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    Re: Lunar mechanics and Double Alts.
    From: Doug Royer
    Date: 2003 Apr 29, 13:41 -0700

    Reflected Altitudes it is.My wording in all this is incorrect.I forgot the
    closest or furthest edge can be used,so I just used the edge of the Moon
    that was closest to each body.If I can remember things like the above I
    believe I've grasped the mechanics of this to have a go at the whole
    proceedure in May.Mars was to the South and West of the Moon.The Moon's
    cresant was on the further side away from Mars,so I used the shaded edge of
    the Moon which was closest to Mars for the sight and called it the disk for
    lack of words..Enif was to the North and West of the Moon,almost over the
    upper horn of the cresant.Venus was North and East of the Moon,so I used the
    lighted cresant for that sight.Fomalhaut was to the South and East of the
    Moon,almost under the lower horn of the cresant.I could see the Moon after
    sunrise and had no real trouble takeing those sights.Because of where I live
    all bodies must have an altitude of about 11* before I can view
    them.Fomalhaut was the hardest because it was almost totally washed out by
    the light.I didn't try anything on 04-27.No,I didn't try a star reflection
    other than Sirius but will in the very near future.
    If L + C didn't take the altitudes of the bodies,thier watches and chrono
    were suspect by themselves I read,what purpose did the exercise serve?
    -----Original Message-----
    From: George Huxtable [mailto:george@HUXTABLE.U-NET.COM]
    Sent: Tuesday, April 29, 2003 05:33
    Subject: Re: Lunar mechanics and Double Alts.
    1. Congratulations to Doug Royer for his well-spent Saturday taking on-land
    sextant observations. He got far more out of it than I expected, and far
    more than most of us would have got, I think. This is where his experience
    at sea and his regular sextant practice have paid off.
    2. However, it leaves a few questions outstanding. Doug refers to "Moon's
    upper horn-Enif" etc. While the horn of a crescent Moon might appear to
    provide a nice well-defined point to measure to, there's no simple way that
    I know of to correct a lunar distance measured to a horn, to compare with a
    lunar distance to the centre of the disc (which is the distance one can
    deduce from the Almanac). I think measurements to a horn are a waste.
    3. Following from that, I'm unsure what Doug refers to as Moon's disk in
    his "Moon's disk - Mars combination". A lunar distance is always measured
    to the "Moon's limb", so that the dot of Mars (for example) just brushes
    the outer, sharper edge of the apparent Moon as the sextant is tilted. This
    may be the Moon's nearer limb or the further limb to Mars (or other
    object), depending on how the Moon is being lit by the Sun at that time. So
    it will be greater or less than the distance to the Moon's centre,
    accordingly, by a Moon semidiameter. Attempts to estimate the unseen centre
    of the Moon's disc, and measure to that point, won't be accurate enough for
    a lunar distance. I don't know if that was what Doug was doing when he
    referred to measurement to the "Moon's disk": if it was, I am warning
    against it.
    Mars itself will (depending on its semidiameter) sometimes show in a 6x
    telescope as a visible crescent (I think) rather than a point, and when
    this happens with a planet it's best to allow the Moon's edge to bisect the
    light from that part-disc. A modern almanac is adjusted to give the
    position of the centre-of-light, not the centre of the planet. It's a tiny
    effect, though.
    4. Doug measured "0703 and 0849zt Moon-Sun". Where I live, it was 100%
    cloud that day. It would be interesting to know if Doug could readily find
    the pale Moon in the daytime sky. Did it help, that he had been watching it
    since before dawn and had a good idea where to find the Moon with respect
    to the Sun? Was the Sun at 0703 at a usable altitude (more than 10 degrees,
    say) so that its refraction correction could be relied on? No doubt by 0849
    it was well up. Did he look out next day, Sunday, and (if the weather
    remained clear), could he see the Moon at all? Clear mountain air may have
    helped him: here, even when there's no real cloud, the skies are seldom
    5. Glad that he found a good reflector material. I don't know what dark
    Karo syrup is. The main reason for choosing a dark liquid is to prevent a
    view of the bottom of the tin from confusing the reflected image.
    6. Doug uses the term "Double Altitudes" to describe altitudes measured in
    a reflector. This can be a bit confusing in the context, as "double
    altitudes" is a recognised procedure for obtaining latitude and local time
    from two altitudes of the same body, usually the Sun, measured (usually but
    not necessarily) before and after meridian transit, and well-separated in
    time. For what Doug was doing, I suggest the term "reflected altitudes"
    would be better.
    7. He says he got good reflections even on Sirius at twilight. Of course,
    with a reflector, star altitudes can be measured at any time of night, with
    a really black sky, because there's no need for twilight to see a horizon.
    Could Doug see fainter stars, such as Polaris, in a reflector at night,
    well enough for measuring?
    8. Doug said-
    >A good
    >many people responded that they calculate the alt. of each body.Is this or
    >actually takeing the Double Alts.the preferred way?If one doesn't really
    >know precisely where one is wouldn't measureing the alts. give you a better
    >end result of the Lunar than calculateing the alts.?Is calculateing the
    >alts. a step saver or am I just not seeing something? I need guidance on
    >this matter.
    To do the whole job properly, a measurement of the altitudes is called for.
    Otherwise, if you calculate the altitudes from a clock time, then you are
    assuming what you are trying to obtain: it's a circular procedure. Doing it
    that way, using GMT from a watch, and known longitude, allows you to
    predict what the lunar distance should be, so it allows you to check how
    accurately you are measuring it, but that's about all. Not very satisfying,
    really. Perhaps Arthur Pearson takes a rather different view.
    With at least one altitude observation (a "time-sight", away from the
    meridian) and a known latitude, you have enough data to work out local
    apparent time. From that, you can obtain calculated altitudes from the
    Almanac, and use that information to correct your lunar, and obtain GMT and
    hence your longitude. See "About Lunars, Part 4a" for details.
    I think measuring the observed altitudes of the two bodies was far more
    satisfying and was considered the right way to do the job by the mariners
    of the lunar era, even though it restricted star and planet lunars, at sea,
    to dawn and dusk twilights.
    9. Doug ended-
    >From reading the stories about the L + C exp.,they measured the
    >alts. instead of calculateing them.Does calculateing the alts. give you a
    >better time factor to work with?
    For those unacquainted with the history of the exploration of the American
    continent, L & C refers to the explorers Lewis and Clark.
    Lewis and Clark neither measured the altitudes of the bodies involved, nor
    did they calculate them. They simply noted the measured lunar distance to a
    body, and noted the corresponding watch-time, and left it at that, hoping
    that others would do the calculations on their return (which didn't happen,
    until very recently).
    They were familiar with the techniques of using a liquid reflector to
    measure altitudes (using a water surface, Bruce Stark tells me): that was
    how they obtained their latitudes. But even their latitudes were sometimes
    way out from the today's presumed positions of their camps. See
    Richard.S.Preston, "The Accuracy of the Astronomical Observations of Lewis
    and Clark", table, pages 185-186, to be found at
    www.aps-pub.com/proceedings/jun00/Preston.pdf   .
    If their latitudes could be 25 arc-minutes out, what value can be placed on
    their lunar observations? I no longer put a high value on the astronomical
    expertise of Lewis and Clark.
    George Huxtable.
    contact George Huxtable by email at george@huxtable.u-net.com, by phone at
    01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
    Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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