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    Re: Lunar mechanics and Double Alts.
    From: Herbert Prinz
    Date: 2003 Apr 29, 21:43 +0000

    "Royer, Doug" wrote:
    > 04-26 turned out to be the perfect day to attemp this.Atmosphere was crystal
    > clear and between 50*F at the start and 68*F at the close with not a cloud
    > all day.
    Mr. Royer, I am glad that your observations worked out so well. From the data
    you posted I gather that you adopted the right strategy to overcome the time
    constraints that you were facing. You shot each object right after it came over
    your visible horizon at  10 or 11 deg altitude. It reminds me of a clay pigeon
    shooting in slow motion. Well done!
    > 1st round of sights at 0458zt.Moon's disk-Mars combination.
    By this you mean the far limb, right?
    > 0548zt Moon-Venus.
    I would probably have chosen to do Mars - Moon again, with the latter now
    definitely being out of the dangerous low altitudes and Mars being even higher.
    > 0504zt Moon's upper horn-Enif.
    > 0610zt Moon's lower horn-Fomalhaut.Could barely
    > see Fomal. at this time but compleated it.
    George Huxtable was already wondering about  this. I realize that you probably
    did not mean to measure the distance from the horn, but you just could not help
    it. The near limb _was_ at the upper horn. This in itself is an indication that
    Enif was an extremely unsuitable star to use. Enif is actually not a "lunar
    distance star"; it was not included in the distance tables of olden days
    almanacs. Enif is flanked by Markab and much brighter Altair, which both were
    tabulated. All three suffer from their far distance to the ecliptic of  ca. 20
    deg, which renders them useless in a situation where the Moon is too close to
    them. If you tried to reduce the sight, you will already have noticed yourself
    that the true distance between Enif and Moon hardly changed 10' per hour.
    In order to give observers in both hemispheres a chance, Fomalhaut was included
    in the list of "LD" stars despite of its SHA being nearly the same as that of
    Markab. Fomalhaut is similarly problematic, as it is as far to the south of the
    ecliptic as Markab is to the north. On the day of your observation, Formalhaut
    was unsuitable for distance observation. You would not have found it in the
    almanac on that day. Like Enif, it was positioned in a direction perpendicular
    to the path of the moon. This made it difficult to decide which limb was the
    correct one. I actually believe that you picked the wrong one by choosing the
    "lower horn". The correct limb would have been the far limb, near the upper
    (eastern) horn. (I have not seen the moon lately as it was raining on Saturday
    here on the East Coast. I am concluding this from almanac data and could have
    made an error in my computation.) At any rate, the question is irrelevant. The
    change in distance Moon-Fomalhaut at the time of your observation was around 10'
    / h and highly non-linear. One does not want to compute GMT from such an
    I warned you away from Altair, to which all the above comments apply also, but
    missed out on Fomalhaut, which I did not expect you to see at all. Partly so,
    because I based my predictions on latitude 40, not knowing yours, and partly
    because I am not used to visibility conditions like you seem to have had. The
    sun was already well over the astronomical horizon when you sighted Fomalhaut,
    but must have been hidden behind the mountains.
    As I suggested in my previous message, Antares was probably the only suitable
    star for distance observation last Saturday. Did you get a chance at all to try
    > 0703 and 0849zt Moon-Sun.
    It appears that you shot the sun as early as possible. May I infer from the
    timing of the second sight that this was the last time that you could obtain a
    clear image of the moon for the rest of the day?
    What we can learn from the unfortunate star sights is that, without an almanac
    feeding us the "distances of the day", it is upon us to be vigilant about the
    proper selection of suitable objects. Some criteria will be obvious from almanac
    data, such as whether a star is visible in the morning, evening, or not at all.
    Others will be seen easier in the sky itself, such as proper geometry. Around
    Full Moon, the limb can pose another delicate problem,  the correct choice
    sometimes easier deduced with arithmetic than from appearance.
    > I spent the rest of the day and evening doing Double Altitudes because I
    > haven't much experiance doing them.
    > 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.
    Ironically, Double Altitudes are the proper solution to the problem. George
    Huxtable suggests that you are mis-using the term for art. horiz. observations.
    But if you really mean by it the technique to observe two altitudes (e.g. of the
    Sun at different times) for the purpose of establishing your latitude and local
    time, then you are exactly on the right track. In order to compute the altitude
    of a star, you need neither GMT nor longitude. Latitude and local sidereal time
    (=LHA Aries) are sufficient. Think of what you do when computing an altitude for
    an intercept: You get the required LHA of the star by subtracting its GHA from
    yours (aka longitude). The GHA of Aries cancels out!
    So the principle of the operation is this: Use the sun altitude observations
    gathered during the day to establish your position with respect to the sky (NOT:
    Greenwich) at the moment of one of these observations. Advance this position to
    the moment of your lunar sight by means of a watch of known rate. Using this
    information, you can compute the required altitudes.
    A minor complication comes from the fact that the moon (fortunately!) does not
    move at the same rate as stars or sun, whence its LHA and Dec is strictly known
    only after GMT has been established. Therefore it is necessary to make an
    initial rough guess at GMT. This does not change or invalidate the principle.
    George Huxtable's objection against computing altitudes is only valid if these
    altitudes were computed from GMT and known longitude. I recommend this useful
    technique for practice shots, but it has little to do with the classical problem
    of finding longitude. Clearly, the whole point of LDs is missed, if you can't
    finally do it without knowledge of GMT and longitude. But it is important to
    understand that the question of using GMT for computing altitudes is different
    and much narrower than that of whether altitudes should or may be computed at
    all for solving the longitude problem.
    We have had this discussion of computed versus observed altitudes over and over.
    Will you indulge me if I put a view on it from yet another angle?
    In order to properly perform an LD using observed altitudes, we need four(!)
    officers on deck. Short of that, we have to cheat. Since one person can't
    measure the altitudes at the same time as the distance, if one is alone, the
    altitudes at the time of the distance observations have to be inferred (=
    computed!) from altitudes taken at other times. This is the logical principle,
    which remains unchanged regardless of the techniques being employed. Now, one
    way of computing the altitude is to compute it as the arithmetic mean of two
    altitudes taken before and after the distance observation. Obviously, there are
    limits to this method, since the altitudes do not change in a linear fashion.
    Outside the limits of where linear interpolation is permissible, we have to use
    a fancier method which we call "method of computed altitudes"; inside the
    limits, we call it "method of observed altitudes". Obviously, working out an
    arithmetic mean is not enough of a computation for some. Equally obvious is that
    the difference between the methods is merely a quantitative and very fluid one,
    depending on one's demands on accuracy. The methods differ only by the amount of
    sophistication that one puts into the effort of computing the altitudes at the
    required moment from the altitudes measured at a more convenient moment.
    It is unshakeable fact that you need to measure two altitudes in the course of
    the day. Whether you do it when you measure the distance, or at some other
    moment, is at your discretion, as long as you have a watch.
    Herbert Prinz

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