# NavList:

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

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Re: Haversine formulae for Great Circles
From: Bill Noyce
Date: 2001 Nov 19, 8:42 AM

```George Huxtable's note includes this discussion of azimuth:

> Having calculated the altitude of a body, many navigators seem to
obtain
> the azimuth from-
>
> asn ((cos (90 - hour angle)*cos dec) / cos altitude)
>
> This is a terrible choice of formula. It gives a completely ambiguous
> result, for any azimuths that are near 90 degrees (and also near 270).
For
> example, an angle of 80 degrees has exactly the same sine as an angle
of
> 100, so the formula is quite unable to distinguish between these two
> solutions. And I know of no way of distinguishing between these
solutions
> "by inspection". If anyone else knows how to do this, I would be
interested
> to learn. Avoid this method

This is the formula used in Ageton's method, but there the ambiguity
is easy to resolve.  Ageton divides the navigational triangle with a
perpendicular from the star to the observer's meridian, and starts
by computing the length of this perpendicular and the latitude at which
it intersects the meridian.  If this latitude is north of the observer,
then the resulting azimuth is closer to north than south, and vice
versa.
```
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