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    Re: Lunar question
    From: Frank Reed CT
    Date: 2006 Apr 12, 20:03 EDT

    Greg, you wrote:
    "Perhaps this is a naive  question but I was wondering; If you were to
    only use stars that were at the  same declination, and within say 10 to 20
    degrees of the moon couldn't you  dispense or greatly simplified the lunar
    distance clearing procedure? I  understand that this puts conditions &
    limits on usage, (maybe needing to  get up at 2am) but it should work just
    the same."
    Declination isn't  the critical parameter. But there is a way to simplify the
    calculations:  consider a star that is directly above or below the Moon. Then
    the correction to  the distance between the two is just the difference in the
    altitude corrections.  Generally (ignoring higher order effects for the
    moment), the corrrection to the  lunar distance can be written
    (Moon's altitude  correction)*cosA+(Sun's altitude correction)*cosB
    where cosA is the cosine of  the angle at the Moon between the vertical and
    the lunar arc (the great circle  between the Moon and the Sun) and cosB is the
    same for the star. If the two  objects are aligned vertically and on the same
    side of the sky, cosA=+1 and  cosB=-1 or vice versa. Now if those angles are
    less than 2 or 3 degrees, the  cosines will still be very close to 1. That
    means that the vertical alignment  does not have to be exact. You still need to
    measure the altitudes of both  objects in order to determine the values of the
    altitude corrections (taken from  the standard almanac tables or their
    In the general case,  you calculate the values of cosA and cosB. This is not
    difficult because we know  all three sides of the triangle (details under Easy
    Lunars on my web site). The  supposedly "difficult" calculational part of
    clearing a lunar distance --the  part where a 19th century navigator would have
    to turn to the tables of  logarithms-- was no more difficult than the ordinary
    time sight which was  required for "longitude by chronometer" sights.
    You also  asked:
    "Also why not just look for a star to go into  conjunction?"
    I think you probably mean occultation. These are rare. Also  the calculation
    to convert the time of the event into a longitude is very long.  The results
    can be quite accurate but still not perfect --the limiting factor  turns out to
    be the mountains of the Moon
    42.0N 87.7W, or 41.4N  72.1W.

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