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    Frank's formulas, was: Lunars: altitude accuracy
    From: Alexandre Eremenko
    Date: 2004 Nov 2, 12:43 -0500

    I verified Frank's formulas. They are indeed correct,
    and I have a rigorous proof of this.
    (Assuming no refraction).
    Another way to write them is this:
    
    ErDist(MA)=P.cot(dist).cos(MoonAlt).ErMoonAlt,
    
    where ErDist(MA) is the error in the cleared distance due
    to the moon altitude error, and P the numerical value
    of maximal parallax that is P=0.016; the ratio of the Earth
    radius to the distance to the Moon. Its reciprocal value
    is the factor 6' in Frank's formulas.
    
    ErDist(SA)=P.csc(dist).cos(StarAlt).ErStarAlt,
    
    where ErDist(SA) is the error in the cleared distance due
    to the star (or Sun) altitude error, and P is the same as
    before. (csc is cosecant, reciprocal to sine).
    
    So indeed everything deteriorates when the distance becomes
    small; but when the distance is near 90 deg, Moon's
    alt becomes irrelevant. Furthermore, when the altitude
    of the Moon or of the star is close to 90 d, this altitude
    becomes irrelevant:-)
    
    Nice formulas, indeed!
    
    Alex.
    
    On Sun, 31 Oct 2004, Frank Reed wrote:
    
    > I general, good (slightly approximate) expressions for the required accuracy
    > of the altitudes are:
    > AccuracyBody = 6' * sin(Distance) / cos(BodyAltitude)
    > AccuracyMoon = 6' * tan(Distance) / cos(MoonAltitude).
    > I have never seen these expressions in print anywhere.
    
    
    

       
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