Theorie analytique programmee de la libration physique de la lune

Résumé La rotation de la Lune autour de son centre de gravité est traitée par une méthode analytique, en tenant compte de son mouvement orbital. On développe une théorie Hamiltonienne en utilisant les variables d'Andoyer et l'on démontre que les écarts, purement périodiques, à trois relations de résonances similaires aux lois de Cassini, sont les variables canoniques du problème. Le potentiel est exprimé dans ces nouvelles coordonnées et l'Hamiltonien est développé jusqu'au deuxième degré en les petites variables. Un système d'équations donne le vrai centre de libration qu'on trouve proche du centre défini par les lois de Cassini. Un second système, résolu par un processus d'iterations, donne les séries de la libration, analytiques par rapport aux constantes du potentiel de la Lune et trigonométriques en les arguments de Delaunay. La question de convergence est brièvement abordée, mais sans démonstration.

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The rotation of the Moon about its center of mass, taking into account the orbital motion, is treated analytically. A Hamiltonian theory is developed in terms of the Andoyer variables. The periodic parts of departures from three resonances, equivalent to Cassini's laws, are found to be the canonical variables of the problem. The potential is expressed as a function of these new coordinates and the whole Hamiltonian is developed to the second degree in these small variables. One system of equations gives the real center of libration which is found to be near the center defined by Cassini's laws. A second system solved by iterations, gives the libration as analytical series in the constants of the Moon's potential, and trigonometric series in Delaunay arguments. The question of convergence is briefly exposed without any demonstration.

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Ce travail a été soutenu par une bourse du Centre National d'Etudes Spatiales.     

Étude de la position de la lune sur champ stellaire

In order to improve our knowledge of the astronomical constants, great interest must be paid to accurate positions of major planets and their satellites. Likewise, accurate astrometry of the Moon on stellar background is essential to determine the ephemeris time. Both programs are pursued by Bordeaux Observatory.     

Analyse photométrique de la pénombre pendant les Éclipses de lune

Sommaire L'analyse photométrique de la pénombre pendant 21 éclipses de 1921 à 1968 sur la base d'un matériau homogène d'observations revèle des anomalies explicables par la luminescence du sol lunaire excitée par les radiations UV-X solaires dont les sources se situent dans la basse couronne et au-dessus des plages K-3. L'influence de la haute atmosphère terrestre se manifeste au bord de l'ombre.

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Photometric analysis of the penumbra during 21 eclipses between 1921 and 1968 based upon the homogeneous observational material reveals some anomalies which may be explained by the lunar luminescence excited by UV-X solar radiations whose sources are located in the low corona and above the K-3 plages. The influence of the terrestrial upper atmosphere is detectable on the border of the umbra.

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Ex-astronome à l'Observatoire de Bordeaux.

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En congé de l'Institut Astronomique de l'Académie des Sciences, Prague.     

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.      

Analyse photometrique de l'eclipse de lune du 16 Septembre 1978

Sommaire La discussion de l'éclipse du 16.IX.1978 basée sur la comparaison des mesures photométriques de l'ombre avec la théorie basée sur l'atmosphère terrestre (pure). Les différences de la densité observée et de la densité calculée sont partiellement dues à l'absorption dans la couche d'ozone, mais le reste doit être attribué à l'absorption dans le milieu situé au-dessus de la couche d'ozone.

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The discussion of the eclipse 1978.IX.16 based on the comparison of the photometrical measurements of the shadow with the theory based on pure terrestrial atmosphere, is presented. The differences between the observed and computed density of the shadow are partly due to the absorption in the ozone layer, and the remainder can be attributed to the absorbing medium above the ozone layer.

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Décédé subitement le 2 décembre, 1979.     

Etoile centrale et condition d'ionisation de l'enveloppe de la nova Delphini 1967

After correcting the observed flux of the forbidden lines for the supplementary reddening (due to the circumstellar envelope), we have recalculated the electron density and temperature of the envelope of the Nova. We have determined the temperature and radius of the Nova and obtained values of 1.03×10⁵ K, 1.15×10⁵ K and 1.21×10⁵ K for the temperature and values of 8.49×10¹⁰ cm, 4.32×10¹⁰ cm and 1.18×10¹⁰ cm for the radius of the Nova for 1968, 1969 and 1970, respectively. Using the temperature and radius of the Nova the electron density and temperature of the envelope and the degree of ionization, we have determined the optical depth of the envelope in the Lyman continuum, and found that it is of the order of 10 during the nebular stage.Considering the stratification of the envelope in different regions of ionization, we have determined the radius of the inner and outer edge and the electron temperature of every region. We found that the electron temperature of the inner part of the envelope is at least three times greater than that of the outer part. The variation of electron temperature as a function of the radius of the ionization region considered shows an abrupt increase of theT _e whenR/R _out(env) is between 0.44 and 0.54.     

