La diffusion des spicules dans la couronne solaire

Résumé Sur les films de R. B. Dunn, on a mesuré la largeur () des spicules en fonction du temps (Figure 1a et 2). On constate un très net phénomène d'élargissement, qui est dû à la diffusion des spicules dans couronne. On donne également un modèle empirique de spicules (tableau I) qui est comparé à la couronne environnante (Figure 4). Il est calculé un bilan des masses entre les spicules et les flocculi.

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Summary The width of spicules as a function of time was measured on films taken by R. B. Dunn (Figures la and 2). We could establish very clearly a broadening phenomenon, due to the diffusion of spicular matter into the corona. An empirical model of spicules is given (Table I) and compared with that of the surrounding corona (Figure 4). The mass-balance between spicules and flocculi is computed.

     

Influence des perturbations thermiques de l'atmosphère sur la qualité des images solaires

Résumé Le Pic du Midi de Bigorre étant pris comme site expérimental, l'influence sur la qualité des images solaires de deux types de perturbations thermiques de l'atmosphère est examinée, celles-ci étant dues respectivement au sol local et à la convection au sein de l'écoulement incident. Une méthode pyrhéliométrique permettant la détection de la convection en ciel clair est exposée.

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A parameter characterizing the quality of photospheric images has been defined through a three class distribution; it has been estimated over various samples taken during 230 hours of observing time at the Pic du Midi Observatory.Its occurrence is compared to that of two types of atmospheric thermal disturbances, one being created by the local ground and the other brought along by the incident flow and due mainly to convection.The time-derivation of the temperature, which is, under some conditions, well related to the nearby thermal field, may be taken as a characteristic atmospheric parameter, and it is shown that the best quality for solar images occurs only - and then with a fairly good frequency - when its value is slightly positive.A method is described which aims at the detection of convection in the clear atmosphere; as the upward motions are bringing aerosols from the lower layers, a less transparent volume is ascending during the first part of the day and then, its top may intercept the optical axis of the telescope. The diurnal variation of the atmospheric transparency, as observed with a pyrheliometer, shows clearly this occurrence, which may be quite different from one day to another.

     

Principe cosmologique,principe variationnel et theorie des groupes

The Friedmann universes are built on the cosmological principle only. The Robertson-Walker metric is common to all the theories based on a homogeneous, isotropic and irrotational universe. In the present work we examine ways of constructing a metric conformal with that of Robertson and Walker, by means of a variational principle which takes into account the cosmological principle as stated by Weinberg (1972), and based on the existence of orbits generated by a one-parameter group of diffeomorphisms of physical space. The application of the cosmological principle to variational methods allows the determination of first integrals which can characterize the physical properties of the Universe. To this end, we show that the Lagrangian of the Universe, considered as a mechanical system, can be chosen from the germs of functions, and that the form variations δq ⁱ are tangent vectors of the group orbits in a Riemannian manifold. Thus the variation of the action vanishes automatically. There appears a first integral of the Euler equations, which is δq ⁱ (?L/?q1 ⁱ ) = C ^te , and also the condition ?L/?t=0, which means the uniformity of time in a Lagrangian conservative system, and which is a direct application of the cosmological principle. These conditions allow the effective determination of a form invariant Lagrangian in the case of isometries. These conditions can be generalized to the case in which the group trajectories are a partition of physical space. Thus, it is possible to define a time from the group trajectories inV ₃: a second of the group time is a lengthm measured along any orbit θ _p of the group. Any pointp of the manifold can then be considered as the starting point of a bundle of orbits, along which the tangent vectors δq ⁱ could be calculated. From this group time, we can build a metric ds ² conformal to the initial ds ² and for which the orbits, which are geodesic, are orthogonal to the transitivity surfaces of the group in the manifold. This implies new statements of the cosmological principle:

1. At any point of space-time it is possible to construct a metric ds ² from the trajectories generated by a one-parameter group of diffeomorphisms ofV ₄.
2. Any two points of space-time can always be joined by means of trajectories of group.

