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    Re: lunars with and without altitudes
    From: Frank Reed CT
    Date: 2006 Nov 21, 17:21 EST
    Hello Alex, in reply to my message asking for clarification of an earlier message,
    you wrote:
    "I was refering to the method of determining position
    by two observations of the Moon-star distances, without taking
    any altitudes. To my understanding, no chronometer was required
    because the GMT can be determined from one of the distances."
    Ok. That confirms my impression that you were talking about something rather different. I don't recall anyone suggesting a circumstance where you could get a complete position fix in latitude and longitude and *also* determine GMT from this pair of sights. That wouldn't work in any case, unless I've missed something.
    Here's the procedure I've described:
    1) Shoot some lunar distances involving two stars (or one star, or the Sun, separated by a few hours for a running fix). Record GMT for each sight.
    2) Clear the lunars and find the set of points where the lunar clears to zero error. You will find that the result is a line of position for each sight.
    3) Where the lines cross is your positional fix.
    4) Each line of position is really the intersection between a "cone" of position (with its apex at the Moon) and the surface of the Earth. If the Moon is high in the observer's sky, the cone of position always intersects the Earth's surface almost vertically. If the Moon is low in the sky and the star is directly above or below the Moon, the accuracy of the LOP is diminished by a factor of sin(altitude) because the cone of position intersects at a low angle. However, if the Moon is low, and the star is low, too, there is no decrease in accuracy because the cone of position still intersects the Earth's surface almost vertically.
    So why is this procedure interesting?
    Well, first of all, there's the simple interest of knowing what it is that a lunar distance sight is telling us. Naturally, historically, GMT was considered an unknown and the whole point of the sight was to determine GMT. Today, and for the foreseeable future, it's nearly impossible to imagine a "realistic" case where GMT might be lost, so it's interesting to ask whether any other navigational information can be derived from the same sight. And sure enough, there is indeed navigational information in a lunar distance sight. Each LD sight at known GMT yields a line of position which can be used just like any other LOP in celestial navigation, with the important caveat that an error of 0.1 minutes of arc in the measured distance implies an error of 6 nautical miles in the resulting line of position. More importantly, this lunar distance line of position requires no horizon --no horizon at all, natural or artificial. This is certainly an unusual thing in celestial navigation: the possibility of determining your position with a sextant when you cannot see the horizon and you have no workable artificial horizon.
    Could anyone ever use this today?
    To the extent that people still use celestial navigation, sure, why not. Suppose you're sailing in the Bermuda race in June, 2007 and you decide to enter under the celestial navigation rules (apparently you get a 2% time advantage if you do so). It is not particularly uncommon in the Atlantic between New England and Bermuda to find that the stars and Sun and Moon are visible but the horizon is lost in haze (and in addition, this area is prone to extreme, unpredictable refraction). So shoot a set of lunar distances, and work up your position from them. Don't worry about the calculational work; the rules permit computing devices for working any and all sights. You get a true position fix, and you get bragging rights to spare. As long as the Moon is in the sky, you can get a line of position and combine it with whatever other positional information you may have.
    Or perhaps you're playing modern-day Arctic explorer sailing up above the Arctic Circle next summer, near Spitzbergen perhaps, among ice flows and sea fog and weird refraction --no place to measure altitudes unless you have no other option. You were smart enough to bring a spare GPS to replace the primary, which has failed, but not quite smart enough to bring batteries for the spare. Luckily, one member of your group is a Navigation List lunarian and has brought along a sextant. The horizon is a mess, so you shoot a lunar distance between the Sun and the Moon (at known GMT), wait four hours, and shoot another. Cross the lines of position and you've got a position fix (accurate to about +/- 6 nautical miles *if* you're skilled enough with your sextant to measure angles to +/- 0.1 minutes of arc). [note that you can try this in a hypothetical case to verify that it works]. Of course, if you have a bubble sextant, you would almost certainly prefer to use that. Like anything in celestial navigation, there is a time and a place for every trick.
    42.0N 87.7W, or 41.4N 72.1W.

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