Analyse de l'Ombre extérieure pendant les Éclipses de lune

Sommaire L'analyse photométrique de l'ombre extérieure pendant 20 éclipses de 1921 à 1968 sur la base d'un matériau homogène d'observations révèle l'existence de la luminescence du sol lunaire excitée par les radiations corpusculaires solaires. L'influence de la haute atmosphère terrestre vers 25 km d'altitude se manifeste au bord de l'ombre.

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Photometric analysis of the peripheric umbra during 20 eclipses between 1921 and 1968 based upon the homogeneous observational material reveals the existence of the lunar luminescence excited by solar corpuscular radiations. The influence of the terrestrial upper atmosphere at about 25 km height is detectable on the border of the umbra.

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En congé de l'Institut Astronomique de l'Académie des Sciences, Prague.     

Irradiation et pré-irradiations de la brèche 14307

Sample 14307,30, a gas-rich breccia (Group 1 of Warner, 1972) has been studied by coupling track method and light noble gas isotopic analysis. The breccia is made of a glassy dark matrix with embedded millimeter to sub-millimeter sized angular ligth xenoliths. These ones are breccia fragments of higher grade metamorphic facies (Group ? 2). A lighter strata (～ 0.5 cm thick) intersects the dark matrix. Noble gas analysis have shown the dark matrix (³⁶Ar = 5.4 × 10^?4 cc STP/g) to be enriched in solar type gases with respect to the light fractions (³⁶Ar ? 2.2 × 10^?4 cc STP/g). Themean value of the bulk ‘exposure age’ for different samplings is 180 ± 20 × 10⁶ yr, as calculated from spallogenic³He,²¹Ne and¹²⁶Xe contents, using our data and those of Bogard and Nyquist (1972). After appropriate correction for radiogenic⁴⁰Ar, the ratio⁴⁰Ar_exc/³⁶Ar_tr is about 5. A total of 390 crystals coming from 11 locations either in the dark matrix, the lighter strata or a light xenolith (0.25 cm diam), have been studied by track analysis using optical and scanning electron microscopy. 181 crystals were thoroughly investigated by means of the latter technique. The following results were obtained:

1. 72 crystals (70-300µm diam) from one location (No. 12) in the matrix show aminimum track density distribution spreading over 3 orders of magnitude (from 2 × 10⁶ up to 2 × 10⁹ cm^?2). The spectrum has at its lower edge a well defined peak (～ 50% of total crystal number) around 3 × 10⁶ cm^?2). Grains with track density variations over a factor of 3 have a low abundance as compared to average lunar soils. Moreover the mineralogy of this location is peculiar due to its large abundance in orthopyroxenes. Considering the lower edge of the track density distribution amaximum surface residence time of 5 × 10⁶ yr can be set for rock 14307 in itspresent shape;
2. 11 feldspars (1-15µm diam) and 22 clinopyroxenes (70-130µm) have been studied in the light xenolith. All crystals have minimum track densities larger than 10⁸ cm^?2. No spatial variation of track-densities (2.5 ± 0.5 × 10⁹ cm^?2) were found in feldspars inside a millimeter-sized polished section. Clearly these tracks were not acquired by an irradiation of the xenolith as an individual entity, but survived its own formation as a breccia of Group 2. Therefore, solar energetic iron particle tracks have not been erased despite a complex mechanical and thermal history involved by two subsequent brecciation processes;
3. in the 10 other locations, crystals (70-200µm diam) either from the dark matrix or the lighter strata show a significant departure from the pattern observed in lunar soils; namely:

1. the minimum track density distribution is strongly peaked at high values (～ 1-4 × 10⁹ cm^?2) for ～ 95% of the crystals, the remaining ～ 5% having low-values (0.2-1 × 10⁷ cm^?2);
2. the abundance (2%) of crystals with track density variation over a factor of 3 is about one order of magnitude less than in average lunar soils;
3. the magnitude of track density gradients within single crystals is small. In fact, thelargest track density variation versus depth found can be described by the relation? α D^?0.5, in contrast with soil grains which generally exhibit a variation of the form? α D^?1.1±0.4.

The above observations imply that the peculiar irradiation characteristics of these fossilized soils are more likely to be attributed to some wide scale process rather than to some accidental or local phenomena. Attempts to account for these findings by present solar VH particle flux and energy distribution (as determined by Crozaz and Walker, 1971; Fleischeret al., 1971b; Priceet al., 1971), current estimates of lunar fine scale erosion, accumulation and turn-over rates, have proven essentially negative. The bulk ‘exposure age’ of the breccia, rather low by lunar soil standards, makes things even worse. For lack of any better explanation, the above observations could be more easily understood by postulating a higher flux (by factors from ～ 10 up to 200) and a harder energy spectrum (at least for particles with rigidity less than 0.3 GV) for the solar cosmic rays at the time the constituents of the breccia were part as loose grains of the lunar regolith.     

