A Task that Exceeded the Technology: Early Applications of the Computer to the Lunar Three-body Problem

In: Revue de Synthèse

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.

  • Airy (George Bidel), 1886, Numerical Lunar Theory, London, Eyre and Spottiswoode.

  • Airy (George Bidel), 1888, “The Numerical Lunar Theory”, Monthly Notices of the Royal Astronomical Society, t. 49, p. 2.

  • Akera (Atsushi), 2007, Calculating a Natural World: Scientists, Engineers, and Computers During the Rise of U.S. Cold War Research, Cambridge (MA), MIT Press.

    • Search Google Scholar
    • Export Citation
  • Barrow-Green (June), 1997, Poincaré and the Three Body Problem, Providence, American Mathematical Society.

  • Bashe (Charles. J.), 1982, “The SSEC in Historical Perspective”, Annals of the History of Computing, t. 4, n° 4, p. 296-312.

  • Bashe (Charles. J.), Johnson (Lyle R.), Palmer (John H.), Pugh (Emerson W.), 1986, IBM’s Early Computers, Cambridge (MA), MIT Press.

    • Search Google Scholar
    • Export Citation
  • Brennan (Jean F.), 1971, The IBM Watson Laboratory at Columbia University: A History, New York, International Business Machines.

  • Brewster (David), 1860, Memoirs of the Life, Writings, and Discoveries of Sir Isaac Newton, Edinburgh, Edmonston and Douglas.

  • Brouwer (Dirk), 1939, “Ernest William Brown”, Monthly Notices of the Royal Astronomical Society, t. 99, n° 4, p. 302.

  • Brown (Ernest William), 1919, Tables of the Motion of the Moon, New Haven, Yale University Press.

  • Brown (Ernest William), 1938, “The Equations of Motion of the Moon”, American Journal of Mathematics, t. 60, n° 4, p. 785-792.

  • Brown (Ernest William), 1960, An Introductory Treatise on Lunar Theory, New York, Dover Publications.

  • Bullynck (Maarten), “Programming Men and Machines. Changing Organisation in the Artillery Computations at Aberdeen Proving Ground (1916-1946)”, Revue de synthèse, t. 139, 7e sér., n° 3-4, p. 239-264.

    • Search Google Scholar
    • Export Citation
  • Butrica (Andrew), 2014, The Navigators: A History of NASA’s Deep-Space Navigation, Charleston (SC), Independent Publishing Platform.

    • Search Google Scholar
    • Export Citation
  • Campbell-Kelly, (Martin), 1990, “Chapter Four: Punched-Card Machinery” in Computing Before Computers, Aspray (William) (ed.), Ames (Iowa), Iowa State University Press, p. 122-155.

    • Search Google Scholar
    • Export Citation
  • Chapront-Touzé (Michelle) and Chapront (Jean), 2000, “Analytical Ephemerides of the Moon in the 20th Century” in Astronomical Amusements: Papers in Honor of Jean Meeus, Bònoli (Fabrizio), De Meis (Salvo), and Panaino (Antonio), Milan, Associazione Culturale Mimesis Alzaia, p. 33-62.

    • Search Google Scholar
    • Export Citation
  • Clemence (Gerald), Brouwer (Dirk), and Eckert (Wallace John), 1960, “18. Planetary Motions and the Electronic Calculator.” in Shapley (Harlow)(ed.) Source Book in Astronomy 1900-1950, Cambridge (MA), Harvard University Press, p. 93-102.

    • Search Google Scholar
    • Export Citation
  • Comrie (Leslie John), 1932, “The Application of the Hollerith Tabulating Machine to Brown’s Tables of the Moon”, Monthly Notices of the Royal Astronomical Society, t. 92, n° 7, p. 694-707.

    • Search Google Scholar
    • Export Citation
  • Croarken (Mary), 1990, Early Scientific Computing in Britain, Oxford, Clarendon Press.

  • Dallas (Sarterios), 1970, Technical Report 32-1267: Prediction of the Position and Velocity of a Satellite After Many Revolutions, Pasadena, California, Jet Propulsion Laboratory, California Institute of Technology.

  • Dick, (Steven J.), 2002, Sky and Ocean Joined: The U. S. Naval Observatory 1830-2000, Cambridge, Cambridge University Press.

  • Eckert (Wallace John), 1935, “The Computation of Special Perturbation by the Punched Card Method”, Astronomical Journal, t. 64, p. 177-182.

