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    Re: long lost lunars
    From: Frank Reed CT
    Date: 2003 Dec 6, 22:43 EST
    Last week, George Huxtable wrote:
    "Are you a new name to our list? If so, you are indeed welcome, especially with the message you bring. Lunar observers, as opposed to lunar pontificators, are few and far between. "

    Hey I can pontificate with the best of 'em <g>, but the proof is in the practice. I decided last year when I got back into lunars that I couldn't talk about them unless I could do them well myself.

    And thank you for your welcoming words. I think I should describe my background and interests. First, I'm a physicist by training specializing in gravitation. But my real interest has always been astronomical calculation and the practical arts connected to such calculations. I grew up in the Mystic, Connecticut area, and a year ago I moved back here to Mystic to work on a project for the local planetarium and celestial navigation center (just to be clear, I'm done with that project now so I don't presently work there and do not represent them in these messages). I am also the author/developer of the "Centennia Historical Atlas" CD-ROM which is required reading for all students at the US Naval Academy but that's another story.

    Mystic is the home of "Mystic Seaport", a museum dedicated to America's maritime heritage with a focus on the 19th century. For those who don't know of it, Mystic Seaport has a large collection of small boats, vessels, and several large ships including three National Historic Landmarks. The centerpiece of the collection is the Charles W. Morgan --the last of the wooden whaling ships and the oldest commercial vessel in the United States, built in 1841.

    The Planetarium at Mystic Seaport naturally emphasizes the history of celestial navigation in its daily programming though somewhat indifferently before I started working there last year. Many visitors to Mystic Seaport are at least aware of the story of Harrison and his chronometers from Dava Sobel's little book and the various tv documentaries and other multimedia that it spawned. It occurred to me that Mystic Seaport could capitalize on that familiarity by telling the other side of the story --the one in which Maskelyne is no villain. And so I began an effort to bring back "the long lost lunars".

    Step One: shoot some. Twenty-five years ago (when I was 17) I bought a Davis plastic sextant (the same model which is currently priced at about $195). It's a nice instrument and works well. I started there. To reduce my sights, I began by using Arthur Pearson's spreadsheet. I discovered that I could get 1-2 minute accuracy in the lunars using my plastic sextant. This depended on careful and frequent index correction measurements since plastic sextants change their adjustment with temperature. But I couldn't do better than that and I often found that the error would jump for no apparent reason to 3 or more minutes in a series of sights. After some experimentation, I discovered that the most serious flaw in the Davis plastic sextant is in the shades. In the middle of the night, I often needed a horizon shade to reduce the Moon's brilliance when using one of the fainter "lunars stars" (especially Hamal, Alpha Arietis). But the shades produced bad errors (presumably "prismatic error"). Now I might have been able to develop procedures to work around this problem, but at this point I decided it was time to get serious and switch to a high quality sextant.

    The Seaport Planetarium has a small collection of sextants for celestial navigation classes (and of course also a collection of preserved instruments). I borrowed the sextant from the class collection that I felt would best suit my needs for shooting lunars. It's a brass Plath sextant estimated to be from the late 1940s. Its best feature for lunars is a 6x30 monocular which makes the Moon nice and big in the field of view. This high-power monocular makes a BIG difference. With this instrument in hand, my lunars immediately improved in quality and the process started to seem even "practical" (I place that word in quotation because there is scarcely any part of celestial navigation that really qualifies as practical now that GPS has solved the problem of navigation).

    Mostly I shot my lunars from my backyard and calculated the altitudes. I also wrote my own version of Arthur Pearson's spreadsheet calculator but set up as a web page. I have designed my web calculators with small screens in mind. This means I can view them from a portable device --like my cell phone. Why a cell phone? Mostly because kids like them. Celestial navigation is dusty and moldy to most young people and lunars even more so. Pulling out a cell phone to work a lunar has an amazing effect on younger students. To give it a try, visit "fer1.com" (a short address since it's intended to be entered on a cell phone). The lunar distance calculator is on the page named "Moon and Sun". [please note: fer1.com is presently set up entirely for my entertainment so there are many sections that are "not ready for prime-time"]. I would also be happy to talk about calculations at some point if anyone is interested, but it's a big topic so I'll save that for another message.

    I also did a half-dozen lunars sets by shooting the altitudes along with the lunar distance. I did these from shore points near here where I could see the horizon. I also did one set from a boat but only a few miles offshore. Even in the middle of the night, shooting the altitudes along with the lunar presented no difficulties at all. My procedure was to shoot two altitudes of each object first, then shoot four to six lunar distances, and follow that up with two more altitudes of the objects taking note of "watch time" for each observation. I would average the lunars graphically and take out the time of the "best lunar". With that time I would interpolate the objects' altitudes. This interpolation is more than adequate to get the objects' altitudes to +/-6 minutes of arc which is all that is required to reduce the lunar distance sight. This graphical interpolation method works great and the whole process takes no more than ten to fifteen minutes. But for the most part, I no longer bother with direct measurement of the altitudes; I've satisfied myself that I can make the measurements when and if I need to do so.

    I usually do the lunars observations themselves with both hands on the sextant frame since the angle at which you have to hold the sextant is often awkward --and even painful after a few minutes. Holding he instrument stably is critical. To make this work, I would alternate between adjusting the sextant angle, making small adjustments of the micrometer, with the actual process of looking through the sextant. The lunar distance changes so slowly that you don't really need to keep a hand on the micrometer while observing (as is essential with altitude observations).

    A very accurate index correction and careful adjustments to eliminate perpendicularity error and the other sextant errors are essential for these delicate observations. I find that the best index correction observations come from "limb to limb" observations of the Sun or the horns of the Moon. Be careful if you try this with the Sun: if you forget the horizon shades, you'll shoot your eye out!

    It's also critical to get accurate altitude corrections including the effect of temperature and pressure. You can't ignore these if you want accurate results from the reduction of your lunar observations. This is one minor problem with some of the spreadsheet solutions and also Letcher's method which folds the refraction calculation directly into the reduction process. The method I use to reduce lunars when I want to be very accurate is based on the approach in Chauvenet and is closely related to Letcher's technique (I derived it myself but it's in the same family as those two methods).

    Shooting "practical lunars" for many months taught me one important lesson about chronometers: you need one. The only way to do navigation "purely" by lunars is to stay in port for three or four days every month around New Moon. If that's unacceptable (and I think it's clear that it is) then you need a chronometer that can run accurately for three or four days. Of course once you have that, it's not much of a jump to acquire a chronometer that will run well for the entire duration of a typical 18th/19th century sea voyage. The chronometer had to be developed to cover the period around New Moon. The lunar distance method was not complete without the chronometer.

    In over 250 planetarium lectures in 2003, I discussed the Moon as a "natural clock in the sky" and the fact that it was used by early 19th century navigators to cross oceans. I also invited a few dozen museum visitors over the summer to shoot their very own lunar (when weather and timing and moon phase would permit it). I've also shot lunars from the shores of Lake Michigan and from a half-dozen spots along Interstate-80 as I drove from Illinois to Connecticut --I can claim that I've crossed 800 miles of the United States using lunar distances to determine my longitude (well, ok, the road signs helped a little... <g>). So they're not dead yet, and maybe the 21st century is the time to breathe some life into the long lost lunars.

    Frank E. Reed
    75% Mystic, Connecticut
    25% Chicago, Illinois
    (I'm suposed to be in Chicago right now but we're getting buried by a blizzard in Connecticut this weekend so my travel plans have been pushed back a few days).

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