Evolution du spectre de la Nova Delphini 1967 en 1971 et 1972

Continued spectroscopic observations of Nova Del 67 during 1971 and 1972 show a general decrease of the nebular and coronal emission with respect to the local continuum. The continuous spectrum exhibits a strong Balmer emission (figure 1). Equivalent widths of Hi, Hei, Heii, Oi, [Oi], Oii, [Oii], Oiii, [Oiii], Niii, [Sii], [Aiii], [Neiii], [Nev], [Fevi], [Fevii], [Fex], [Fexi], [Fexiv], [Nixvi], [Nixv] are listed in tables 1 and 2.Figures 5 to 10 show several line profiles, which can be interpreted in terms of a model proposed by Hutchings (1972). Kinematical properties of the nova envelope do not seem to have changed in the 1968–1972 time interval. However, a study of the [Oiii] (4959 Å) line indicates that the physical conditions in the polar blobs in 1972 (T _e=10 660 K,N _e=5,5×10⁵ cm^–3) are different from those prevailing in equatorial rings (T _e=9×100 K,N _e=7×10⁵ cm^–3).

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Le matérial d'observation utilisé pour cette étude a été obtenu à l'aide de téléscopes de 120 cm, 152 cm et 193 cm de l'Observatoire de Haute-Provence (CNRS).     

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.

     

Theorie generale planetaire etendue au cas de la resonance et application au systeme des satellites galileens de Jupiter

We consider a system of planets defined by a given distribution of mean mean motions and masses: we represent the osculating elliptic elements of their heliocentric orbits by quasi-periodic functions of time, through a method adapted to the commensurability case; these functions are the sum of the general solution of a critical system, expressed in long-period terms, and of a particular solution. As in the B. Brown's method (applied to the galilean satellites), the critical system contains the secular terms, the longperiod terms (great inequalities), and the resonant terms; the particular solution consists of short-period terms only, whose amplitude is an explicit function of the solution of the critical system.If all the long-period terms in the critical system are harmonic of one fundamental term, we can perform a simple change of variables which transforms the critical system in an autonomous one, and thus we reduce the resolution to an eigenvalue problem. Applying that to the galilean satellites of Jupiter and neglecting the solar perturbations, we obtain a differential system with constant coefficients, whose linear part concerns all the variables (including the major-axes and the mean longitudes) and gives, as a first approximation, the great inequalities, the free oscillations and the libration; nevertheless this solution agrees already with known results, but should be improved by taking into account the non-linear parts and the solar terms in a new approximation.

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Proceedings of the Conference on Analytical Methods and Ephemerides: Theory and Observations of the Moon and Planets. Facultés universitaires Notre Dame de la Paix, Namur, Belgium, 28–31 July, 1980     

Sur l'effet d'une correction de la constante de la précession

Sans résuméPresented at IAU Colloquium No. 9, The IAU System of Astronomical Constants, Heidelberg, Germany, August 12–14, 1970.     

La lune mange-t-elle les couleurs?

The hydrogen radicals play an important role in the photochemistry of the troposphere of the Earth. The chemistry of OH, HO₂ and H₂O₂ is linked directly to the photodissociation of O₃ through the production of O(¹D). Gaseous H₂O₂ (hydrogen peroxide may be removed by heterogeneous reactions involving aerosols and liquid water. During the day and the night the solubility of ambient H₂O₂ in water is estimated and the oxidant capacity of H₂O₂ may explain the bleaching properties of the dew used in the past. This phenomenon may also explain some old maxims concerning the properties of the Moon's light to corrupt colors.     

Photometrie photographique de la couronne solaire

Solar Physics - A series of plates of the solar corona were obtained during the total solar eclipse of July 10th, 1972 near Anadyr (U.S.S.R.) using a standard eclipse coronagraph of Ø = 20 cm...     

Carte de la Lune de J. D. Cassini

Sans résuméPresented at the IAU-COSPAR Julius Schmidt Symposium on 100 Years of Lunar Mapping held at Lagonissi, Greece, 25–27 May, 1978.     

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.

     

La distance de la Nova Delphini 1967

The good agreement found between the observed flux of radio emission of the Nova Delphini 1967 and that calculated theoretically enables us to deduce the angular diameter of the Nova's envelope. This result, when combined with the known linear diameter of the envelope, gives a distance of the order of 885 pc for Nova Delphini.     

