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Downloaded from Brill.Com09/24/2021 10:06:53AM Via Free Access 268 Revue De Synthèse : TOME 139 7E SÉRIE N° 3-4 (2018) Chercheur Pour IBM REVUE DE SYNTHÈSE : TOME 139 7e SÉRIE N° 3-4 (2018) 267-288 brill.com/rds A Task that Exceeded the Technology: Early Applications of the Computer to the Lunar Three-body Problem Allan Olley* Abstract: The lunar Three-Body problem is a famously intractable problem of Newtonian mechanics. The demand for accurate predictions of lunar motion led to practical approximate solutions of great complexity, constituted by trigonometric series with hundreds of terms. Such considerations meant there was demand for high speed machine computation from astronomers during the earliest stages of computer development. One early innovator in this regard was Wallace J. Eckert, a Columbia University professor of astronomer and IBM researcher. His work illustrates some interesting features of the interaction between computers and astronomy. Keywords: history of astronomy – three body problem – history of computers – Wallace J. Eckert Une tâche excédant la technologie : l’utilisation de l’ordinateur dans le problème lunaire des trois corps Résumé : Le problème des trois corps appliqué à la lune est un problème classique de la mécanique newtonienne, connu pour être insoluble avec des méthodes exactes. La demande pour des prévisions précises du mouvement lunaire menait à des solutions d’approximation pratiques qui étaient d’une complexité considérable, avec des séries tri- gonométriques contenant des centaines de termes. Cela a très tôt poussé les astronomes à chercher des outils de calcul et ils ont été parmi les premiers à utiliser des calculatrices rapides, dès les débuts du développement des ordinateurs modernes. Un innovateur des ces années-là est Wallace J. Eckert, professeur d’astronomie à Columbia University et * Allan Olley, born in 1979, he obtained his PhD-degree from the Institute for the History and Philosophy of Science Technology (IHPST), University of Toronto in 2011. His dissertation focused on Computers and Celestial Mechanics in the work of Walace J. Eckert. He is an independent scholar, whose research focuses on the history of computers and celestial mechanics. He has taught on the history of engineering at the University of Toronto, as a sessional lecturer. © fondation « pour la science » & koninklijke brill nv, leiden, 2019 | doi:10.1163/19552343-13900014 Downloaded from Brill.com09/24/2021 10:06:53AM via free access 268 revue de synthèse : TOME 139 7e SÉRIE N° 3-4 (2018) chercheur pour IBM. Ses travaux illustrent des aspects intéressants de l’interaction entre ordinateurs et astronomie. Mots-clés : histoire de l’astronomie – problème des trois corps – histoire de l’ordinateur – Wallace J. Eckert Eine Aufgabe, welche die Technologie übersteigt : Frühe Anwendungen des Computers für das Dreikörperproblems des Mondes Zusammenfassung: Das Dreikörperproblem auf den Mond angewandt ist bekanntlich ein unnachvollziehbarer Aspekt der Newtonschen Mechanik. Die Nachfrage nach präzisen Voraussagen über die Bewegung des Mondes führte zu praktischen Näherungsmethoden grosser Komplexität, die aus trigonometrischen Reihen mit Hunderten von Gliedern bestehen. Es nimmt deshalb nicht Wunder, dass schon von den Anfängen des Computers an, die schnelle Maschinenberechnung von Astronomen beson- ders gefragt war. Wallace J. Eckert, Astronomieprofessor an der Columbia University und Forscher für IBM, war einer der ersten Innovatoren auf diesem Gebiet. Sein Werk zeigt einige interessante Aspekte der Interaktion zwischen Computern und Astronomie auf. Schlagworte: Geschichte der Astronomie – Dreikörperproblem – Geschichte des Computers – Wallace J. Eckert Downloaded from Brill.com09/24/2021 10:06:53AM via free access a. Olley : A Task that Exceeded the Technology 269 ANALYSE ’astronomie entretient depuis toujours une relation étroite avec les mathématiques et le calcul. En particulier, les aspects peu maîtrisables de la mécanique classique, commeL le problème des trois corps, demandent d’énormes calculs approximatifs. La théorie de la lune est un cas particulier de ce problème qui, depuis Newton et sa théorie de gravitation, a donné lieu au développement de nouvelles techniques et algorithmes d’approximation. Au début du XXe siècle, la théorie de Brown-Hill était la théorie la plus perfectionnée. Les équations qu'elle mettait en jeu comportaient toutefois plus de 1400 termes, et leur application au calcul des positions de la lune nécessitait un savoir-faire et une masse de travail extrêmement importants. A travers l’étude de la carrière de Wallace J. Eckert, cet article montre comment l'utili- sation des ordinateurs pour résoudre ce problème a modifié la portée et les objectifs des efforts déployés, tout en insistant sur le rôle majeur qu'ont continué à jouer l'expérience et les pratiques des astronomes dans les choix de méthodes effectués alors. Wallace J. Eckert, un étudiant de Brown, a entrepris dans les années 1930 de reprendre une autre théorie du mouvement de la lune, celle développée par George Bidel Airy à la fin du XIXe siècle. Cette théorie, malheureusement, menait à l’évaluation de séries trigo- nométriques à des centaines de termes. Le calcul de ces séries étant impossible à l’époque, Airy avait abandonné cette théorie, mais Eckert pensait que l’on pouvait la développer plus loin si on utilisait des machines à calculer d’IBM. Dans les années 1930, Eckert a fait une première tentative avec les machines comptables d’IBM, pour l’abandonner ensuite et reprendre le projet en 1957 avec ses assistants Jones et Smith. Eckert a d’abord utilisé un IBM 650, puis un IBM 701 et finalement un IBM 7090 transistorisé. Le problème néces- sitait de résoudre quelques 3000 équations à 3000 inconnus. La quantité des calculs les ont ainsi poussé à utiliser des méthodes subtiles et logiquement complexes comme des méthodes de relaxation pour inverser des matrices de dimensions 300×300. Les résul- tats du projet n’ont été publiés qu’après la mort d’Eckert, dans les années 1970 par Harry Smith. En revanche, Eckert avait commencé vers la fin de sa vie à perfectionner et à amé- liorer la théorie de Brown-Hill, en utilisant des ordinateurs IBM 1620 et IBM 360. Après sa mort en 1971, ce projet a été poursuivi jusqu’en 1979, quand il est devenu apparent que le schéma de calcul fait par Eckert entraînait des marges d’erreurs supérieures à d‘autres projets qui calculaient les mouvement de la lune. Cette étude de cas met ainsi en lumière la manière dont les théories et les méthodes de calcul sont adaptées au fur et à mesure que la technologie se développe. Même si une théo- rie semble impossible à calculer de manière concrète à une époque donnée, elle peut l'être quelques décennies plus tard. Cette accélération dans le calcul change profondément les attitudes des astronomes : alors que l'élaboration d'une théorie de la lune était aupara- vant l'œuvre de toute une vie, un astronome pouvait espérer, au XXe siècle, développer et tester différentes approches au cours de sa carrière. Downloaded from Brill.com09/24/2021 10:06:53AM via free access 270 revue de synthèse : TOME 139 7e SÉRIE N° 3-4 (2018) Mais les travaux d’Eckert pour résoudre le problème des trois corps par ordinateur montrent également que ses choix et ses approches du problème ne dépendaient pas uni- quement de la puissance informatique dont il disposait. Ses travaux reposaient plutôt sur le répertoire des techniques développées par les astronomes ayant travaillé sur ce pro- blème avant lui, et étaient guidés par des valeurs esthétiques et des jugements imprégnés de cette tradition. En soulignant l’importance de cet héritage et le rôle des contingences historiques, cet article nous rappelle que ce ne sont les hommes, et non les ordinateurs, qui décident de la manière dont les équations seront résolues et que, pour ce faire, ils doivent exploiter pleinement le patrimoine mathématique et intellectuel dont ils disposent. Les travaux d‘Eckert montrent comment les théories et les méthodes de calcul sont adaptées au fur et à mesure que la technologie se développe. Même si une théorie semble impossible à calculer de manière concrète à une époque donnée, elle peut l‘être quelques décennies plus tard. Cette accélération dans le calcul change profondément les attitudes des astronomes. Downloaded from Brill.com09/24/2021 10:06:53AM via free access a. Olley : A Task that Exceeded the Technology 271 ince its beginnings in Antiquity, astronomy has had a special relationship with mathematical computing. Astronomy has sometimes acted as a catalyst leading toS innovation in computing practices, think of tables of logarithms or Schickhard’s calculating machines in the 17th century.1 Conversely, new computing practices have helped to verify existing theories or have even led to better or improved astronomical models. There are numerous problems in classical mechanics that are of direct practi- cal interest in astronomy that cannot easily or directly be derived and calculated, but must laboriously be worked upon and approximated through many exacting compu- tations. One classical example is the three body problem in astronomy that consists of finding a general expression for the trajectory of three celestial bodies in mutual gravitational attraction. Unlike the two body problem that admits of various ready solutions, such as the famous Kepler ellipses for the sun and the earth, the three body problem is famously intractable with no definitive solution for the general case and this has made it the focus of a great deal of intellectual effort. The first manifestation of these difficulties was Newton’s attempts to use his theory of gravity to derive adequate predictions of the motion of the Moon. The labour of analyzing the Moon’s motion under gravity was so difficult that it reputedly gave him headaches, and the explana- tion of several elements of the Moon’s motion eluded Newton.2 In the 18th century, research into lunar theory drew reputed mathematicians such as Euler, Clairaut and T. Mayer to compute and recompute lunar tables using observational data and devel- oping and reformulating theories of the moon’s motions, while testing new computing procedures to master the imposing calculations.3 In this paper I will show how when computers were employed in the solution of this problem they changed the scope and goals of efforts.
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