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    Re: Working a lunar
    From: Christian Scheele
    Date: 2009 Aug 6, 22:30 +0200
    I forgot to add to question 2:
     
    It's not just precession and nutation that effect your "geometric locus". It also changes position because orbiting celestial bodies such as the earth, planets and the moon move at different relative speeds and the time difference between culminations change as a consequence. Also, the planets change speed as their distance to the sun changes throughout orbit. Then there is the matter of the parallax, most notably with regard to the moon, which will cause the line marking the half-time difference to deviate from a great circle track, which will complicate its derivation.
     
    Christian Scheele
     
     
    ----- Original Message -----
    From: Hanno Ix
    Sent: Thursday, August 06, 2009 7:34 PM
    Subject: [NavList 9388] Re: Working a lunar

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    George:

    Thank you for taking the time to think through this concept of mine - as of yet still half baked.

    Let me get to the core of the concept in form of a couple of questions:

    1. Is it true that:

    on land, the culmination of a heavenly body, including the moon, can be established rather accurately in reference to altitude and in reference to time as indicated by a stable local clock?

    Neglect for now culminations near the horizon.

    Typcally, on land a transit is being used for this measurement.

    How well the observed culmination refers to the real local Noon or GMT is not at issue in this question. The "stable" clock need only proceed accurately from second to second, but may not indicate GMT or even the local time.


    2. Is it true that:

    for any given time, there exists on the surface of the Earth a Geometric Locus of all those positions that have the same time difference DT between the culminations of two heavenly bodies?

    (The Geometric Locus need not be contiguous over the surface of the Earth and will change with GMT.  I assume it to be close to a straight line locally.)

    Affirmative ansers to these two questions form my basic assumptions. If they are not valid I will hold my peace.

    Best regards.

    H

    PS: Found your prior article and enjoyed it.



    --- On Thu, 8/6/09, George Huxtable <george{at}hux.me.uk> wrote:

    From: George Huxtable <george{at}hux.me.uk>
    Subject: [NavList 9385] Re: Working a lunar
    To: NavList@fer3.com
    Date: Thursday, August 6, 2009, 1:29 AM


    Hanno Ix suggested a different approach to lunars.

    I don't follow some details of that proposal. He wrote-

    "A ship reaches land of unknown coordinates. Land makes it practical for the
    navigator to measure the meridian passages of Heavenly Bodies rather
    reliably. Given GMT, he can calculate LAT and LONG. (One shot method.)"

    What is this "one shot method", which allows both lat and long to be
    obtained? Does it exist?

    However, leaving that aside, Hanno seems to be reinventing the wheel, as he
    suspected, when writing "I doubt if it is new".

    Obtaining time, and thus longitude can, in theory at least, be done by
    measuring simultaneous (or nearly so) altitudes of the Moon and
    another-body, rather than the lunar distance, across the sky, between them.
    Effectively, two-time-sights are being taken, which, because of the motion
    of the Moon with respect to any other-body, will only correspond to each
    other if the correct GMT has been assumed. Just as with any other
    time-sight, it's most accurate when the altitude changes rapidly with time,
    so is worst anywhere near meridian passage.

    Such a method has been proposed several times over the years, notably by
    Francis Chichester, in an article in "Journal of Navigation", misleading
    named "longitude without time", and followed up in other forums. It's
    described best, I think, in chapter 17, "Time by lunar lines of position",
    of John Letcher's book "Self-contained celestial navigation with H.O. 208"
    (1977).

    The method has been discussed on this list a few times, under various
    threadnames which I can't now recall, but that's no reason why Hanno
    shouldn't raise it again.

    The proposed method has the advantage of using the sextant, and making the
    corrections, in a familiar way, unlike lunar distances; hence its appeal.

    But it has serious snags. The lunar-distance method itself has the great
    drawback of lack-of-precision. A lunar distance, measured with an accuracy
    of 1 arc-minute, can establish longitude only within an error 30x greater,
    or 30' of longitude. So it has been useful in marginal circumstances when
    any rough notion of longitude is better than no notion at all: but not much
    better than that.

    The lunar-by-altitudes method is, most of the time, significantly less
    accurate, even, than lunar distances, for several good reasons, and that's
    enough to rule it out of court, or it least to outweigh any advantage it
    might have.  With a lunar, the thing hinges on a measurement of a single
    quantity, the angle in the sky itself. Provided the observer possesses
    enough skill, and the ship's motion is kind, this can be measured with some
    accuracy, because the horizon isn't involved (except for use with auxiliary
    corrections, not needed to high precision). In contrast, in any altitude
    observation, uncertainties in the horizon itself provide most of the
    inherent errors, and there have to be two such altitude measurements, not
    one, so increasing the scatter.

    With a lunar distance, angles between Moon and other-body are changing,
    increasing or decreasing, at a rate that's always in the region of 30' per
    hour, provided certain simple rules are followed. That can also apply to
    altitude measurements made in the tropics, when the Moon and other-body will
    pass nearly overhead, but not from higher latitudes, when the rate-of-change
    will always be less, and indeed much less when anywhere near meridian
    passage.

    These are practical problems that conspire against the altitude method;
    sufficient to explain why it has never been adopted in practice.

    If I've misunderstood what Hanno was proposing, perhaps he will explain
    further.

    George.

    contact George Huxtable, at  george{at}hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.


    ----- Original Message -----
    From: "Hanno Ix" <hannoix---.net>
    To: <NavList@fer3.com>
    Sent: Thursday, August 06, 2009 6:57 AM
    Subject: [NavList 9382] Re: Working a lunar


    Gentlemen:

    I am a novice to CelNav, and I certainly have no experience in lunars.

    Some algorithm occurred to me, though, that I would like to share and
    discuss. However, given the age of this business, if it is a valid one I
    doubt it is new. If anyone has seen it before, please let me know, so I
    could read up on it. The objective is to find GMT and location.

    Let's make a Gedanken experiment:

    A ship reaches land of unknown coordinates. Land makes it practical for the
    navigator to measure the meridian passages of Heavenly Bodies rather
    reliably. Given GMT, he can calculate LAT and LONG. (One shot method.)

    But now we pose GMT as unknown. Sitting on land, measure the meridian
    passages of, say, sun and moon which moves. Can I find GMT, too, using the
    now available data not using the classical moon distance methods?

    If I see things right, there must be a LOP which connects all locations on
    Earth with a given, fixed difference DT between the meridian passages of sun
    and moon.

    However, along this LOP, the same DT occurs at a different GMT. In this
    scenario, the LOP referring to a given DT is pre - calculated, listed in an
    almanac and annotated with GMT at each LAT. So, by having found the LAT
    before we just read the GMT of the DT-specific LOP.

    There is another opportunity:

    By accepting preliminarily this GMT, we can calculate LAT again, namely from
    the meridian passage of the MOON, and compare both values found. If there is
    a gross difference we must have made an error. This, by itself, would be of
    value. Otherwise, though, we have good reasons to accept the GMT we found.

    I appologize if I am talking about a method I have not gone through myself
    yet! I fear there is a hick-up in this somewhere. But I would like to hear
    the critique of you specialist navigators before I spend alot of time trying
    to do something long known as wrong.

    If, however, you find it sound, and has not done before I will pusue it.

    Best regards




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