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Thèses De L'entre-Deux-Guerres THÈSES DE L’ENTRE-DEUX-GUERRES V. GROUYITCH Réduction et discussion des occultations d’étoiles par la lune observées à Strasbourg de 1925 à 1932 Thèses de l’entre-deux-guerres, 1933 <http://www.numdam.org/item?id=THESE_1933__152__1_0> L’accès aux archives de la série « Thèses de l’entre-deux-guerres » implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commer- ciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou im- pression de ce fichier doit contenir la présente mention de copyright. Thèse numérisée dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ Série E N° D'ORDRE : 39 THESES PRESENTEES A LA FACULTÉ DES SCIENCES DE L'UNIVERSITÉ DE STRASBOURG POUR OBTENIR LE GRADE DE DOCTEUR ES SCIENCES MATHÉMATIQUES' PAR V. QROUYITOM Diplômé de l'Université do Belgrade 1*° THÈSE. — RÉDUCTION ET DISCUSSION DES OCCULTATIONS D'ÉTOILES PAR LA LUNE OBSERVÉES A STRASBOURG DE 1925 A 1932. 2e THÈSE. — PROPOSITIONS DONNÉES PAR LA FACULTÉ. Soutenues le Q Décembre 1933, devant la Commission d'Examen MM. R. THIRY, Président. A. DANJON ) A.VÉRONNETS ORLÉANS IMPRIMERIE HENRI TESSIER 8 bis et 8 ter, rue du Faubourg Madeleine 1933 ENS BM M026588 UNIVERSITÉ DE STRASBOURG FACULTÉ DES SCIENCES Doyen M. E. ROTHÉ, Professeur de Physique du Globe. Doyen honoraire M. E. BATAILLON. l MM. E. CHATTON, E. ESCLANGON, M. FRÉCHET, G. FRIEDEL, Professeurs honoraires. M. GIGNOUX, L. HACKSPILL, G. RIBAUD, E. TOPSENT, ( H. VILLAT. MM. G. VALIRON Analyse supérieure. P. WEISS Physique générale. H. OLLIVIER Physique générale. H. GAULT Chimie organique. C. HOUARD Botanique. E. TERROINE Physiologie générale. J. DE LAPPARENT Minéralogie et Pétrographie. R. THIRY Mécanique rationnelle. G. CERF CaVul différentiel et intégral. G. DUBOIS Géologie et Paléontologie. P. FLAMANT Mathématiques générales. Professeurs E. CORNEG Chimie générale. A. DANJON Astronomie. P. DE BEAUCHAMP Zoologie et Anatomie comparée. L. BOUNOURE Biologie génerale. N Chimie minérale. N Physique expérimentale. G. FOEX Physique générale. H. CHERMEZON Botanique. G. REMPP Physique du Globe. R. ROMANN Chimie ph\sique et électrochimie. J. LACOSTE Physique 'du Globe. G. HUGEL Chimie du Pétrole. H. WEISS Physico chimie du Pétrole. MM. CH. STAEHLING Chimie appliquée. P. SOLEILLET Pnysique mathématique. R. BONNET Physique et Chimie biologiques. J. JUNG Géolopie du Pétrole. l A. ROUSSEL Mathématiques générales. Maîtres de conférences < A. CHRÉTIEN Chimie appliquée. J. MARESQUELLE Botanique. R. I1OVASSE Biologie générale. H. CARTAN Mathématiques. N Minéralogie. N Mathématiques. N Zoologie. Secrétaire G. CUVIER. A MONSIEUR A. DANJON DIRECTEUR DE L'OBSERVATOIRE DB STRASBOURG PROFESSEUR A LA FACILTÉ DES SCIENCES Hommage respectueux et reconnaissant. TABLE DES MATIÈRES Pagei INTRODUCTION i PREMIÈRE PARTIE. - Catalogue 7 DEUXIÈME PARTIE. — Mouvements propres 43 TROISIÈME PARTIE. — Réduction des Occultations et Discussions des résultats.' 66 SOMMAIRE 110 PREMIÈRE THÈSE RÉDUCTION ET DISCUSSION DES OCCULTATIONS D'ÉTOILES PAR LA LUNE OBSERVÉES A STRASBOURG DE 1925 A 1932 INTRODUCTION La théorie de la Lune qui préoccupait depuis longtemps les astronomes et les mathématiciens paraissait terminée par la publication des Tables lunaires de Hansen (1857). En effet, ces Tables représentaient très bien les observations faites de 1750 à i85o. L'écart O — C ne dépassait jamais les limites de préci- sion des observations (1" h 2"). Quelques années après la publication des Tables, celles-ci cessèrent d'être exactes, étant donné que l'écart augmentait de plus en plus pour atteindre, en 1890, 18". La qucslion se posait de savoir si les Tables de Hansen, qui ne représentent pas le momement de la Lune fuec la précision voulue après 1860, étaient exactes avant 1750 ? — Cette question a été com- plètement résolue par Newcomb dans le mémoire : « Iîcscarchcs on Ihe Molion of the Moon. Part. I Réduction and Discussion of Observations of Ihe Moon before 1750 » (Washington, Observations, for 1875. — Appendix II). Dans ce mémoire, Newcomb a rassemblé toutes les obserxations de la Lune et les a comparées avec les positions théoriques tirées des Tables de Hansen. Il a constaté qu'il existait un écart entre l'observation et la théorie de Hansen et que par consé- quent les Tables étaient incapables de représenter le mouvement de la Lune avant 1750. Newcomb a démontré alors que Hansen n'a pas tenu compte des observations antérieures à 1750 et que c'est grâce à ce fait qu'il a pu obtenir un si bon accord, d'ailleurs pour une période limitée. Comme on ne pouvait pas arriver à mettre d'accord l'observation et la théorie, on se trouvait en présence de cette alternative : ou bien mettre en cause la théorie dans son principe ou dans ses méthodes de calcul, c'est-à-dire aban- donner la loi de la gravitation universelle de Newton, ou bien si on voulait con- — 2 — server cetle dernière