The variational implications of these two principles are the appearance of spectral line shifts such as 1+z=F(p, t _p)/F(q, t_q), wherep andq are arbitrary points of the manifold, andF the transformation function which allows passage from one metric to another. The identification of group trajectories with physical trajectories depends on these two principles. The photon trajectories inV ₃ is an example of this identification. The trajectories of charged particles inV ₄ are another. Principle (b) stated an entropy condition; its application allows a new expression of action variation, this one leading to a general formulation of the shift of spectral lines by a variational method. If we choose the parabolic Friedmann universe as a realistic model, it is the expansion itself which is the generator of the diffeomorphisms allowing the establishment of a group structure in the manifold. The photons are carried away by expansion and do not resist it. The massive particles moderate this expansion locally, and their trajectories inV ₃ are the result of the reaction. In this scheme there is no theoretical difference between the treatment of particles of vanishing proper mass and massive particles. The Robertson-Walker metric fork=0 corresponds to a picture of the Universe which can be drawn by study of the movement of photons in physical space. Only the study of particles can allow the generalization of this scheme and, from this, make a real Universe which is not just a reflection of the physical properties of the photons alone.     

Relation entre l'equation de szebehely du probleme inverse de la mecanique et la theorie de hamilton-Jacobi

For any family of orbits having the same energy constant and orthogonal to a surface, we show the equivalence of Szebehely's equation of the inverse problem and the major result of Jacobi's theorem i.e. there exists a velocity potential.      

Projet d'observation par satellite des irregularites d'ionisation alignees sur le champ magnetique dans la magnetosphere

A study is made of conditions under which a signal of variable frequency emitted from a satellite may be guided by an ionization irregularity existing along a power line of the Earth's magnetic field, as well as conditions under which it may be reverberated to the satellite. Cases are considered of frequencies inferior and superior to the electronic gyrofrequency. From this the form of echoes is deduced, which one may expect from a satellite gravitating up to 2 Earth's radii and it is shown, by analyzing these echoes, that it may be possible to determine the characteristics of existing irregularities in the magnetoshpere along the low-latitude lines of force.

Abstract

Иэyхaoтcя ycлoвия, пpи кoтopых cигнaл c пepeмeннoй хacтoтoй, иcхoдящий oт cиyтникa, мoжeт yпpaвлятьcя нeoднopoднocтью иoнизaции, cyщecтвyющeй вдoль cилoвoй линии мaгнитнoгo пoля зeмли, a тaкжe ycлoвия, в кoтopых этoт cигнaл мoжeт быть cиoвa нaпpaвлeн cпyтникy. paccмaтpивaютcя cлyхaи хacтoт нижe и вышe ∂лeктpoннoй гиpoхacтoты. шз ∂тoгo зaклюхyoт вид ∂хo, кoтopoгo мoжнo oжидaть oт cпyтникa, пepeдвигaющeгocя вдoльopбиты нa paccтoянии дo дв paдиycoв зeмли, пpихeм yкaзывaeтcя кaк, пyтeм aнaлизa ∂тoгo ∂хo, мoжнo ycтaнoвить хapaктepиcтикy нeoднopoдиocтeй, coдepжaщихcя в мaгнитoceфpe вдoль cилoвых линий, нa низких шиpoтaх.     

Etude d'une solution de la theorie litterale du probleme principal du mouvement de la Lune convergence formelle

Résumé Dans l'exposé qui va suivre, nous rappelons d'abord le système d'équations et le mode d'intégration que nous avons utilisés pour construire une théorie littérale du problème principal du mouvement de la Lune. En particulier, puisque, du fait de la présence des petits diviseurs, nous avons à effectuer plusieurs itérations à un ordre donné, pour obtenir tous les termes correspondant à cet ordre, nous allons étudier un système d'équations réduit qui se substitue au système complet, après la première intégration à un ordre donné. Ce système permet d'alléger au maximum les calculs.Nous étudions alors la convergence formelle de la solution littérale obtenue. Cette démonstration est faite par récurrence. Au cours de celle-ci, nous avons utilisé les propriétés du système d'équations réduit (C1, C2, C3, C4, C5, C6, C7, C8, C9, C10, C11, et C12), système dont nous donnons dans les tableaux I à IV, les coefficients et les arguments. L'étude de l'ordre des termes engendrés par ce système nous permet de conclure que, si l'on connaît tous les termes d'ordren–1 alors on peut déterminer tous les termes d'ordren.Enfin, nous indiquons les résultats que nous avons actuellement obtenus par cette méthode.

