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Equation of Time

From: Andres Ruiz (no email)
Date: Thu Aug 21 2003 - 10:46:37 EDT

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    The Sun, approximate coordinates: (RA, Dec)
    Sun's right ascension and declination
    // D: the number of days and fraction (+ or -) from the epoch referred
    to as J2000.0,
    // which is 2000 January 1.5, Julian date 2451545.0:
    // JD: the Julian date
    day = day + (hour+min/60.0+sec/3600.0)/24.0;
    JD = JulianDate( day, month, year );
    D = JD-2451545.0;
    // all the constants (therefore g, q, and L) are in degrees.
    g = 357.529+0.98560028*D;
    q = 280.459+0.98564736*D;
    // L: approximation to the Sun's geocentric apparent ecliptic longitude
    (adjusted for aberration).
    L = q+1.915*SIN( g )+ 0.020* SIN( 2.0*g );
    // Reduce g, q, and L to the range 0º to 360º
    g = ang_0_360( g );
    q = ang_0_360( q );
    L = ang_0_360( L );
    // Sun's ecliptic latitude, b, can be approximated by
    b = 0.0;
    // The distance of the Sun from the Earth, R, in astronomical units (AU)
    R = 1.00014-0.01671*COS( g )-0.00014*COS( 2.0*g );
    // mean obliquity of the ecliptic, in degrees:
    e = 23.439-0.00000036*D;
    // right ascension in degrees
    // RA is always in the same quadrant as L.
    // RA = ATAN( COS( e )*SIN( L )/COS( L ) );
    // the proper quadrant will be obtained.
    RA = ATAN2( COS( e )*SIN( L ), COS( L ) );
    // right ascension in hours
    RA = RA/15.0;
    // Reduced to the range 0h to 24h
    RA = time_0_24( RA );
    // declination
    Dec = ASIN( SIN( e )*SIN( L ) );

    // The Equation of Time, apparent solar time minus mean solar time
    // Eqt and RA are in hours and q is in degrees.
    EqT = q/15.0 - RA;
    // angular semidiameter of the Sun in degrees
    SD = 0.2666/R;

    See at: http://www.geocities.com/andresruizgonzalez/

    More accurate algorithm: Astronomical Algorithms. by Jean Meeus, 2 Ed
    edition (December 1998). ISBN: 0943396638


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