Re: What is the lunar-distance method of calculating longitude?

Stan,

I understand your frustration. It can be quite difficult to find information via the World Wide Web. Either the search engines haven't catalogued what you want or it is difficult to narrow the search.

I spent about 45 minutes to an hour looking up what little I found. I strongly suggest you continue your efforts at the largest library you can find.

One of the best references I found was the following: http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Longitude1.html

In 1514 Johann Werner published a translation of Ptolemy's Geography. In 
his commentary on Chapter IV, Werner put forward what became known as the 
lunar distance method for determining longitude. The method uses the fact 
that the Moon moves fairly quickly against the background stars, moving 
through its diameter in about one hour. If tables are given for the 
distance of the Moon from certain stars then it is possible in principle to 
determine an absolute time for the place of observation and thus to 
determine the longitude by comparing the absolute time with the local time 
in the same way as Hipparchus had proposed for his lunar eclipse method. 
Werner proposed using a cross-staff, an instrument derived from the Jacob 
staff of Levi ben Gerson, to measure the distance of the Moon from the 
chosen stars. He writes:-


Therefore the geographer goes to one of the given places and from there 
observes, by means of this observational rod at any known moment, the 
distance between the Moon and one of the fixed stars which diverges little 
or nothing from the ecliptic.


The method is theoretically correct but Werner had not solved the longitude 
problem since the 
cross-staff could not make accurate enough measurements, 
and more seriously there was no mathematical theory of the Moons orbit (and 
even when Newton gave his theory of gravitation 150 years later the Moon's 
motion, a three body problem, was beyond solution). Thus compiling tables 
of the Moon's position was only possible by collecting data and 
extrapolating to obtain predictions of the position which soon deviated 
from the actual position.

I also found this: http://www.britannica.com/bcom/eb/article/1/0,5716,115621+11,00.html

One of the earliest tabulations of the day-to-day positions of the heavenly 
bodies was Ephemerides, compiled by the German astronomer Regiomontanus and 
published by him in NŸrnberg in 1474. This work also set forth the 
principle of determining longitude by the method of lunar distances, that 
is, the angular displacement of the Moon from other celestial objects. This 
method, which was destined to become the standard for a time during the 
19th century, remained impracticable for more than three centuries because 
of the inaccuracy of the existing lunar tables, and because special 
knowledge and tedious computations were necessary in its use.

The first reference gives the best answer that I've found on the web. However, you are likely to find better information from books. I suggest, again, a good library and a good librarian. To get you started, try these

from http://www-groups.dcs.st-and.ac.uk/history/HistTopics/References/ Longitude2.html

A history of navigation is provided in J.E.D. Williams, From Sails to 
Satellites: The Origin and Development of Navigational Science (1992). 
General works include Nathaniel Bowditch, American Practical Navigator, 
rev. ed. by the United States Defense Mapping Agency Hydrographic/
Topographic Center (1984); Harold Gatty, Nature Is Your Guide (1958, 
reprinted as Finding Your Way on Land or Sea: Reading Nature's Maps, 1983); 
Alton B. Moody, Navigation Afloat: A Manual for the Seaman (1980); Malcolm 
C. Armstrong, Practical Ship-Handling (1980); Bruce Fraser, Weekend 
Navigator (1981), a good introduction; Tom Bottomley, Practical Piloting 
(1983), a useful training guide; Jeff Markell, Coastal Navigation for the 
Small Boat Sailor (1984), a manual for those with some sailing experience; 
Benjamin Dutton, Dutton's Navigation & Piloting, 14th ed. by Elbert S. 
Maloney (1985), a standard text; and Richard R. Hobbs, Marine Navigation: 
Piloting and Celestial and Electronic Navigation, 3rd ed. (1990), an 
introduction.

Celestial navigation is treated in John S. Letcher, Jr., Self-Contained 
Celestial Navigation with H.O. 208 (1977); Mortimer Rogoff, Calculator 
Navigation (1979); Mary Blewitt, Celestial Navigation for Yachtsmen, 10th 
ed. (1990); and Charles H. Cotter, The Elements of Navigation and Nautical 
Astronomy, rev. 2nd ed. (1992).