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In this paper, we first recall the set of equations and the method of integration for a literal solution of the main problem of the lunar theory. As, owing to small divisors, we have to make many iterations at a given order to obtain all the corresponding terms, we study a restricted set of equations which replaces the complete system after the first integration at a given order. This set helps to make the calculations less bulky.Then we study the formal convergence of the literal solution thus obtained. The demonstration uses a recurrent process in which we made use of the properties of the restricted system of equations (C1, C2, C3, C4, C5, C6, C7, C8, C9, C10, C11 and C12), the coefficients and arguments of which are given in Tables I to IV.The study of the order of magnitude of the terms formed by this system leads to the conclusion that if then–1 order terms are known, all then-order terms may be determined.In the end, we show the results obtained so far with this method.

     

Sur la stabilité des points d'équilibre triangulaires dans le problème restreint elliptique

Résumé La stabilité du mouvement d'un petit corps au voisinage des points triangulaires dans le problème restreint elliptique est discutée. Les courbes de stabilité dans le plan (,e) sont obtenues jusqu'au quatrième ordre ene par la méthode du prolongement analytique. Les coefficients des séries obtenues sont donnés de façon exacte. Ensuite, les exposants caractéristiques du système des équations aux variations sont obtenus par un procédé d'intégration matricielle.     

Emissions ‘froides’ dans la couronne solaire

Prominences have been photographed through a coronagraph and an H Lyot filter with long exposure times. Faint H emissions are often detected down to the threshold 2 × 10^-6 times of the Sun's brightness; they show definite structures but their relations to the low-level ordinary prominences are not very clear. Estimates are given for the density and thickness of such cool regions.     

Elimination des noeuds dans le probleme newtonien des quatre corps

Résumé Nous appliquons la méthode des transformations canoniques à variables imposées à la réduction du problème newtonien des quatre corps. L'élimination du centre de gravité étant supposée faite, le problème est ramené à celui des trois corps fictifs. Alors nous menons à bien la réduction dûe aux intégrales des aires explicitement sous forme Hamiltonienne en tenant compte de l'aspect géométrique d'élimination des noeuds préconisé par Jacobi.Nous nous imposons trois fonctions comme nouvelles variables: la troisième intégrale des aires et deux fonctions in variantes; ces deux dernières fonctions resteront nulles lorsque nous prendrons comme troisième axe de coordonnées l'axe défini par le moment cinétique des quatre corps; elles sont choisies en involution avec la troisième intégrale des aires et de crochet un entre elles. Cela nous conduit à déterminer un système de quatorze variables canoniques que nous interprétons géométriquement. Il y a effectivement élimination des moeuds: il s'introduit un pseudo-noeud commun aux deuxième et troisième corps fictifs qui concide avec le noeud du premier corps fictif; ces noeud et pseudo-noeud sont repérés par un paramètre ignorable.

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Elimination of nodes in the Newtonian four-body problem

We apply the method of canonical trasformations with imposed variables to the reduction of the Newtonian four-body problem. After the elimination of the center of gravity, the problem is reduced to that of three fictitious bodies. Then we proceed to the actual reduction using the integrals of angular momentum, in Hamiltonian formulation, and considering the geometrical aspects of the elimination of the nodes advocated by Jacobi.We impose three functions as new variables: the third integral of angular momentum and two invariant functions; these last two functions will remain null when we take as third coordinate axis the axis, defined by the momentum vector of the four bodies; they are chosen in involution with the third integral of momentum and so that their Poisson bracket is equal to one. Then we determine a system of fourteen canonical variables which have a simple geometrical interpretation. It is an actual elimination of the nodes: a pseudonode for the second and third fictitious bodies is introduced which coincides with the node of the first fictitious body; the node and the pseudo-node are referred to by an ignorable parameter.

     

Sur le développement de la fonction des forces dans le problème de deux corps finis

Il est envisagé dans ce travail la procédure du développement de la fonction des forces de deux corps finis, dont les particules élémentaires s'attirent mutuellement par la force proportionnelle à un certain puissance de leur distance.Chaque corps, possedant une forme et une structure bien déterminées, peut avoir une, deux ou trois dimensions.     

Le Fe XII dans la couronne d'émission

Résumé En supposant le FeXII réduit à 16 niveaux d'énergie, nous avons étudié l'intensité relative de 21 raies spectrales en fonction des deux paramètres température et densité électronique. Les résultats sont brièvement discutés, et sont résumés dans les Figures 1–21.

