Article ID: CBB000930138

The Nub of the Lunar Problem: From Euler to G. W. Hill (2008)

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For a century Euler's dare found no response from lunar theorists. Then in two papers of 1877 and 1878, George William Hill (1838--1914), a mathematician in the U.S. Nautical Almanac Office, accomplished all that Euler could have wished.4 (We have no evidence that Hill ever read Euler's paper of 1766, but he was familiar with Euler's third lunar theory of 1772, which proceeds along the lines of the 1766 paper.) In his paper of 1878, Hill solved the very problem that Euler had proposed. He computed with high precision (to 15 decimal places) the numerical parameters defining the orbit that yields Tycho's Variation (he dubbed this orbit the `Variation Curve'). His method was such as to permit increasing the precision to any degree that might be required. Moreover, he laid out a plan for developing the entire lunar theory on the basis of the Variation Curve.5

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Description On Euler's challenge to solve the problem of variations in the lunar orbit, solved by Hill in the 1870s.


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Authors & Contributors
Gough, Thomas T.
Chabás, José
Mitton, Jacqueline
Wlodarczyk, Jaroslaw
Wilson, Curtis
Venugopal, Padmaja
Concepts
Astronomy
Celestial mechanics
Moon
Sun
Cosmology
Astrophysics
Time Periods
19th century
Medieval
Ancient
20th century, early
18th century
Ming dynasty (China, 1368-1644)
Places
Scotland
Spain
Mesopotamia
Sydney (Australia)
Middle and Near East
England
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