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    Re: Lunars - Oblateness Correction
    From: Andr�s Ruiz
    Date: 2008 Jul 15, 08:14 +0200

    The Oblateness is a negative correction:
    
    (ref: Corrections for sextant altitude, at my web page)
    For the Moon, the Oblateness of the Earth will be taken into account:
    OB = 0.0032*(SIN(2B)*COS(z)*SIN(H)-SQ(SIN(B))*COS(H)) [�]
    Where:
    *   B: latitude of the observer 
    *   z: azimuth of the Moon
    Approximate values are sufficient for the calculation.
    At mid-latitudes and for altitudes of the Moon below 60�, a simple approximation is made:
    OB = - 0.0017 * cos H
    
    The correction for parallax is:
    PA = HP * COS( H ) + OB
    
    Flattening: f=1-b/a 
    For WGS84 f = 1.0/298.257223563
    HP*f = 0.0032 aprox 1/300
    
    In Lunars this equation is approximate to avoid the use of the azimuth, removing the 3rd order terms by:
    PA = HP * COS( H ) * (1-(sin(B))^2/300)
    
    
    Am I wrong? This is the formula that I use in lunar calculations.
    Or is PA = HP * COS( H ) * (1+(sin(B))^2/300)
    
    Andr�s
    
    -----Mensaje original-----
    De: NavList@fer3.com [mailto:NavList@fer3.com] En nombre de frankreed@HistoricalAtlas.net
    Enviado el: domingo, 13 de julio de 2008 3:02
    Para: NavList@fer3.com
    Asunto: [NavList 5817] Lunars - Oblateness Correction
    
    
    Since this has come up in a several recent messages, I thought I would spell 
    out the way it's handled in my online lunars calculator. 
    
    The approach is straight out of Chauvenet. What we call "oblateness" is the 
    slight flattening of the Earth at the poles relative to the equator 
    converting it into an "oblate spheroid" rather than a perfect sphere. The 
    degree of flattening is approximately one part in 300 (1/297 is closer but 
    not significantly so for these purposes). Chauvenet usually refers to this 
    property as the "compression" of the Earth's spherical shape. 
    
    There are two pieces to the correction. First, you correct the HP taken from 
    the almanac (this is Chauvenet's "Table XIII" correction):
     HP=HP0*(1+(sin(Lat))^2/300).
    This is a small correction. On average, the error from ignoring it is 
    roughly 0.05 minutes of arc in the clearing process which corresponds to an 
    error in longitude of about 1.5' or about 1 nautical mile on average. The 
    correction is larger at higher latitudes, but of course this has a smaller 
    impact on the position fix since the longitude lines converge. 
    
    Second, you correct the lunar distance (after clearing it, but it doesn't 
    really matter whether you do it at the beginning instead) with a small 
    increment:
     inc_LD=sin(Lat)*[(HP/150)*(sin(Dec2)/sin(LD)-sin(Dec1)/tan(LD))]
    where Dec1 is the declination of the Moon and Dec2 that of the Sun or other 
    body. The error in longitude, converted to nautical miles, that would result 
    from ignoring this second small correction would be, on average, about equal 
    to
     (1.35 n.m.)*sin(2*Lat).
    By the way, Chauvenet has a factor of "A" in his equation and tells the 
    reader to look it up in a small table giving log(A) as a function of 
    latitude. If you're trying to figure it out from that table, bear in mind 
    that the table actually shows log(A)+10 which was normal back then. The 
    small variation of A with latitude is not at all important. Chauvenet had 
    the clever idea that most of this small correction could be included in the 
    lunar distance tables in the almanac. Then the correction would have been 
    simply
     inc_LD=sin(Lat)*x
    where x is equal to everything in the square brackets above. I have 
    considered adding this little addition to the predicted lunar distance 
    tables on my web site. Anybody want it? 
    
    PLEASE NOTE: these corrections have been included in the calculations of the 
    lunar distance clearing tool on my web site for over three years. You can 
    directly assess the significance of the total oblateness correction by 
    selecting "Ignore Oblateness" in the "Options" section. If you're trying to 
    get an exact assessment of your skill or your sextant's arc error, there's 
    no reason to turn off the oblateness calculation. But for historical 
    NAVIGATIONAL calculations or just for general understanding, there may be 
    times when you want to turn off the oblateness correction. 
    
    Incidentally, there's no real reason to bother with the remaining details of 
    Chauvenet's own, rather idiosyncratic method of clearing lunars. It was 
    rarely used, and it offers no really significant advantage. But the general 
    discussion in his book is definitely worth reading. 
    
     -FER
    www.HistoricalAtlas.com/lunars 
    
    
    
    
    
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