The Hill-Brown Theory of the Moon’s Motion

Its Coming-to-be and Short-lived Ascendancy (1877-1984)

  • Curtis Wilson

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Hill Lays the Foundation (1877–1878)

    1. Front Matter
      Pages 1-1
    2. Curtis Wilson
      Pages 3-8
    3. Curtis Wilson
      Pages 31-53
    4. Curtis Wilson
      Pages 55-68
    5. Curtis Wilson
      Pages 69-72
  3. Brown Completes the Theory (1892–1908), and Constructs Tables (1908–1919)

  4. Revolutionary Developments in Time-Measurement, Computing, and Data-Collection

  5. Back Matter
    Pages 319-323

About this book


The Hill–Brown theory of lunar motion was, from its completion in 1908 to its retirement in 1984, the most accurate model of the moon’s orbit. The mathematical, philosophical, and historical interest in the analytic solution of the lunar problem using the Hill–Brown method still engages celestial mechanicians, and is the primary focus of this work. This book, in three parts, describes three phases in the development of the modern theory and calculation of the Moon's motion. Part I explains the crisis in lunar theory in the 1870s that led G.W. Hill to lay a new foundation for an analytic solution, a preliminary orbit he called the "variational curve." Part II is devoted to E.W. Brown's completion of the new theory as a series of successive perturbations of Hill's variational curve. Part III describes the revolutionary developments in time-measurement and the determination of Earth-Moon and Earth-planet distances that led to the replacement of the Hill–Brown theory in 1984. Although some calculus and differential equations are included, the text is largely accessible without advanced knowledge in these areas. Amateurs of astronomy, as well as instructors and scholars of the general history of science, will find this book of significant interest.


Astronomical history Celestial mechanics E.W. Brown G.W. Hill Hill-Brown Theory History of Mathematics Lunar ephemerides Lunar motion Lunar tables

Authors and affiliations

  • Curtis Wilson
    • 1
  1. 1.St. John's CollegeAnnapolisUSA

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