shows considerable variation from place to place over the quiet chromosphere.An alternative procedure which obviates these difficulties is suggested. It is also based on Beckers' model and yields a calibrated measure of the velocity in terms of ₀ (assumed constant) which is independent of spatial variations in S and t ₀.     

Взаимодействие вещества и излучения В Горячей модели вселенной

. , , . , t>10¹⁰ ( z<10⁵) .

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In this paper we continue the work of Weymann, investigating the causes of distortion of the spectrum of the residual radiation from the Planck curve. We discuss the distortion to the spectrum, resulting from recombination of primeval plasma.We then derive an analytic expression for the distortion to the equilibrium spectrum due to Compton scattering by hot electrons. On the basis of the observational data we conclude that a period of the existence of neutral hydrogen is inescapable in the hot model of the universe. It is concluded that any injection of energy att>10¹⁰ sec (red shiftz<10⁵) give the distortions of the equilibrium spectrum.

     

Spectre continu dans le proche infrarouge de deux étoiles Be: HD 50138 et HD 51585

Continuous spectra of the Be objects HD 50138 and HD 51585 have been investigated between 1.6 and 1.2 ^-1. The infrared gradient _IR of HD 50138 (B5eV) is found to be 2.09±0.10, while the typical B5V star And indicates _IR=1.17. A B5V (HD 16219) star located at about the same distance as HD 50138 has _IR=1.29 and it is shown that interstellar reddening may account for _IR between HD 16219 and And. The difference in gradient between HD 50138 and HD 16219 ( _IR=0.8) may be explained by a continuous reemission in a lenticular envelope with a radius equal to 4R _*. The peculiar object HD 51585 exhibits a B0.5 continuous spectrum, for which the value d logI /d(1/) should be 1.13 according to model atmospheres computations. The distance as derived from color excess leads to disagreement between measured and computed (for a B0.5 star) values of d logI /d(1/). The reddening may be explained by reemission in an envelope the radius of which is smaller than 5R_*. In conclusion, the narrowness of the spectral range under consideration does not permit to decide whether the observed reddening is due to recombination to the third level of the hydrogen atom or whether it is part a thermal reemission in a circumstellar cloud at lower temperature, as it has been observed around 10 by various authors.

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Les spectres utilisés dans ce travail ont été obtenus à l'aide des téléscopes de 193 cm et 120 cm de l'Observatoire de Haute-Provence (CNRS).     

Linear analysis of the light curves of eclipsing variables

In this paper, general model analysis of the form c _{i i} () for the fractional loss of lightf() exhibited by a close binary system will be considered in the sense of the least-squares criterion. A general recursive method will be established for constructing the normal equations for the most useful functions _i (), and an economical storage of the method on a digital computer, with its computational steps, will also be given. Moreover, a full recursive computational algorithm for the least-squares approximation will also be established. By means of this algorithm, all the solution vectors, the variance for different orders of fit and the corresponding variance-covariance matrix could be computed once and for all and, moreover, recursively. The economical storage of the algorithm and its computational steps will be given. Finally, some of the practical difficulties encountered in the application of the least-squares criterion will be analysed, and some techniques for detecting and controlling these difficulties are also given. Numerical examples on the Algol system using a Fourier cosine series of the form c _i cos [(j - 1) /] will be given for illustration.     

On a transformation of the differential equations of the lunar theory

This work contains a transformation of Hill-Brown differential equations for the coordinates of the satellite to a type which can be integrated in a literal form using an analytical programming language. The differential equation for the parallax of the satellite is also established. Its use facilitates the computation of Hill's periodic intermediary orbit of the satellite and provides a good check for the expansion of the coordinates and frequencies. The knowledge of the expansion of the parallax facilitates the formation of differential equations for terms with a given characteristic. These differential equations are put into a form which favors the solution by means of iteration on the computer. As in the classical theory we obtain the expansions of the coordinates and of the parallax in the form of trigonometric series in four arguments and in powers of the constants of integration. We expand the differential operators into series in squares of the constants of integration. Only the terms of order zero in these expansions are employed in the integration of the differential equations. The remaining terms are responsible for producing the cross-effects between the perturbations of different order. By applying the averaging operator to the right sides of the differential equations we deduce the expansion of the frequencies in powers of squares of the constants of integration.Basic Notations f the gravitational constant - E the mass of the planet - M the mass of the satellite - t dynamical time - x, y, z planetocentric coordinates of the satellite - u x+y–1 - s x–y–1 - the planetocentric distance of the satellite - w 1/ - ₀ the variational part of - w ₀ the variational part ofw, - n the mean daily sidereal motion of the satellite - a the mean semi-major axis of the satellite defined by means of the Kepler relation:a ³ n ²=f(E+M) - a the mean semi-major axis defined as the constant factor attached to the variational solution - e the constant of the eccentricity of the satellite - the sine of one half the orbital inclination of the satellite relative to the orbit of the sun - c(n–n) the anomalistic frequency of the satellite - c ₀ the part ofc independent frome,e, and - g(n–n) the draconitic frequency of the satellite, - g ₀ the part ofg independent frome,e, and - exp (n–n)t–1 - D d/d - e the eccentricity of the solar planetocentric orbit - a the semi-major axis of the solar orbit - n the mean daily motion of the sun in its orbit around the planet - m n/(n–n) - a/a-the parallactic factor - the disturbing function