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At [NavList 8049], Peter Hakel wrote
:
==========================

Thank you, Frank, for the detailed discussion of the rapid-fire fix from
multiple observations of a single body during a very short time
interval.  Coincidentally I have just been looking into the rather academic
problem of obtaining a fix from the altitude and azimuth of a body. I
understand that this is not done in practice because azimuth is
difficult/impossible to measure to sufficient accuracy.  Nevertheless, I
would like to know just how accurately one can measure azimuth in the
field/ocean and what portable devices (besides compasses), are available
for this (if any).

I hereby display the solutions to this "one-body fix" problem, if only as a
curiosity.  I expect that these have been worked out before but I haven't
found them anywhere so far (references would be much appreciated).  The
known quantities are the GP (Dec, GHA), observed altitude (Ho), and azimuth
to GP (Zn).  From the navigation triangle we can calculate the LHA and then
the Latitude:

==========================

If your position is unknown, the problem with measuring azimuth is knowing
where True North is. If you can see Polaris, measuring azimuths on land is
not a problem, just use a theodolite. Though for latitudes higher than
about 50 degrees it would be difficult to get your eyeball behind the
telescope, unless you have a 'broken' theodolite. Too, the errors in
measuring azimuths go as (the error in how level your instrument is) times
(the tan of the altitude), so the chosen bodies need to be low in the sky.

Given a reasonable 30x telescope on an average theodolite, the surveying
books say you should be able to see Polaris on a clear day. On a trip to
Egypt last November, I spent a frustrating afternoon trying to see Polaris
in a reasonably clear sky. No luck. I think it has to be a very clear sky
to see this second magnitude star in the daytime.

The other thing is that azimuths are not like position lines, which are
equally useful regardless of the azimuth of the celestial body. Consider a
one-body fix on Polaris, for example. The altitude of Polaris will give you
your latitude (pretty much) and the azimuth of Polaris tells you.... what?
Regardless of where you are in the Northern Hemisphere, the azimuth of
Polaris is going to be pretty much the same and tells you not much more
than you are in the Northern Hemisphere! So a one-body fix on Polaris will
not be much use to fix your position. Now consider the sun rising in the
East or setting in the West at the equinoxes. The local time of this event
will give you your longitude - but anybody anywhere on that longitude will
see the same event (sunrise in the East or sunset in the West) at the same
time, so an azimuth of the sun will not tell you much.

So, for useful azimuth measurements, use bodies low in the sky, avoid
bodies at the Cardinal points.

Geoffrey Kolbe


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