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    Re: Moon altitude problems.
    From: George Huxtable
    Date: 2006 Aug 20, 17:49 -0500

    I had written on this topic, as a step in deciding which Moon limb to
    use for measuring altitude, near full Moon-

    | "Whatever the phase of the Moon, if we observe it near the moment of
    | meridian passage, its shadow-pattern will always be symmetrical
    about a
    | horizontal line through its centre. In that case, there's always a
    | sharp line round 180 deg of its edge, from its upper limb to its
    lower
    | limb, on one side or the other, with a fuzzy edge on the other side.
    In
    | that case, it doesn't matter which limb is used, because there will
    | always be a crisp edge or cusp extending to both upper and lower
    | limbs."

    And Frank Reed has found the flaw in that argument-

    | That's not quite right. Consider the case of the First Quarter Moon
    | around 6pm local time on December 21. As its crossing the meridian,
    | nearly on the celestial equator, the line of cusps will be tilted by
    | about 23 degrees with respect to the meridian. An observer in
    | mid-northern latitudes would see the Moon on the merdian "tilted"
    | towards the southwest horizon, where the Sun set an hour or more
    | earlier. The navigator would then have to use the Lower Limb (also
    for
    | a substantial period before meridian passage).

    Frank is quite right, and my view was over-simplistic (i.e. wrong);
    that argument is hereby withdrawn. It is indeed the case, as he points
    out,  that the line between the Moon's cusps may not indeed be
    vertical when the Moon is on the meridian, giving an example at Moon
    quadrature in Northern Winter, when it isn't. So my argument was
    certainly invalid, in that it doesn't apply "whatever the phase of the
    Moon", as I had claimed.

    Rather more relevant to our discussion is the situation, not near
    quadrature (first or last quarter), but near full Moon. Neglecting the
    small lilt of the Moon's orbit plane to the ecliptic, the line of
    symmetry of the Moon's illumination will always be in the plane of the
    ecliptic, it seems to me. Some experimenting with a globe has now
    convinced me that that when a nearly-full Moon is on the meridian,
    that line of symmetry will by tilted from the horizontal by up to 23
    degrees either way, greatest at the equinoxes. So that invalidates the
    whole of my earlier argument. The situation is indeed more complex
    than my simple view could handle. Sorry about that, and thanks to
    Frank for his scrutiny.

    Frank goes on to say-

    | The condition to find the correct limb is easy to describe and use
    | visually, and not too tough to calculate.
    |
    | Visually, you look at the line of cusps (or near Full Moon the line
    | running more or less from the Moon's north to south pole which an
    | experienced observer should know from the appearance of the bright
    and
    | dark patches on the Moon's face --see PS). If the line of cusps is
    | vertical, neither limb is prefered. If the line is tilted so that
    the
    | upper cusp is to the right of the lower cusp (and the Sun is to the
    | right), then the Lower Limb should be used. Tilted the other way (or
    | with the Sun to the left), the Upper Limb is used.

    That's all very well, but the tricky situation we are considering is
    when it is so near to full Moon that no line of cusps is apparent. The
    discrepany, between a full Moon disc and a slightly-shadowed one, is
    invisible to the eye, but significant in terms of a precise sextant
    observation. And it's so near full Moon that it is by no means obvious
    whether the Sun is to the left or to the right. It's in those
    circumstances that the difficulty occurs, in making the necessary
    choice between upper and lower limb.

    Of course, once the nearly-full Moon disc has lost its apparent
    roundness, and the direction of the cusps and incident light is clear,
    there's no difficulty for an observer to choose the appropriate limb.
    It becomes obvious.

    George.

    contact George Huxtable at george@huxtable.u-net.com
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.


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