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    Re: Lunar confusion
    From: Herbert Prinz
    Date: 2003 Apr 30, 10:27 +0000

    Dear Mr. Royer,
    Just a few notes in answer to your questions.
    >  ... some concept about the distance ...
    1) Easy: Sun and Moon.
    What  you really need to come up with is the distance between the centers of the
    two bodies, because that's the one that was tabulated or that you can compute
    from the almanac. You cannot measure this distance directly as the centers are
    not marked and you have no guidance where to point the sextant telescope. But
    imagine to stretch a rope between the centers. This fictitious rope describes a
    great circle in the sky. It intersects the limbs of the two bodies in two
    points. The distance between these two points is the shortest distance between
    the two bodies. Measure this, then just add the two semidiameters of Sun and
    Moon and you get the distance center to center. Now, this is a mathematically
    clearly defined concept, but how do you get these two intersection points
    without actually having the rope? These point are not marked, either! Answer: By
    bringing together the images of the limbs that face each other until they "kiss"
    each other. It is essential to the process to "swing the arc", just like you
    would do with a regular altitude sight over the horizon. This always works
    because the bright limb of the Moon is always towards the Sun.
    2) Almost as easy: Moon and star.
    When star and Sun are on opposite sides of the Moon, the "rope" between star and
    Moon runs through the dark part of the Moon. Since it would be extremely
    elaborate to compute the distance of the point where the rope intersects the
    terminator (=shadow border) on the Moon, it is not done. Rather, you extend the
    rope straight to the opposite limb, and instead of adding the Moon's
    semidiameter, you subtract it from the measured distance. The point where the
    extension of our fictitious rope intersects the limb is found in exactly the
    same way as in the first case: by swinging the arc.
    3) Matter of taste: Moon and planet.
    Planets appear as tiny disks in the telescope. Some try to estimate the center
    of the planet, some try to make contact of the limbs and correct for
    semidiameter of planet. Otherwise, same as Moon and star.
    4) Impossible: Star and Sun at right angles.
    Not that you want to try to use a star in this position ever again, but you see
    now why you had trouble finding the right point of contact with Fomalhaut: You
    can't swing the arc properly if you have only half or less than half of the
    limb. The horns are fading out slowly and you have no way of knowing whether our
    fictitious rope would intersect one horn or the other.
    > what you mean by the almanac providing "distances of the day".
    Like the "soup of the day" in most restaurants: The repertoire is fairly limited
    to start with, and within this you are offered a daily selection. When lunar
    distances were still tabulated in the almanac, only the sun, 4 planets and 9
    stars were used at all. Of these, not every object was listed every day. In the
    middle of the synodic month, you might get up to six choices. Towards New Moon,
    the selection would shrink to two or three. There was no point in listing an
    object that either could not be seen, or that was in a bad position on a
    particular day. If, on the other hand, a star was listed, you could more or less
    trust that it was usable. Using the tabulated distances was thus somewhat
    restrictive, but fool proof. Nowadays, when you compute your own distances, you
    are left to your own devices to avoid bad stars.
    > I was under the impression that the stars had to be close to the ecliptic
    >  or at least to the Moon to do this.
    No! That's dangerous. Close to the ecliptic AND close to the Moon might be O.K.
    Far from the ecliptic and close to the Moon is worse than far from the ecliptic
    and far from the Moon.
    > I"ve been sitting here for some time thinking through the movements of the
    > bodies and I think I see what you're getting at.Antares was moving almost
    > directly away from the Moon while the Moon kept almost between Enif and
    > Fomalhaut the entire time.
    That's exactly right.
    Best regards
    Herbert Prinz

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