intacte, on était obligé de supposer que l'étalon de temps (jour sidéral) subit des fluctuations irrégulières. Déjà, vers 1870, S. Newcomb a eu l'idée qu'il existait des fluctuations irrégulières de la rotation de la Terre qui se traduisaient sur le mouvement apparent de la Lune. Si cette idée de Newcomb était juste, on devrait trouver des fluctuations de même allure que celles de la Lune, sur les autres astres du système solaire qui n'ont pas de lien direct avec notre satellite. Pour vérifier cette idée, Newcomb voulait étudier les phénomènes des satellites de Jupiter, les passages de Mercure sur le Soleil et le mouvement en longitude de Vénus. — II mourut en 1909 î?ans a\oir pu arriver aux résultats définitifs. Son travail, qui exigea un labeur énorme, fut continué et grâce à l'effort collectif de plusieurs astronomes (Brown, Fotheringham, Innés, Glauert, Ross, de Sitter), on peut le considérer comme terminé. M. E. \Y. Brown a consacré de nombreuses années de travail pour donner une nouvelle théorie de la Lune au sujet de laquelle H. Andoyer dit : « La théo- rie du mouvement de la Lune édifiée par AI. E.-W. Brown est sans doute défini- tive ». {Sur la Théorie analytique du mouvement de la Lune, p. 1). M. Brown a introduit toutefois dans ses Tables lunaires le grand terme empirique (G. E. T.) qu'il retrouve comme Newcomb dans les résidus de la longitude de la Lune O — C. G. E. T. = 13^,00 sin (1390 T + 2840,2) où T est le nombre de siècles à partir de 1800,0. Les Tables de la Lune de M. Brown sont actuellement adoptées par toutes les grandes éphémérides. Dans la publication : « The Evidence for Changes in Ihe Baie of Rotation of Ihe Earth and Iheir Geophysical Conséquences, wilh a Summary and Discussion of the Devialion of Ihe Moon and Sun from Iheir Gravilalional Orbils » (Transactions of the Astronomical Observatory of Yale Univorsity. Vol. 3, Part. II) M. Brown, en étudiant le mouvement do la Lune et du Soleil (l'étude du mouvement du Soleil n'était pas prévue dans le programme de Newcomb), met en évidence la fluctuation irrégulière de la vitesse de la rotation de lo Terre. D'après M. Brown, le mouvement de la Lune peut être représenté par la théorie en lui ajoutant le grand terme empirique et les petites fluctuations dues à l'irrégularité de la vitesse de la rotation de la Terre. M. de Sitler a repris à son tour le travail de Newcomb et en 1926 il publia ses résultats dans l'article : « On the secular Accélérations and the Fluctuations of the Longitudes of the Moon, Ihe Sun, Mercury and Venus » (Bulletin of the Astro- nomical Institutes of the Netherlands, Vol. IV, n° 124). Dans ce travail, M. de Sitter étudie les mouvements de Mercure, de Vénus, du Soleil et de la Lune, et — 3 — il trouve une accélération de ces astres qui est pour tous proportionnelle à leurs moyens mouvements. Cette accélération provient de changements brusques du moment d'inertie de la Terre. Ces changements se manifestent par des fluctua- tions irrégulières de la rotation de la Terre. Par conséquent, tous les astres du système solaire paraissent cire en avance ou on retard sur la théorie suivant que nos pendules, réglées par les passages des étoiles, c'est-à-dire par la rotation de la Terre, retardent ou avancent par rapport au temps newtonien. La Terre, considérée comme horloge, présente donc des écarts accidentels de marche. Ces écarts ne peuvent pas être prévus, mais ils peuvent être constatés et calculés à l'aide des observations. A certaines époques, ils avaient atteint 20 à 3o secondes de l'avance ou du retard. Ensuite, M. de Sitter montre qu'une variation irrégulière de l'effet des marées affecte doublement la Lune, en apparence et réellement. Elle est affectée en apparence parce que l'étalon de temps est variable, et réellement, parce que son moyen mouvement est perturbé. Par contre, l'effet des marées terrestres ne fait subir aucune perturbation au Soleil et aux planètes ; ils» sont affectés seulement en apparence. Il a déterminé les époques de discontinuité du moment d'inertie de la Terre et celles du frottement des marées, que nous reproduisons. Époques de discontinuité du moment d'inertie de la Terre : E. d\ /I 1667 + 1,54.10-8 1758 - 0,52 1784 - 2,06 1864 - 3,09 1876 -f 1,98 1897 •• + 3,92 ^ - 3,92 Epoques de discontinuité du frottement des marées : Perte d'énergie de rotation E. en ergs par seconde •*• Ui 1870 4,7 Ce tableau nous montre que le moment d'inertie de la Terre, ainsi que le frottement des marées, varient par sauts brusques, séparés par des longues périodes de stabilité. Grâce au travail de M. de Sitter, on peut représenter le mouvement de la Lune et celui des planètes au moyen de la théorie de Newton, sous la seule con- dition de tenir compte de petites corrections du temps déterminé par la rota- tion de la Terre, ou sous la seule condition d'utiliser le temps newtonien au lieu du temps terrestre.
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