    • Search Google Scholar
    • Export Citation
  • Eckert (Wallace John), 1940, Punched Card Methods in Scientific Computation, New York, The Thomas J. Watson Astronomical Computing Bureau.

    • Search Google Scholar
    • Export Citation
  • Eckert (Wallace John), 1948, “Electrons and Computation”, Scientific Monthly, vol. 67, n° 5, p. 315-322.

  • Eckert (Wallace John), 1958, “Improvement by Numerical Methods of Brown’s Expressions for the Coordinates of the Moon”, Astronomical Journal, t. 63, n° 1264, p. 415-418.

    • Search Google Scholar
    • Export Citation
  • Eckert (Wallace John), 1973, “The Solution of the Main Problem of the Lunar Theory”, in Sovremennye Problemy Nebesnenoĭ Mehaniki i Astrodynamiki [Contemporary Problems in Celestial Mechanics and Astrodynamics], Moscow, Izdatfly’stvo Nauka [Science Publishing], p. 65-75.

  • Eckert (Wallace John), Bellesheim (Sarah), 1976, “The Solution of the Main Problem of Lunar Theory by the Method of Hill and Brown”, Unpublished manuscript, 71 numbered pages plus 4 page preface, title page and table of contents. Box 2, Folder 2-4. Wallace J. Eckert Papers (CBI 9), Charles Babbage Institute, University of Minnesota, Minneapolis.

  • Eckert (Wallace John), Eckert (Dorothy), 1967, “The Literal Solution of the Main Problem of Lunar Theory”, Astronomical Journal, t. LXXII, n° 10, p. 1299-1308.

    • Search Google Scholar
    • Export Citation
  • Eckert (Wallace John), Smith (Harry F. Jr.), 1961, “Results to Date in the Numerical Development of Harmonic Series for the Co-Ordinates of the Moon”, Transactions of the International Astronomical Union, t. XI B, p. 447-449.

    • Search Google Scholar
    • Export Citation
  • Eckert (Wallace John), Smith (Harry F. Jr.), 1966, “The Equations of Variation in a Numerical Lunar Theory”, The Theory of Orbits in the Solar System and in Stellar Systems: International Astronomical Union Symposium, no. 25, 1964, London, Academic Press, p. 242-260.

  • Eckert (Wallace John) and Smith (Harry F. Jr.), 1976, The Solution of the Main Problem of the Lunar Theory by the Method of Airy, Astronomical Papers Prepared for the Use of the American Ephemeris and Nautical Almanac, t. 19, n° 2. Washington, D.C., U.S. Government Printing Office, p. 185-282.

    • Search Google Scholar
    • Export Citation
  • Eckert (Wallace John), Jones (Rebecca), Clark (H. Kenneth), 1954, “Construction of the Lunar Ephemeris”, in Improved Lunar Ephemeris: 1952-1959, Washington, D.C., U.S. Government Printing Office, p. 283-363.

    • Search Google Scholar
    • Export Citation
  • Eckert (Wallace John), Walker (M. Judith), Eckert (Dorothy), 1966, “Transformation of the Lunar Coordinates and Orbital Parameters”, Astronomical Journal, t. 71, n° 5, p. 314-332.

    • Search Google Scholar
    • Export Citation
  • Gluchoff (Alan), 2011, “Artillerymen and mathematicians: Forest Ray Moulton and changes in American exterior ballistics, 1885-1934”, Historia Mathematica, t. 38, n° 4, p. 506-547.

    • Search Google Scholar
    • Export Citation
  • Grier (David Alan), 2005, When Computers Were Human, Princeton, Princeton University Press.

  • Gutzwiller (Martin), 1976, “Preface” in Eckert (Wallace John), and Bellesheim (Sarah), 1976, “The Solution of the Main Problem of Lunar Theory by the Method of Hill and Brown” Unpublished manuscript, 71 numbered pages plus 4 page preface, title page and table of contents. Box 2, Folder 2-4. Wallace J. Eckert Papers (CBI 9), Charles Babbage Institute, University of Minnesota, Minneapolis, p. i-iv [unnumbered pages designated i-iv by me].

  • Gutzwiller (Martin), 1979, “The Numerical Evaluation of Eckert’s Lunar Ephemeris”, Astronomical Journal, t. 84, n° 6, p. 889-899.

