# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Lunars Tables**

**From:**Frank Reed

**Date:**2007 Dec 03, 01:22 -0500

Scott, you wrote: "Bought a copy of Bruce Starks, Tables for Clearing the Lunar Distance a few weeks ago. From the archives it looks as though Bruce was a regular contributor but I did not see anything of late." Something I've been meaning to say about Bruce's tables: while the development of another clearing method holds some technical interest (how much depends on your tastes for such things), Bruce Stark's book had a really significant impact on modern navigation education that I don't think is widely enough recognized. He brought back lunars almost single-handedly. By publishing his book and spending cash to advertise it and making it available to distributors, he helped make people aware of this once arcane historical method and sparked a lot of curiosity among practical navigators. Bruce Stark's book, combined with the generally too negative, albeit very prominent, account of lunars in Sobel's "Longitude," generated most of the modern interest in lunars among navigation enthusiasts. Of course, once the Navigation list started generating significant traffic, everything changed, and this is now "lunarian central." But Bruce Stark's tables started it all. You asked: "1) Are these the tables most members use for reducing Lunar observations or is there some other preferred method/tables? [I know there are many methods to do this, I'm just trying to get a feel for what method list members are using and what may be considered the most accurate method.]" Most? Probably not. There are as many answers to this as there are lunarian enthusiasts. When you first start thinking about lunars, you have to ask a number of questions (and everyone answers them differently). 1) Why shoot them? Is it for historical interest (either serious historical analysis, perhaps of old logbooks, or even just antiquarian re-enactment), or is it for modern entertainment (just something new and challenging to do with your sextant), or for modern practical use (as a method for testing your sextant), or for modern disaster thinking (hard to imagine losing GMT but lunars will get it back if you do)? 2) How will you observe them? With an antique or traditional sextant (related to the question of historical interest above), or a modern sextant (probably, but how much are you willing to "cheat" with modern technology)? And after you've observed them or acquired observations from a historical document, 3) how will you clear them? With a "historical" computer method (in other words, use software but base the algorithms on traditional methods in order to see how well they work), with a historical pen-and-paper method (this is much more practical today than even five years ago since you can download 19th century editions of Bowditch, Norie, etc. and use the old tables directly), or wih a modern computer method (the tools on my web site, for example, which include the almanac data thus making very short work of the whole process), or FINALLY will you use a modern pen-and-paper method (for which the best, maybe only, option is Bruce Stark's tables)? With so many options and possible ways of answering all these questions, it's not hard to see that relatively few people end up using Stark's tables exclusively. There have been a couple of list members, though, who really enjoy them (Mike B, where are you?). You asked: "2) Is anyone familiar with the trig/math that Bruce used to derive his lunar tables? If so, does anyone know if Bruce is amenable to posting it on the list or has it been posted in the past and I just missed it in the archives?" You probably know this bit already, but at the basic level, it's really simple. You set up the Sun-Zenith-Moon spherical triangle with the observed altitudes (zenith distances actually) of the bodies and the observed Sun-Moon distance. You use that to calculate, very exactly, the difference in azimuth between the Sun and the Moon. Next you correct the altitudes for refraction and parallax (just as you would clear normal altitudes --but use the bubble sextant rules in the Nautical Almanac altitude correction tables) and then since the difference in azimuth is NOT changed by the altitude corrections, you reverse the triangle and calculate the cleared distance. Compare that with known values of the distance at Greenwich for known values of GMT and a simple interpolation gives GMT at your location. This is a "direct" solution to the problem. Historically, and sometimes on this list, this was erroneously called a "rigorous" solution ("series" solutions which were morepopular historically were sometimes dismissed as "approximate"). Bruce Stark's tables are a clever, modern re-working of this "direct" solution. There's an easy way to find posts describing his tables in the archive. Go here: http://www.fer3.com/arc and in the search box, type "Stark's tables" (quotes not needed in this case). Click search and you should find about 87 matching pages. You can find all the details you want regarding the underlying calculational method by browsing through those messages. Somewhere along the way, you should find one from Bruce Stark himself describing the mathematical tricks he used. Follow the link after my initials for the online clearing tool on my web site. If there's sufficient demand, I am prepared to make a stand-alone tool with all the bells and whistles people ask for (historical clearing methods, graphing tools, automatically generating arc error from long series of observations, star-star distances, etc.), but I find that many lunarian enthusiasts are graduates of the "roll-your-own" school. They would rather build their own calculating tools carefully suited to their own personal answers to all those questions I described above... -FER http://www.HistoricalAtlas.com/lunars --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to NavList@fer3.com To unsubscribe, send email to NavList-unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---