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    Re: Lunars
    From: George Huxtable
    Date: 1999 Mar 25, 12:23 PM

            A thread about Lunar distance measurements was active here until 16
    Feb 99, when a long posting by Mike Wescott
     appeared to finish it off. However, it
    seems to me that a few loose ends remain from this thread, and I aim here
    to tease them out and tie them off.
            Mike's mailing quoted an earlier submission to this list, undated,
    from Peter Smith, psmith{at}wellspring.us.dg.com, which in turn quoted a
    contribution made back on 18 Dec 95 by gottfred{at}agt.net (Jeff Gottfred). It
    seems to me that some of Jeff's statements from his 95 mailing could
    mislead readers. He is no longer a member of this mailing list, but is
    still a very active observer (land-based) of lunar distances. I have been
    in touch with him and he agrees that some of his procedures and
    recommendations, made back in 95, no longer represent his present thinking
    or practice. In addition, some of what he says refers specifically to his
    interest in land-based lunars, and would not apply to an ocean navigator.
    His present ideas and mine now largely agree; perhaps it would help readers
    if I note down where I differ from his mailing of 95. In general terms, I
    think he would now back most of what I say.
            Jeff Gottfred said in 95-
            " For my first attempt (in the absence of better information-- but
    more on that later), I simplified the problem of parallax by making my
    observation at the moment of lunar transit, and ignoring refraction by
    making sure to keep my observation above 20 degrees apparent altitude for
    both bodies. To make it easy with a reflecting horizon, I used the sun as
    the second body."
            My comments on this passage follow-
            There is no simplification (neither in observation nor in
    calculation) to be found by restricting Lunar distance observations to the
    moment of Lunar transit. An argument to justify this restriction is
    presented in Jeff's next paragraph, but I do not think it is well founded.
    The observer is free to choose his time of observation as he wishes, as
    long as the angle between the Moon and the other body (Sun or star) are
    within the range of his sextant, 120 degrees or so. Both bodies should also
    be more than 20 degrees or so in altitude, to ensure that local refraction
    anomalies near the horizon have no influence, and to ensure that the
    effects of refraction are small enough and predictable enough to be
    corrected for with precision.
            It is bad advice to suggest that refraction can be ignored if the
    altitude is over 20 degrees. For two objects on opposite sides of the
    zenith, the angle between them could easily be in error by 3 minutes of arc
    or more if refraction was neglected, which would put the longitude out by
    90 minutes; a 90-mile error in position if near the equator. Quite
    intolerable. No, all corrections to the observation, including refraction,
    have to be made to the highest possible precision, for a successful Lunar
    distance sight.
            It is very restrictive to confine Lunar distance measurements to
    those between Sun and Moon, neglecting the opportunity of using stars.
    Sextants won't cope with an angle measurement of much more than 120
    degrees, and there's a period of 10 days or so in each month, around Full
    Moon,  when the Sun-Moon angle exceeds this. (That's why the quintant was
    developed, to extend this range.) Taken together with the few days either
    side of New Moon, when Lunar distances can't be used because the Moon is
    then invisible, this would leave precious few days in each month for Lunars
    to be usable. So an ocean navigator needs to cope with star-Lunars as well
    as Sun-Lunars. Maybe it's different for an on-land navigator, if he can
    stay put for a few days and wait for the right time of the month.
            Jeff's reference to a "reflecting horizon" is because on land he
    doesn't have a natural horizon to measure altitudes from, so has to use a
    reflecting fluid pool in a dish, which gives 2 x altitude.
            Jeff's mailing said, earlier-
            "First, you must set your watch to local time-- I use solar time
    because its easier, and my watch is then useful for other purposes, but you
    could use any convenient body. Once you have set your watch to local
    apparent time, you apply the equation of time correction (as found at the
    bottom of each page in the Nautical Almanac) to set your watch to local
    mean time (NB, this is NOT the same as mean zone time!!) so you can relate
    it to the time data in the almanac, which uses the mean sun."
            My own comments follow-
            Personally, I would avoid all this "setting" of a watch, and so, I
    think, would most navigators. Instead, we would simply record the moment of
    local noon as read on the dial, without altering its setting. In this
    respect, Jeff and I still appear to disagree.
            As for correcting for the equation of time, to get the watch set to
    mean time, this is a consequence of the way Jeff has had to compute his
    Lunar distances. Let me quote what he says about this..."Lunar distance
    tables haven't been produced for over 80 years so I generated a little
    visual basic program that would crank out lunar distance solutions for
    every ten seconds for the hour of the observation--i.e., just enter the
    sun's GHA & dec, and moon's GHA and dec, and solve the problem..." Not
    surprisingly, his lunar distance computations were based on modern
    predictions for Sun and Moon position, which relate to mean time, as is
    always the case in modern astronomy.
            However, the lunar distance predictions that were tabulated in the
    old almanacs, up to the early years of this century, were, as I understand
    it, based on apparent time (the time given by a sundial) at Greenwich, not
    on mean time. This makes sense; mean time is only relevant to someone who
    possesses an accurate chronometer, which would generally exclude navigators
    who used Lunars. Longitude is measured as the difference between the
    apparent time according to the Sun at Greenwich and the observer's own
    local apparent time, by the Sun. The equation of time didn't come in at
    all. So, for those navigators who used Lunars in real life, with the tables
    of their day, the equation of time didn't need to be considered.
            Jeff ends with the following statement-
            "In the best case, you use three observers to measure the alitiude
    of the moon, the altitude of the sun, and the lunar distance at the same
           If you are doing this alone, then you must take a few obs of the
    lunar and solar altitudes, then measure the distance, then a few more lunar
    and solar altitudes. You must then plot the altitudes and pick the
    altitudes at the instant of the lunar distance measurement. One of the
    benefits of Young's method is that slight errors in the altitudes do not
    have a large effect on the result."
            Here are my comments-
            The most important part of this passage is in the last sentence.
    Although it's necessary to know the altitudes of the two bodies, this is
    only for the purpose of calculating the small corrections for parallax,
    refraction, and semidiameter. The observed altitudes appear to be
    thoroughly tangled up into Young's formula, but when the calculation is
    done, the effect of altitudes nearly cancels out. As a result, there's no
    need at all for any ritual of simultaneously measuring the altitudes and
    the lunar distance, nor any real need to bracket the altitudes round the
    Lunar distance shot. The altitudes can be measured, before or after the
    lunar distance, in a leisurely manner, and will be quite accurate enough.
    However, this only applies if the Lunar site is being used to determine
    time only.
            If the observer has an almanac of the position in the sky of the
    Moon and the other object, then once the time has been determined from the
    lunar distance, it can be used to obtain predicted altitudes for the two
    objects, and these can be compared with the observed altitudes, making the
    relevant corrections, to obtain two position lines. This, then, produces a
    fix. In that case the timing of the two altitudes becomes more important.
    They don't have to be measured at the same instant as the lunar distance,
    however, as long as the time offsets are known and allowed for.
            It's difficult, sometimes impossible. to measure altitudes at
    night, when taking a star-Lunar, and the horizon can't be seen. In that
    case, it's possible to get the time from a Lunar without measuring
    altitudes at all; instead, approximate altitudes are calculated from the
    almanac for the Moon and the other body, assuming an approximate time and
    position. Because the time obtained from a Lunar is so insensitive to the
    altitudes, this allows the accurate time to be deduced.
            I would like to thank Jeff Gottfred for the assistance he has given
    in putting this mailing together.
            George Huxtable.
    George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    Tel, or fax, to 01865 820222 or (int.) +44 1865 820222.
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