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(meteorobs) algorithm for Solar Coordinates (including sun's true longitude)

>Welcome back Wayne!!
>
>Hope the trip wasn't too bad....
>
>
>> are evening or morning, related to our position on the earth; UT of course
>> gets converted to Solar Longitude, our position in the orbit.
>
>What would the calculation for this be? How to change the UT to the
>Solar Longitude??
>
>Kim
>
>***************************************************
>Moonlight Cascade Observatory/BBS
>44.28.28.9N 76.29.45.9W
>Astronomy-RASC,SARA,ALPO/AAVSO-Solar Section
>NAMN-Meteor Observing,Ham Radio-VA3KDH
>***************************************************


Let me know if this is accurate enough.

      Solar Coordinates
    This algorithm is capable to calculate the geocentric position of
    the Sun with an accuracy of 0.01 degree. With this method the
    perturbations by the Moon and the planets are neglected. The method
    is based on a purely elliptical motion of the Earth around the Sun.

    Let JD be the Julian (Ephemeris) Day. Then the time T, measured in
    Julian Centuries of 36525 ephemeris days from the epoch J2000.0
    (2000 January 1.5 TD), which is given by:

    T = (JD - 2451545.0) / 36525

    This quantity should be calculated with a sufficient number of
    decimals. One minute in time corresponds with a difference of
    0.000000019 in T.

    Then the geometric mean longitude of the Sun, reffered to the mean
    equinox of the date, is given by:

    L0 = 280°.46645 + 36000°.76983 T + 0°.0003032 T 2

    The mean anomaly of the Sun is:

    M = 357°.52910 + 35999°.05030 T - 0°.0001559 T 2 - 0°.00000048 T 3

    The eccentricity of the Earth's orbit is:

    e = 0.016708617 - 0.000042037 T - 0.0000001236 T 2

    Then find the Sun's equation of center C as follows:

    C = (1°.914600 - 0°.004817 T - 0°.000014 T 2) sin M + (0°.01993 -
    0°.000101 T) sin 2M + 0°.000290 sin 3M

    Then the Sun's true longitude is:

    S = L0 + C

    and it's true anomaly is:

    v = M + C

    The Sun's radius vector, or the distance from the Earth to the Sun,
    expressed in astronomical units, is given by

    R = (1.000001018 (1 - e 2)) / (1 + e cos v)

    The Sun's geometric equatorial coordinates can be calculated by:

    tan R.A. = (cos E sin S) / cos S
    sin Decl. = sin E sin S

    in which E is the obliquity of the ecliptic, which has the value of
    23°26'21".448 = 23°.4392911 for the epoch of J2000.0 and
    23°.4457889 for B1950.0. You should remember that the tangent
    function does not always return the correct value of R.A.. The
    value is correct when it is in the same quadrant as S.
    --------------------------------------------------------------------
    Example

    Calculate the Sun's position on 1992 October 13 at 0h TD (= JDE
    2448908.5).

    We find successively:

    T = - 0.072183436
    L 0 = - 2318°.19281 = 201°.80719
    M = - 2241°.00604 = 278°.99396
    e = 0.016711651
    C = - 1°.89732
    S = 199°.90887 = 199°54'36"
    R = 0.99766 AE

    With:

    E = 23°.4392911

    we find for:

    R.A. = 198°.39082 = 13h.225388 = 13h13m31s.4
    Decl. = - 7°.78507 = - 7°47'06"

    --------------------------------------------------------------------

    The 'correct' values, calculated by means of the complete VSOP87
    theory, are :

    S = 199°54'26".18
    R = 0.99760853 AE
    R.A. = 13h13m30s.749
    Decl. = - 7°47'01".74
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