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    Re: Moon - Antares
    From: NavList
    Date: 2009 Jan 26, 07:38 -0800

    Mr. Reed, I believe that civil discourse requires a bit of formality, 
    particularly due to some of the invective found in the archives.  Topics that 
    involve intellectual discourse can become testy, so for now, I will stick to 
    the nee-plus-ultra formality.  
    I have been considering the statement by Mr. Reed that the changes in 
    elevation at the moon's limb may result in "seconds" of variation with 
    respect to the time of an event
    The minimum distance from the earth's center to the moon's center is given by 
    the Astronomical Almanac (USNO, 2009) as 0.00238 astronomical units.  
    Further, the Astronomical Almanac gives an astronomical unit as 149597871 
    kilometers.  Therefore, the distance betwixt centers is 
        356,043 km = 14959871 km * 0.00238
    The radius of the moon is given as 1737.4 km, so we can calculate the semi-diameter as
        16.775 arc-minutes = DEGREES(arctangent (1737.4 km / 356043 km))* 60
    This agrees, in general, with the Nautical Almanac (USNO, 2009)
    The radius of the earth is given as 6378.14 km, so we can calculate the horizontal parallax as
        61.5775 arc-minutes = DEGREES(arctangent (6378.14 km / 356043 km)) *60
    Again this agrees, in general, with the Nautical Almanac.
    The angular rate of the moon is given in the Nautical Almanac,  in the 
    increments section, as 14 degrees 19 minutes per hour (examine the increment 
    for 59 minutes and 60 seconds).  Because mountains on the moon will be small 
    compared to the radius, we must convert to arc-seconds of arc per seconds of 
    14.31666 arc-seconds/second = 14.31666 degrees/hour * (3600 arc-seconds/degree) / 3600 seconds/hour
    We can therefore calculate the height of the mountain required to obtain 1 
    full second, which is the tangent of the angular rate multiplied by the 
    distance from the earth to the moon. 
    24.712 km = tangent(RADIANS(14.31666 arc seconds/second)) * 356,043 km
    Next we should find the highest mountains on the moon.  While this is subject 
    to some debate, as there is no sea level on the moon, we can find tall 
    mountains quite readily by internet search.  We will ignore the placement of 
    these mountains on the moon, for the purposes of this argument, we will 
    assume that they are precisely on the moon's limb.  The tallest mountains 
            Mons Huygens        5.5 km
            Mons Hadley     4.6 km
            Mons Bradley        4.2 km
    These mountains fall short of the 24.712 km threshold for 1 second of time.  
    We can calculate the angle subtended by these mountains, and by application 
    of the angular rate of the moon, the time.
    Angle Subtended, arcseconds = DEGREES(arctangent(mountain height / earth moon distance))*3600
    Time, seconds = Angle Subtended * Moons Angular rate
            Mons Huygens        0.222 seconds
            Mons Hadley     0.186 seconds
            Mons Bradley        0.169 seconds
    In short, the tallest mountains on the moon, even if on the limb, fall far 
    short of "seconds" of time.  One can make arguments that the numbers can be 
    juggled to affect the result.  For example, we can subtract the earth's 
    radius from the distance, because the observer may be examining at the 
    zenith, yet these only affect the result in a marginal way.  
    From a different standpoint, lunar calculation for longitude could not have 
    been successful had the limb provided such variation in precision as seconds 
    of time.  Observers, of necessity, bring the object to the moon at different 
    limb locations as a function of the close proximity of the moon to the earth. 
     If seconds of variation existed, then the longitude could not have been 
    determined with the degree of accuracy necessary.
    I look forward to a spirited, if polite, discussion of this topic.
    Best Regards
    Brad Morris
    [Sent from archive by: bmorris-AT-tactronics.com]
    Navigation List archive: www.fer3.com/arc
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