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    Re: About Lunars, part 3
    From: George Huxtable
    Date: 2002 Feb 15, 23:16 +0000

    Chick Griffiths said-
    >While I was waiting for the Moon to reappear in the evening sky to play around
    >with lunar distances I've been measuring interstellar distances (as is
    >often put
    >forward as a method to check one's sextant for accuracy) for practice. This has
    >raised a couple of questions in my mind. First, the easiest way to deal with
    >refraction when measuring interstellar distances is to use two stars at equal
    >altitudes and not correct for refraction, would this be such a special
    >case when
    >measuring lunar distances that we should forget this as a possibility?
    George Huxtable replies-
    No, Chuck has this wrong. Even if two stars have equal altitudes, so they
    have the same refraction, the interstellar distance is still affected by
    that refraction. And the same applies to lunar distances.
    Try this out on a globe of the world, in exaggerated form. Forget about the
    continent-markings on it, we aren't using it as a model of the World, just
    as a sphere to show up the spherical geometry. In fact, we only need the
    upper hemisphere.
    The equator represents the plane of the observer's horizon, and the
    observer is at the centre of the globe.
    Mark a spot at say zero longitude, 30 N latitude, and another at 90
    longitude, 30N latitude. These spots represent the two stars, in GHA and
    altitude.  Measure the distance between the spots (the interstellar
    distance) with a piece of string, along the shortest path (a great circle).
    This length corresponds to the length of the ars between the two stars as
    seen by the observer.
    Now put in the refraction, but to show the effect, exaggerate it vastly.
    Imagine that the refraction for each star was 5 degrees. So move the spot
    representing each star down by 5 degrees, to 25N. Now measure the
    interstellar distance again, with the string, and you will see a
    significant increase.
    To calculate the effect numerically, see my "About Lunars, Part 3". and put
    some trial numbers into the "Letcher's method" calculation for refraction,
    putting identical values into m and s.
    >does choosing good moon star or moon planet combinations require that we give
    >some thought to the location of the other body relative to the path of the
    Yes, indeed it does. George.
    >I'm thinking that the optimum second body would be exactly in the path of the
    >moon's track though the sky. I also imagine that if the second body chosen were
    >"abeam" the moon as it passed, the measured lunar distance would change less
    >with time than if the second body were more or less ahead or behind the moon's
    >position but in it's path.
    >Chuck Griffiths
    Yes, you have expressed it very clearly. When the other body is "abeam" of
    the Moon as the Moon passes it, then the lunar distance is not changing at
    all, so it is then useless as a measure of time.
    When it is significantly "off-line" from the Moon's track, then two
    problems occur-
    1,  The bigger the off-line angle, the more slowly the lunar distance is
    changing, and so the lunar distance becomes a less-precise measure of time
    for that reason.
    2.  For large off-line angles, the variation of lunar distance with time
    becomes more non-linear. That assumption of linearity underlies the limit
    of 3-hours-or-less in the interpolation interval for time. If interpolation
    within a one-hour interval was chosen, then I think non-linearity would
    never be a problem.
    The lunar-distance measurement is rather forgiving, and can tolerate quite
    a large off-line angle, perhaps 30 degrees. It can be a problem when
    measuring stars, even those on the recommended list, or planets, when they
    are very near to the Moon. The direction of travel of the Moon in the sky
    is always, roughly speaking, close to its line of symmetry that bisects the
    Moon between its "horns". If you are measuring from the Moon to a close
    star or planet, make sure that it is within 30 degrees of that line of
    symmetry. That rule breaks down near full Moon, and I don't have an
    alternative to offer.
    Between the Moon and the Sun, there's never an out-of-line problem, as the
    Moon is always within 5 deg or so of the path of the Sun, and there's never
    any difficulty as they "pass", because for several days around New Moon the
    Moon can't be seen at all.
    George Huxtable.
    George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    Tel. 01865 820222 or (int.) +44 1865 820222.

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