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George wrote:

> az = arctan2 ( tan dec cos lat - cos LHA sin lat  , - sin LHA)
>
> Really, you don't need to know any of the stuff above, except for that final
> formula for az. But Bill asked...
>
> It will give a true result, for all azimuths, even when the body is actually
> out of sight around the curve of the Earth, below the horizon, with a
> negative altitude.

Thank you very much George. Finally found the time to work through your post
and do some sample calculations on my TI-30XA's. Works just fine in the
rectangular-to-polar mode. Which leads me to another question.

As noted, we plug in two values and get two back.  When doing "flat earth"
trig, the first value returned (radius) is the distance from departure to
destination (when Lat and Lon were converted to miles).  The second value
returned was true course.

The question: When using the equation you posted, the second value is the
azimuth (or initial course in great circle sailing.)  That leaves me with
the mystery first value returned.  In the few trial runs I have done, it is
<1.0,  and it's cosine is in the neighborhood of calculated Hc (which of
course can be used to find distance of vice versa).  Was that pure
coincidence and a useless by-product, or can Hc/great-circle distance be
extracted from the radius value returned?

Bill

   

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