Nouvelle etude de la collision triple alignee

Résumé Dans l'article relatif à mon cours de Cortina [1] j'ai indiqué qu'il existe une séparation remarquable des variables pour le problème desn corps. Prenant un repèreR lié auxn corps en position et grandeur on peut étudier le mouvement dansR puis compléter par quadratures. J'ai appliqué cette méthode à la collision triple alignée: je montre que dansR la solution par homothétie parabolique est une position d'équilibre atteinte asymtotiquement: deux mises en équations sont proposées, l'une liée à l'énergie cinétique, l'autre à l'énergie potentielle.

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This paper follows my course offered at Cortina [1]. Here I discuss two differential systems of the motion of aligned triple collision, in a new space (Q, P), obtained by a variable homothesis, consequence of the homogeneity of the Newtonian attraction. For the first one the homothesis is connected with the potential energy, for the other one it is connected with the kinetic energy. In this space the singular parabolic solution, by homothesis, is represented by two equilibral points, asymptotically approached during the two phases of contraction and expansion.

     

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.     

Loi de titius-bode et formalisme ondulatoire

Several authors (Basano and Hughes, 1979; ter Haar and Cameron, 1963, Dermott, 1968; Prentice, 1976) give the revised Titius-Bode law in the form $$r_n = r_o C^n ,$$ wherer _n stands for the distance of thenth planet from the Sun;r _o andC are constant. They pointed out, in addition, that regular satellites systems around major planets obey also that law. It is now generally thought that the Kant-laplace primeval nebula accounts for the origin and evolution of the solar system (Reeves, 1976). Furthermore, it is shown (Prentice, 1976) that rings, which obey the Titius-Bode law, are formed through successive contractions of the solar nebula. Among difficulties encountered by Prentice's theory, the formation of regular satellites similar to the planatery system is the most important one. Indeed, the starting point of the planetary system is a rotating flattened circular solar nebula, whereas a gaseous ring must be the starting point of satellites systems. As far as the Titius-Bode law is concerned, we have the feeling that orbits of planets around the Sun and of satellites around their primaries do not depend on starting conditions. That law must be inherent to gravitation, in the same manner that electron orbits depend only on the atomic law instead of the starting conditions under which an electron is captured. If it is correct, then one may expect to formulate similarity between the T-B law and the Bohr law in the early quantum theory. Such a similarity is found (Louise, 1982) by using a postulate similar to the Bohr-Sommerfeld one — i.e., $$\int_{r_o }^{r_n } {U(r) dr = nk,}$$ whereU(r)=GM _⊙ /r is the potential created by the Sun,k is a constant, andn a positive integer. This similarity suggests the existence of an unknown were process in the solar system. The aim of the present paper is to investigate the possibility of such a process. The first approach is to study a steady wave encountered in special membrane, showing node rings similar to the Prentice's rings (1976) which obey the T-B law. In the second part, we try to apply the now classical Lindblad-Lin density wave theory of spiral galaxies to the solar nebula case. This theory was developed since 1940 (Lindblad, 1974) in order to account for the persistence of spiral structure of galaxies (Lin and Shu, 1964; Lin, 1966; Linet al., 1969; Contopoulos, 1973). Its basic assumption concerns the potential functionU expressed in the form $$U = U_0 + \tilde U,$$ whereU _o stands for the background axisymmetric potential due to the disc population, and ?«U _o is responsible of spiral density wave. Then, the corresponding mass-density distribution is \(\rho = \rho _o + \tilde \rho\) , with \(\tilde \rho \ll \rho _o\) . Both quantities ? and \(\tilde \rho\) must satisfy the Poisson's equation $$\nabla ^2 \tilde U + 4\pi G\tilde \rho = 0.$$ It is shown by direct observations that most spiral arms fit well with a logarithmic spiral curve (Danver, 1942; Considère, 1980; Mulliard mand Marcelin, 1981). From the physical point of view, they are represented by maxima of ? (or \(\tilde \rho\) ) which is of the form $$\tilde U = cte cos (q log_e r - m\theta ),$$ wherem is an integer (number of arms),q=cte, andr and θ are polar coordinates. The distancer is expressed in an arbitrary unit (r=d/d_o). In the case of an axisymmetric solar nebula (m=0), successive maxima of \(\tilde U\) are rings showing similar T-B law $$d = d_o C^n ,$$ withC=e ^{2 π/q} constant, andn is a positive integer. It is noted, in addition, that the steady wave equation within the special membrane quoted above and the new expression of the Poisson's equation derived from (5) are quite similar and expressed in the form $$\nabla ^2 \tilde U + cte\tilde U/r^2 = 0.$$ This suggests that both spiral structure of galaxies and Prentice's rings system result from a wave process which is investigated in the last section. From Equation (2) it is possible to derive the wavelength of the assumed wave ‘χ’, by using a procedure similar to the one by L. De Broglie (1923). The velocity of the wave ‘χ’ process is discussed in two cases. Both cases lead to a similar Planck's relation (E=hv).