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Assuming that FeXII is reduced to 16 energy levels, we have computed the relative intensities of 21 spectral lines as a function of two parameters, temperature and electron density. Results are briefly discussed and summarized in Figures 1–21.

     

Sur un formalisme explicitant la loi des distances des planetes

The well-known Titius-Bode law (T-B) giving distances of planets from the Sun was improved by Basano and Hughes (1979) who found: $$a_n = 0.285 \times 1.523^n ;$$ a _n being the semi-major axis expressed in astronomical units, of then-th planet. The integern is equal to 1 for Mercury, 2 for Venus etc. The new law (B-H) is more natural than the (T-B) one, because the valuen=?∞ for Mercury is avoided. Furthermore, it accounts for distances of all planets, including Neptune and Pluto. It is striking to note that this law:

1. does not depend on physical parameters of planets (mass, density, temperature, spin, number of satellites and their nature etc.).
2. shows integers suggesting an unknown, obscure wave process in the formation of the solar system.

In this paper, we try to find a formalism accounting for the B-H law. It is based on the turbulence, assumed to be responsible of accretion of matter within the primeval nebula. We consider the function $$\psi ^2 (r,t) = |u^2 (r,t) - u_0^2 |$$ , whereu ²(r, t) stands for the turbulence, i.e., the mean-square deviation velocities of particles at the pointr and the timet; andu ₀ ² is the value of turbulence for which the accretion process of matter is optimum. It is obvious that Ψ²(r _n,t₀) = 0 forr _n=0.285×1.523 ⁿ at the birth timet ₀ of proto-planets. Under these conditions, it is easily found that $$\psi ^2 (r,t_0 ) = \frac{{A^2 }}{r}\sin ^2 [\alpha log r - \Phi (t_0 )]$$ With α=7.47 and Φ(t ₀)=217.24 in the CGS system, the above function accounts for the B-H law. Another approach of the problem is made by considering fluctuations of the potentialU(r, t) and of the density of matter ρ(r, t). For very small fluctuations, it may be written down the Poisson equation $$\Delta \tilde U(r,t_0 ) + 4\pi G\tilde \rho (r,t_0 ) = 0$$ , withU(r, t)=U ₀(r)+?(r, t ₀ ) and \(\tilde \rho (r,t_0 )\) . It suffices to postulate \(\tilde \rho (r,t_0 ) = k[\tilde U(r,t_0 )/r^2 ](k = cte)\) for finding the solution $$\tilde U(r,t_0 ) = \frac{{cte}}{{r^{1/2} }}\cos [a\log r - \zeta (t_0 )]$$ . Fora=14.94 and ζ(t ₀)=434.48 in CGS system, the successive maxima of ?(r,t ₀) account again for the B-H law. In the last approach we try to write Ψ(r, t) under a wave function form $$\Psi ^2 (r,t) = \frac{{A^2 }}{r}\sin ^2 \left[ {\omega \log \left( {\frac{r}{v} - t} \right)} \right].$$ It is emphasized that all calculations are made under mathematical considerations.     

Réflexions sur la contingence des lois de la Nature

There are two fundamental conceptions concerning the laws of nature — these laws are eternal or they may vary in the course of time. We suggest an experiment in order to find an intermediary thesis — i.e. to discover that law, if it really exists, according to which a given law of nature varies, or, at least, to find out the direction in which this variation is performed.     

Temperature et microturbulence dans les regions externes des protuberances

A spectroscopic investigation of a quiescent prominence has been performed: the line profiles of the H and K lines have been carefully determined in all regions of the prominence where these emissions are likely to originate in optically thin layers. Therefore we have been able to study the electron temperature T _e and the microturbulent velocity in the outer parts of the prominence. We find that on the average, T _e = 5700 K (Figure 1) and = 6.7 km s^-1 (Figure 2) which are in very good agreement with classical data. Figure 3 represents the radial velocity measurements and Figure 4 the ratio of the total intensity of H to K lines. Thus the prominence we have observed does not show for T _e and the regular increase outward which has been described by Hirayama (1971). On the other hand increases towards the Equator, in the dynamically active part of the prominence, which could indicate that represents the effect of macroturbulence rather than microturbulence (Kawaguchi, 1966). In this part of the prominence only the K line is in emission and the average value of the microturbulence is 9.4 km s^-1, the radial velocity is also generally increasing. At last, according to the absolute intensities of the H and K lines, the electron density in the outer layers of the prominence is no more than 1 × 10¹⁰ cm^-3.     

