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

Date: Thu Nov 11 01:14:49 1999
Posted By: Troy Goodson, Staff, Spacecraft Navigation, Jet Propulsion Laboratory
Area of science: Earth Sciences
ID: 941852008.Es
Message:

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 Nrnberg 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

• L A Brown, The Story of Maps (New York, 1951).
• S Chapin, A survey of the efforts to determine longitude at sea, 1660- 1760, Navigation 3 (7) (1953).
• R Eck, Tobias Mayer, Johann David Michaelis, Carsten Niebuhr und die Gttinger Methode der Lngenbestimmung, Gauss-Ges. Gttingen Mitt. 22 (1985), 73-81.
• E G Forbes, The scientific and technical bases for longitude determination at sea, NTM Schr. Geschichte Natur. Tech. Medizin 16 (1) (1979), 113-118.
• E G Forbes, Schultz's proposal for finding longitude at sea, J. Hist. Astronom. 2 (1) (1971), 35-41.
• D Howse, Greenwich time and the discovery of the longitude (Oxford, 1980).
• D Howse, Nevil Maskelyne: The seaman's astronomer (Cambridge, 1989).
• W Kokott, Astronomische Lngenbestimmung in der frhen Neuzeit, Sudhoffs Arch. 79 (2) (1995), 165-172.
• E G R Taylor, Old Henry Bond and the Longitude, Mariner's Mirror 25 (1939), 162-169.

from Daniel J. Boorstin, The Discoverers:

Derek Howse, Greenwich Time and the Discovery of Longitude (1980)

also try

The Quest for Longitude : The Proceedings of the Longitude Symposium Harvard University, Cambridge, Massachusetts November 4-6, 1993 William J. H. Andrewes, Harvard university press.

and

Dava Sobel, Longitude : The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time

Finally, here are some references from Encyclopedia Britanica http://www.britannica.com/bcom/eb/article/2/0,5716,115622+1+108753,00.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
ed. (1990); and Charles H. Cotter, The Elements of Navigation and Nautical
Astronomy, rev. 2nd ed. (1992).```

I would be very surprised if the technique could not be done today. It's likely, though, that you'd need a sextant and a copy of The American Ephemeris and Nautical Almanac

I'm very interested to know what you find in your library search. Please email me!

Troy

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