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Bill wrote:
> First, to calculate the precise moment a body will be at 90d or 270d do I
> not need to know my latitude exactly?

Ah; precision precision. You are probably quite correct ... to be
precise. Establishing the latitude is, traditionally, relatively easy.
You could, for example, have worked it out only a few hours earlier at
meridian passage of the sun and are now looking for another position
line to get a fix, by running the earlier sight forward according to
your movement since then. What better than to get an LOP that crosses
your earlier line at exactly 90d, giving you a line of latitude and a
line of longitude, and a fix derived from both.

People have sailed around the world quite happily using only the sun
for navigation.

> If I am that sure of my latitude, why
> not use a time site to extract longitude directly?

You would need a number of bodies to get a fix. Here you need only
one, usually the sun (although, as with meridian passages, any body
can be used, assuming you can see it and the horizon).

Its an alternative to a round of sights of stars at dawn or dusk; a
way to establish a position line that is a local line of longitude
using the one sight. Or, to be precise(!), the one series of sights of
one body over five minutes of time.

There is one limitation in practice - its a summer-time only trick. In
winter months you may not find the sun at 90 or 270d.

> Second, if I understood you correctly am am not clear how the slope is used
> to determine the exact moment, or a are you saying with the slope you can
> use a point between observations that  corresponds to the calculated moment?

That's it. Have another look at the example of a slope. The adopted
time/altitude is independent of any of the observations made. Once you
have established what the precise moment for the desired azimuth is,
you start making timed obs for a few minutes before and continue for a
few minutes after. Then plot the slope. Then choose the precise moment
of time for the azimuth and use it, from where that moment intersects
the slope, together with the accompanying altitude. As a check
calculate the azimuth, it should be 90d or 270d.

> May I impose on you to give me a cook-book version of the method?

I started off intending to use tomorrow's date but its a bit late in
the season at my latitude and the sun turned out to be too low on the
horizon. Autumn is upon us (sigh).

So let's say its the 15 Jan 07 and at 11h 57m 09s, a few hours earlier
than the longitude sight, the observer established the latitude. Being
a conscientious navigator this person has accounted for the boat's
movement since then, and has found the latitude to be S34d 00' at the
time of the second sight (the DR long is E153d 00').

At 15h 36m 30s (local time, 10 hours ahead of GMT) the lower limb of
the sun has been calculated to find itself at an altitude of 40d 08.3'
at an azimuth of 270.0d.

Now the observer knows how to pre-set the sextant and plans to begin
making obs of the sun soon after 15h 30m, finishing before 15h 45m.
Only a period of five minutes including 15h 36m 30s will be used to
plot the slope. Having someone else to record the times and altitudes
enables more sights to be made over the same period.

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