The Hill-Brown Theory of the Moon’s Motion

1. Front Matter

   Pages i-xiv

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2. Hill Lays the Foundation (1877–1878)

   1. Front Matter

      Pages 1-1

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   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

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   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

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.

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

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)

• St. John's College, Annapolis, USA

  Curtis Wilson

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