    • Search Google Scholar
    • Export Citation
  • Gutzwiller (Martin), Schmidt (Dieter), 1986, The Motion of the Moon as Computed by the Method of Hill, Brown, and Eckert. Astronomical Papers Prepared for the Use of the American Ephemeris and Nautical Almanac, vol. 22, n° 1, U.S. Government Printing Office: Washington, D.C., p. 4-184.

    • Search Google Scholar
    • Export Citation
  • Hoffman (Joe D.), 2001, Numerical Methods for Engineers and Scientists, 2nd ed., New York, Marcel Dekker.

  • “In Memoriam: W. J. Eckert (1902-1972)”, 1972, Celestial Mechanics, t. VI, n° 1, p. 2-3.

  • Klock (B. L.), Scott (D. K.), 1965, “An Investigation of the Coefficient to Periodic Term 182 of Brown’s Lunar Theory”, Astronomical Journal, t. 70, n° 5, p. 335-336.

    • Search Google Scholar
    • Export Citation
  • Linton (Christopher), 2004, From Eudoxus to Einstein: A History of Mathematical Astronomy, Cambridge, Cambridge University Press.

  • Mulholland (John Derral), 1969, Letter to Richard Miller, September 4, 1969, JPL Ref. No. 391.13-83, IBM Archives, THP, Master Files, People, W. Eckert, Box 107, F2.

  • Olley (Allan), 2011, Just a Beginning: Computers and Celestial Mechanics in the work of Wallace J. Eckert, PhD dissertation, University of Toronto.

  • Sadler (D. H.) and Clemence (Gerald M.), 1954, “Introduction”, in Improved Lunar Ephemeris 1952-1959, Washington, D.C., United States Government Printing Office, p. vii-xiii.

    • Search Google Scholar
    • Export Citation
  • Schlesinger (Frank), Brouwer (Dirk), 1941, “Biographical Memoir of Ernest William Brown 1866-1938”, Biographical Memoirs of the National Academy of Sciences, t. 21, Washington, D. C., National Academy of Sciences, p. 242-273.

    • Search Google Scholar
    • Export Citation
  • Smith (Harry F. Jr.), 1965, Numerical Development of Harmonic Series for the Coordinates of the Moon, PhD thesis, Columbia University, Department of Mathematics, New York.

  • Smith (Harry F. Jr.), 2007, Interview carried out by Allan Olley, at Wilmington, North Carolina, United States of America, January 15th, 2007.

  • Sternberg (Shlomo), 1969, Celestial Mechanics, Part I, New York, W. A. Benjamin Inc.

  • Szebehely (Victor), 1967, Theory of Orbits: The Restricted Problem of Three Bodies, New York, Academic Press.

  • Szebehely (Victor), 1990, “Foreword”, in The Three-Body Problem, Marchal (Christian), Amsterdam, Elsevier, p. V.

  • Thorvaldsen (Steinar), 2010, “Early Numerical Analysis in Kepler’s New Astronomy”, Science in Context, vol. 23, n° 1, p. 39-63.

    • Search Google Scholar
    • Export Citation
  • Tropp (Henry), 1978, “Eckert, Wallace John”, in Dictionary of Scientific Biography, Gillispie (Charles) (ed.), New York, Charles Scribner’s Sons, t. 15, p. 128-130.

    • Search Google Scholar
    • Export Citation
  • Verdun (Andreas), 2013, “Leonhard Euler’s Early Lunar Theories 1725-1752. Part 1: first approaches, 1725-1730”, Archive for History of Exact Sciences, vol. 67, n° 3, p. 235-303.

    • Search Google Scholar
    • Export Citation
  • Wepster (Steven), 2009, Between Theory and Observations: Tobias Mayer’s Explorations of Lunar Motion, New York and London, Springer.

    • Search Google Scholar
    • Export Citation
  • Wilson (Curtis), 2010, The Hill-Brown Theory of the Moon’s Motion: Its Coming-to-be and Short-lived Ascendancy (1877-1984), New York, Springer.

    • Search Google Scholar
    • Export Citation
  • Woolard (Edgar W.), 1959, Letter from Edgar W. Woolard to Wallace J. Eckert dated April 23, 1959, Box 2, Folder 2–2. Wallace J. Eckert Papers (CBI 9), Charles Babbage Institute, University of Minnesota, Minneapolis.

Content Metrics

All Time Past Year Past 30 Days
Abstract Views 93 93 5
Full Text Views 12 12 0
PDF Downloads 7 7 0