Ernest William Brown

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Ernest William Brown
Ernest William Brown
Born (1866-11-29)29 November 1866
Hull, England
Died 22 July 1938(1938-07-22) (aged 71)
New Haven, Connecticut
Nationality British
Fields Mathematics
Alma mater Christ's College
Doctoral advisor George Howard Darwin
Known for Moon
Influenced Wallace John Eckert
Notable awards Royal Medal (1914)
James Craig Watson Medal (1936)
Fellow of the Royal Society

Ernest William Brown FRS[1] (29 November 1866 – 22 July 1938) was a British mathematician and astronomer, who spent the majority of his career working in the United States.

His life's work was the study of the Moon's motion (lunar theory) and the compilation of extremely accurate lunar tables. He also studied the motion of the planets and calculated the orbits of Trojan asteroids.



Brown was born in Hull, England, the only son of William and Emma (Martin) Brown. He was educated at Hull and East Riding College. After leaving school, he entered Christ's College, Cambridge, where he graduated with first-class honours in mathematics in 1887.[2] He continued with post-graduate studies at Cambridge and worked under the direction of George Howard Darwin. In the summer of 1888, Darwin suggested that Brown study the papers of George William Hill on the lunar theory. As it turned out, this idea for a line of research was to have a major impact on the remainder of Brown's life.

Brown was made a fellow of Christ's College in 1889, and received his master's degree in 1891. He then left England to take up a place as a mathematics instructor at Haverford College, Pennsylvania. There, he rose rapidly to the position of Professor of Mathematics in 1893.

Work on the motion of the Moon

At Haverford, Brown continued with his studies of the lunar theory, and made a thorough review of the work of earlier researchers, such as Hill, Delaunay and Hansen. His mastery of the field was shown by the publication of his first great work, An Introductory Treatise on the Lunar Theory, in 1896, when Brown was still less than 30 years of age. As Brown's work progressed, he gradually evolved a plan to create a completely new lunar theory. This was eventually published as a series of papers in the Memoirs of the Royal Astronomical Society between 1897 and 1908.

In 1907, Brown was appointed Professor of Mathematics at Yale University. He secured an agreement with Yale for funding the massive task of calculating detailed tables of the Moon's motion, based on his lunar theory. After a period of 12 years and a cost of over $34,000, Brown's magnum opus, Tables of the Motion of the Moon, was published in 1919.

Discrepancies between theory and observation

Brown's objective had been to produce an accurate ephemeris of the Moon, based purely on gravitational theory. For the 'main problem' of the Earth-Moon-Sun system, he calculated terms in longitude and latitude down to an uncertainty of 0.001 arcseconds. He also included perturbations due to the other planets (principally Jupiter and Venus) and also accounted for the more difficult problem of the non-spherical nature of the Earth and Moon.

Observations showed that Brown's tables were indeed superior to those of Hansen, which had been in use since 1857, but there was still a large unexplained fluctuation in the Moon's mean longitude of the order of 10 arcseconds. A 'great empirical term', of magnitude 10.71 arcseconds and period 257 years, was introduced to eliminate this as far as possible. Given the precision of Brown's calculations, it must have come as a great disappointment to have to introduce this arbitrary adjustment.

It had been discovered by Edmond Halley over two centuries previously that the Moon's motion appeared to be gradually speeding up. This 'secular acceleration' could not be explained by gravitational theory alone, and it had been suggested by Simon Newcomb that it was in fact due to a gradual deceleration of the Earth's rate of rotation, due to friction generated by the tides. In other words, the Moon was not speeding up – it was time (as measured in terms of Earth's increasingly long day) that appeared to be slowing down. Brown devoted much study to this problem and eventually concluded that, not only was the Earth's rate of rotation slowing, but there were also random, unpredictable fluctuations. Later work has shown this to be true, and astronomers now make a distinction between Universal Time, which is based on the Earth's rotation, and Terrestrial Time (formerly Ephemeris time), which is a uniform measure of the passage of time (see also ΔT).

Later work

Wallace John Eckert already became an instructor at Columbia University while finishing his PhD under Brown. Eckert would improve the pace of astronomical calculation by automating them with digital computers.[3] Brown retained his professorship at Yale until he retired in 1932. As well as continuing his work on the Moon, he also worked on the motion of the planets around the Sun. He co-wrote the book, Planetary Theory, with Clarence Shook, which contained a detailed exposition of resonance in planetary orbits and examined the special case of the Trojan asteroids.

Private life

Brown never married, and for most of his adult life lived with his younger unmarried sister, Mildred, who kept house for him. A capable pianist fond of music, Brown also played chess to a high standard. He loved travelling, hill walking, and detective stories.

A heavy smoker, Brown suffered from bronchial trouble for much of his life. He was afflicted by ill-health during most of the six years of his retirement, and died in New Haven, Connecticut in 1938.


Brown's Tables were adopted by nearly all of the national ephemerides in 1923 for their calculations of the Moon's position, and continued to be used, eventually with some modification, until 1983. With the advent of digital computers, Brown's original trigonometrical expressions, given in the introduction to his 1919 tables (and from which the tables had been compiled), began to be used for direct computation instead of the tables themselves. This also gained some improvement in precision, since the tables themselves had embodied some minor approximations, in a trade-off between accuracy and the amount of labor need for computations using the tables in those days of manual calculation.[4] By mid-century, the difference between Universal and Ephemeris Time had been recognised and evaluated, and the troublesome empirical terms were also removed.[4] Further adjustments to Brown's theory were then also made in a later stage, arising from improved observational values of the fundamental astronomical constants used in the theory, and from re-working Brown's original analytical expansions to gain more precise versions of the coefficients used in the theory.[5]

It was only as recently as in the ephemerides for 1984 that Brown's work was superseded: it was replaced by results gained from more modern observational data (including data from lunar laser ranging) and by altogether new computational methods for calculating the Moon's ephemeris.[6]



Named after him


  1. Darwin, C. G. (1940). "Ernest William Brown. 1866-1938". Obituary Notices of Fellows of the Royal Society. 3 (8): 18–66. doi:10.1098/rsbm.1940.0003. 
  2. "Brown, Ernest William (BRWN875EW)". A Cambridge Alumni Database. University of Cambridge. 
  3. Frank da Cruz. "Professor Wallace J. Eckert". A Chronology of Computing at Columbia University web site. Columbia University. Retrieved 4 June 2010. 
  4. 4.0 4.1 United States Naval Observatory (1954). Wallace J. Eckert, ed. Improved Lunar Ephemeris: 1952 - 1959. US Government Printing Office. 
  5. W. J. Eckert; M. J. Walker; D. Eckert (June 1966). "Transformations of the Lunar Coordinates and Orbital Parameters". The Astronomical Journal. 71 (5): 314–332. Bibcode:1966AJ.....71..314E. doi:10.1086/109923. 
  6. P. Kenneth Seidelmann (1992). Explanatory Supplement to the Astronomical Almanac. Mill Valley, California: University Science Books. p. 317. ISBN 0-935702-68-7. 


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