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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Azimuth Equation
From: T. Shanklin
Date: 2005 Oct 18, 23:12 -0700

```I've been recently programming a TI-81 Calculator to do my sight reductions.
Everything has been going swimmingly, getting closer and closer with my
sights and shooting more stars- until the past week or so when the LHA of
Altair at twilight became closer to 360 degrees.  With all my fiddling, I've
narrowed the problem and any accompanying possibly useful troubleshooting
information down to this:

The calculator will find Hc, but when it tries to calculate the azimuth, it
sends back the error message "Math 04 Error".  When I enter the equation and
values manually as one equation I get the same message after pressing enter.

Strangely it seems, I have found that when the Declination is South (that
is- the dec value is negative) the error message does not occur and
calculator works just fine.

The error message only shows up when the LHA is 345 degrees or greater.

I'm using the azimuth equation out of the Nautical Almanac:
cos-1[(sinDec cosLat)-(cosDec cosLHA sinLat)/cosHc]

To find Hc: sin-1[(sinDec sinLat)+(cosDec cosLHA cos Lat)]
In entering the equation, if the Declination or latitude is South, or the
Longitude is West, the value is negative.

I am unable to figure this out; I've reached the end of my mathematical
tether at this point.  When I work it out manually one step at a time
everything works out fine (e.g. calculate the sin Dec*cosLat, save that
value, calc. cos Dec*cosLHA...)  Does anyone have any clue as to why this is
happening?  Like I said, I had no problems whatsoever until the LHA began to
approach >345 degrees.

One example from my recent sights during which the problem occured:
Altair-10/13/05- 0157:28 GMT
LHA= 349.9983333
Dec= N8.885
Lat=N38.563

Todd Shanklin

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```
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