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    Re: Raw data for bubble
    From: Bill B
    Date: 2007 Mar 22, 22:37 -0400

    Bill B responded to Bill Noyce
    > With LHA and AP lon we can estimate GHA, from which we can derive estimated
    > time of transit within a few minutes or better.
    > With time of transit, we get a closer approximation of declination and GHA.
    > We could use the direct computation of azimuth from the formula George
    > posted a while back as a sanity check.
    > "Tan Z = sin LHA / (cos LHA  sin lat - cos lat  tan dec)
    > and the rules for putting Z into the right quadrant, 0 to 360, clockwise
    > from North, are:
    > --If tan Z was negative, add 180 deg to Z.
    > --If hour-angle was less than 180 deg, add another 180 deg to Z"
    I am sorry, I built a circular argument.  It needs further thought on
    signing conventions for body east or body west, longitude east or west etc.
    but I think I am getting into the ball park. Lets try this:
    --Calculate LHA from the declination at best-guess time of transit.
      cos LHA = tan d / sin L
    --Add or subtract AP long to calculated LHA = GHAc
    --Calculate GHA for that estimated time used from the almanac = GHAa
    --Approx. time off transit in decimal hours
    = ( GHAc - GHAa ) / 15
    --Modify time used for the estimate by the time off.
      That will get you very close to the transit time for the AP.
    Now do a sanity check with the formula George posted to determine azimuth.
    If you are spot on, it will fail as tangent of 90d or 270d won't work on a
    pocket calculator.
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