Skip to main content
SpringerLink
Log in
Book cover

The Hill-Brown Theory of the Moon’s Motion

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

  • Book
  • © 2010

Overview

Authors:
  1. Curtis Wilson

    1. St. John's College, Annapolis, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Illustrates the complete history of the theory begun by G.W. Hill through to its completion by E.W. Brown
  • Numerous historical accounts reveal how and why perspectives on the lunar problem have changed over time
  • Uniquely present the set of lunar properties that made the moon a more difficult subject for celestial mechanicians than any other celestial body
  • Provides elementary explanation of the dynamics involved in the Hill-Brown theory making the book accessible to the non-professional
  • Includes supplementary material: sn.pub/extras

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (25 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Hill Lays the Foundation (1877–1878)

    1. Front Matter

      Pages 1-1
      Download chapter PDF

    2. George William Hill, Mathematician

      • Curtis Wilson
      Pages 3-8

    3. Lunar Theory from the 1740s to the 1870s – A Sketch

      • Curtis Wilson
      Pages 9-30

    4. Hill on the Motion of the Lunar Perigee

      • Curtis Wilson
      Pages 31-53

    5. Hill’s Variation Curve

      • Curtis Wilson
      Pages 55-68

    6. Early Assessments of Hill’s Lunar Theory

      • Curtis Wilson
      Pages 69-72

  3. Brown Completes the Theory (1892–1908), and Constructs Tables (1908–1919)

    1. Front Matter

      Pages 73-73
      Download chapter PDF

    2. E. W. Brown, Celestial Mechanician

      • Curtis Wilson
      Pages 75-77

    3. First Papers and a Book

      • Curtis Wilson
      Pages 79-108

    4. Initiatives Inspired by John Couch Adams’ Papers

      • Curtis Wilson
      Pages 109-122

    5. Further Preliminaries to the Systematic Development

      • Curtis Wilson
      Pages 123-135

    6. Brown’s Lunar Treatise: Theory of the Motion of the Moon; Containing a New Calculation of the Expressions for the Coordinates of the Moon in Terms of the Time

      • Curtis Wilson
      Pages 137-155

    7. A Solution-Procedure Without Approximations

      • Curtis Wilson
      Pages 157-165

    8. The “Main Problem” Solved

      • Curtis Wilson
      Pages 167-170

    9. Correcting for the Idealizations: The Remaining Inequalities

      • Curtis Wilson
      Pages 171-180

    10. Direct Planetary Perturbations of the Moon (The Adams Prize Paper)

      • Curtis Wilson
      Pages 181-191

    11. Indirect Planetary Perturbations of the Moon

      • Curtis Wilson
      Pages 193-200

    12. The Effect of the Figures of the Earth and Moon

      • Curtis Wilson
      Pages 201-206

    13. Perturbations of Order (δR)2

      • Curtis Wilson
      Pages 207-207
Back to top

Keywords

About this book

The Hill–Brown theory of the Moon’s motion was constructed in the years from 1877 to 1908, and adopted as the basis for the lunar ephemerides in the nautical almanacs of the US, UK, Germany, France, and Spain beginning in 1923. At that time and for some decades afterward, it was the most accurate lunar theory ever constructed. Its accuracy was due, rst, to a novel choice of “intermediary orbit” or rst approxi- tion, more nearly closing in on the Moon’s actual motion than any elliptical orbit ever could, and secondly to the care and discernment and stick-to-it-ive-ness with which the further approximations (“perturbations” to this initial orbit) had been computed and assembled so as yield a nal theory approximating the Moon’s path in real space with an accuracy of a hundredth of an arc-second or better. The method by which the Hill–Brown lunar theory was developed held the potentiality for still greater accuracy. The intermediary orbit of the Hill–Brown theory may be described as a periodic solution of a simpli ed three-body problem, with numerical parameters carried to 15 decimal places. George William Hill, a young American mathematician working for the U. S. Nautical Almanac Of ce, had proposed it, and computed the numerical parameters to their 15 places. A self-effacing loner, he had in his privately pursued studies come to see that the contemporary attempts at predicting the Moon’s motion were guaranteed to fail in achieving a lunar ephemeris of the accuracy desired.

Reviews

From the reviews:

“This is the second book on historical aspects of lunar theory to have been published by Springer within a twelve-month period. … the text is largely accessible without specialist knowledge of its central themes. … this text is mainly one for specialists. … the history of lunar theory introduces many fascinating ideas, and it refers very many creative mathematicians and astronomers.” (Peter Ruane, The Mathematical Association of America, August, 2010)

“This excellent book is a cornerstone in the history of astronomy. It deals with the Hill-Brown theory of the Moon’s motion between 1877 and 1984. … This lively written book contains many biographical notes and well-founded historical comments, and thus can be recommended to amateurs in astronomy and science history, and to instructors and scholars interested in the rapid development of astronomy and physics.” (Johannes Viktor Feitzinger, Zentralblatt MATH, Vol. 1202, 2011)

Authors and Affiliations

  • St. John's College, Annapolis, USA

    Curtis Wilson

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation