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    Re: Time Sight Problem: Joshua Slocum Lunar
    From: Frank Reed
    Date: 2011 Mar 25, 16:18 -0700

    Dave F.,

    In the setup for this, I tried to distinguish what was important for the problem at hand from the parts that are just background to the story. But I may not have been clear enough. The "lunar" aspect of this is not significant right now since I didn't give you any information to work it. What I've supplied is the end result of the lunar, namely the GMT to be compared with the time sight. You could just erase everything in the setup for this that relates to "lunars" and instead insert the phrase "You look at your chronometer and record the GMT as..."

    In your message, you wrote:
    "The afternoon solar altitude, given Lat is by definition a LAT measurement. We do not need to know DR Lo at all to obtain this result."

    Right, but you DO need the DR longitude, though not very accurately, in order to interpolate the Sun's Declination for the Noon Latitude. Essentially, you use the DR longitude to estimate the GMT of the Noon Sun. If the estimated GMT is wrong by an hour, and if we're near one of the equinoxes when the Sun is changing its Declination most rapidly, it would only throw off the resulting latitude by 1 nautical mile. Since in fact Slocum was working in mid-June, the estimated GMT is even less important.

    Then you wrote:
    "The afternoon lunar is an ideal sight to obtain Lo given that moon is most rapidly moving object in the sky and its near Prime Vertical position reduce errors in Lo attributable to measurement errors."

    The prime vertical doesn't have much to do with this. We're not using the Moon's altitude for anything at the moment, which is why I didn't give you any numbers for it. Of course, the (relatively) rapid motion of the Moon relative to the Sun is why we use the Moon to determine GMT, but it doesn't enter into this time sight problem.

    And you asked:
    "What is troubling is the lunar sight produced a GMT of 23:50:48. How is that possible?"

    I think you've gotten confused here. I didn't give you any information on the lunar observation. I said we would save that for another time. Rather, I'm giving you the output of working the lunar. After Slocum finished with his tables, he ends up with some value for GMT. We don't know what it was since his logbook from the voyage was presumably lost when he himself was lost at sea some years later. This is just a GMT value handed to you --just as if you had read it off a chronometer.

    You wrote:
    "Given assumed DR and measured altitude I can compute GMT but it has errors carried by the DR in it."

    That's not how a lunar works. We'll talk about that process another time. It doesn't depend on the DR.

    You asked:
    "So What kind of animal would the result be? It is Running since we are combining different times and an estimated position if it depends on DR, a Running Estimated Position?"

    The latitude that you get at noon has to be advanced to the later time. So in that sense, yes, nearly all 19th century fixes were running fixes (and not just 19th century --this was standard navigational practice on many, even most, merchant vessels as late as the 1940s). The longitude determined using the afternoon time sight and the GMT from the lunar is exact, in the mathematical sense since the observations are simultaneous, though naturally it is only as accurate as the observations themselves, and an error of a tenth of a minute of arc in the measured lunar amounts to just about three nautical miles in the longitude. But if you assume for the moment that the GMT is exact, then the error is just as always with altitude sights: one minute of arc error yields a one mile error.

    You concluded:
    "Is there a way to process sun and moon altitudes to extract GMT independent of DR? Are you going to tell us?"

    The way we would get GMT from these observations is by working the lunar observation. That's an angle measured as accurately as possible between the Sun and the Moon. Clearing this sight also depends on the altitudes of the Sun and Moon but they're not required to any great accuracy. For the case at hand, five minutes of arc error in the Sun's altitude is unimportant and half a degree or more error in the Moon's altitude would likely cause no problem.

    And again, we can talk about the details of the lunar another time. For now what we have is "latitude by the Sun's meridian altitude at noon" and "longitude by an afternoon altitude of the Sun (time sight) at a known value of GMT".

    -FER

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