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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.

Bill






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