Remarques sur l'utilisation des profils lunaires pour la reduction des observations d'occultations

It is shown that a rigourous determination of the argument in the limb charts of the Moon leads to a limb correction which, in some cases, may differ perceptibly from the one obtained by the traditional method. In the case of central occultations, the discrepancy may reach a maximum of 0″.9 when the Moon is near its maximum or minimum declination and introduces a statistical uncertainty of 0″.2 in the determination of the position of the Moon.     

Gradient de densité et température dans la basse couronne

Résumé On considère souvent que le milieu coronal est en équilibre hydrostatique si bien que l'étude de la distribution verticale de la matière est censée donner une bonne estimation de la température coronale (Billings, 1966). De fait, le gradient vertical de densité observé dans la basse couronne (altitudes inférieures à 300 000 km) où l'effet du vent solaire est peu important conduit à une température hydrostatique de 1 500 000 K en moyenne, en assez bon accord avec les déterminations fondées sur l'étude du rayonnement radioélectrique et sur celle de l'ionisation. Il semblerait néanmoins souhaitable de chercher à préciser cette concordance moyenne en comparant dans le détail les variations de la température coronale et celles du gradient vertical de densité pour voir si l'hypothèse de l'équilibre hydrostatique est partout vérifiée.Cette comparaison ne peut être tentée qu'à partir d'un jeu d'observations suffisamment variées pour que l'on puisse déterminer de façon indépendante la densité et la température dans une même région de la couronne: un tel matériel est disponible grâce aux observations coronales effectuées entre 1967 et 1969 à l'Observatoire du Pic du Midi, qui comportent notamment, pour 81 journées d'observations, (a) la mesure de l'intensité des raies 5303 Å et 6374 Å, à 1 du bord, tous les 5° autour du Soleil (b) la mesure de la brillance de la couronne K pour les mêmes angles de position, à 15 et à 5 du bord. Sans discuter ici des caractéristiques propres à ces deux catégories d'observations, qui ont déjà été décrites dans d'autres publications, nous allons chercher dans ce travail à les utiliser pour mettre à l'épreuve la validité de l'hypothèse de l'équilibre hydrostatique dans la basse couronne.

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The observations performed at the Pic du Midi Observatory with a K-coronameter at different altitudes above the solar limb allow us to compute the vertical density gradient of the corona, therefore giving the value of the hydrostatic temperature T _h computed under the assumption of hydrostatic equilibrium in the lower corona. We compare T _h with the ratio r = I ₅₃₀₃/I ₆₃₇₄ of the intensities of the green and the red coronal lines observed at the same position angle and on the same day: r is expected to yield the proportion of cold regions and hot regions along the line of sight under study. As a matter of fact no relation appears between individual values of T _h and r nor between averaged values of T _h and r (Figure 1). In a second step we compute the 5303 Å emission which should be observed, for selected position angles where 6374 Å emissions are faint, making use of the electron density values which can be deduced from the K corona observations. The ratio q = (I ₅₃₀₃) obs/(I ₅₃₀₃) calc of observed to computed 5303 Å intensities should depend upon the corona temperature according to the ionization theory. But again, we do not find the expected relation since Figure 2 displays only a large scatter of points. We conclude that large deviations to hydrostatic equilibrium probably occur in the corona but it is still possible that the presence of arch structures in the lower corona makes it unrealistic to interpret a ratio of intensities integrated along different lines of sight in term of a regular density gradient, although this procedure has been universally used up to now.

     

Un modele bidimensionnel du comportement de l'ozone dans la stratosphere

In order to study the behaviour of stratospheric minor constituents related to aeronomic processes and atmospheric transport in the meridional plane, a numerical two-dimensional model is established. The stratospheric dynamics is parametrized by mean motions and large scale eddy diffusion.This model is applied to the study of ozone in a nitrogen-hydrogen-oxygen atmosphere. The analysis of the various results indicates that the distribution of O₃ is related to the existence of a countergradient flux which is responsible for the transfer of these molecules from the equatorial regions where they are produced to the polar regions where they accumulate during the winter season. The model also shows the combined action of nitrogen and hydrogen compounds on the ozone layer. The particular role of nitric acid on the stability of stratospheric ozone is discussed.