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From: George Huxtable (no email)
Date: Sat Jun 04 2005 - 14:16:51 EDT
This discussion has diverged far enough from its original threadname,
"suggestion for a satisfactory celnav narrative", and taken on a life of
its own, so I've changed the threadname.
Fred wrote-
"Without knowing GMT, one could not determine longitude from an altitude of
the Sun when it is due East or West."
Well, yes: this whole discussion about the time to observe the Sun for
longitude has been based on the unstated assumption that the GMT was known.
In the early days, by a lunar. Later, by chronometer. Fred is right to
specify that more clearly.
He continued, referring to observing the Sun's altitude for a time sight,
when it's on or near the East-West "prime vertical"-
I also wonder how much the altitude of the sun varies with azimuth at
various locations when it is due East or West; it's azimuth can only be
measured to perhaps 0.1 degrees, how much would that limit the precision of
the measurement?"
I think measuring the Sun's azimuth to such high precision as 0.1 degrees
is unrealistic; but it's also unnecessary. Yes, it's true, if the Sun's
azimuth is exactly 90 degrees, then the deduced time, and longitude,
becomes completely independent of assumed latitude.
The answer to Fred's question is (as so often) in Bowditch, table 26 in my
2-volume edition of 1981. This shows that for all latitudes up to 48
degrees, the Sun's azimuth can be out by up to 4 degrees (i.e, between 86
and 94) from the East-West line, and even so, an error in the assumed
latitude of 10' will give rise to a resulting error in longitude of only
1'. So only a rough figure for latitude is needed, for a rather precise
result for longitude. Things get a bit more sensitive at higher latitudes.
Peter Fogg has added-
"...the sight must be calculated using the precise moment when the body
(usually the sun) is due east or west. This presents practical problems.
How to ensure that the moment of 'now!' is the desired one?"
As explained above, the timing of this operation doesn't need to be
particularly critical, unless the observer has no knowledge whatsoever of
his latitude (an unlikely state of affairs).
Peter continues-
"LINEAR REGRESSION IN REVERSE
The moment is calculated using the DR (assumed position, and the accuracy
is dependent on this). Then as many sights as possible are made over about
five minutes, a few minutes on either side of the desired moment. These are
then plotted on a simple graph; time on one axis, altitude on the other.
Then the desired moment is
>used to intersect with the slope to indicate the altitude to be used for
>sight reduction. The azimuth is then 90 or 270 degrees, the LOP runs due
>north/south, thus a line of longitude."
I just don't understand what Peter is proposing here. My fault, rather than
his, no doubt.
Could he provide a bit more detail, please, perhaps with an example?
Couldn't the moment, at which the Sun was theoretically on the East-West
line, be precalculated, and then its altitude observed at, or near, that
instant? I can see that making a plot would add something in accuracy, as a
result of the graphical "averaging" processes involved, but is there more
to it than that, that I haven't grasped? Is he proposing some sort of
"reiteration"?
George.
================================================================
contact George Huxtable by email at , by phone at
01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
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