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Re: FW: A noon sight conundrum
From: George Huxtable
Date: 2003 Nov 24, 20:23 +0000

In a mailing earlier today I said-

"When the Sun's declination is moving toward the observer's latitude, then
the moment of maximum altitude is delayed slightly after local noon, and
vice versa. The amount of this delay is calculated by taking the daily rate
of Northerly increase of declination for that date (from the almanac,
perhaps), and multiplying by
0.637(tan lat - tan dec),
where lat and dec are taken to be positive-North. (This is adapted from
Cotter, "History of Nautical Astronomy, page 265.) "

This was sloppy, because I didn't state the units of measurement of the
time-correction, which should have been seconds of time. Sorry about that.

"The Sun's midday altitude changes according to the rate of Northerly or
Southerly motion of the vessel with respect to the Sun's declination,
combined with the rate of change of declination. The North/South component
of a vessel's speed can be 20 knots or sometimes more. In which case the
adjustment between maximum and meridian altitude can become a very
important matter."

I should have pointed out again that in applying the above formula to a
vessel speed of (say) 20 knots Northerly, it's the DAILY rate around noon
that is required, all of 240 miles per day.

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

Zorbec Legras said-

"There is a formula to correct the problem of observing the sun by a
mouving observer:
T0 = ((T 1 + T2) /2) + correction
correction = 15,28 * ( motion in Lat  - motion in dec )*(tan Lat 1 - tan dec 1)"

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

In this expression, I guess that T1 and T2 represent the times of two
equal-altitude observations, so that (T1 + T2)/2 represents the moment of
maximum altitude.

What Zorbec doesn't make clear however, is that his "motion in Lat" and
"motion in Dec" refer to the (Northerly) rate of change in these quantities
PER HOUR, which is why his multiplying constant is just a factor of 24
greater than mine. Then, his correction will, like mine, be in units of
seconds of time, and his formula and mine agree. The remaining puzzle, to
me, is what "Lat 1" and "Dec 1" refer to, and whether they differ from lat
and dec.

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

Bill Arden, no doubt tongue-in-cheek, asked-

Gee, why do we bother trying to take time measurements to the second when
we're taking sights?

Well, any attempt to determine longitude, by chronometer or otherwise,
involves measuring time. As longitude changes with time by 15 degrees per
hour, or 15 minutes of arc per minute of time, then to arrive at a
longitude to within an arc-minute requires a knowledge of time to better
than 4 seconds.

George.

================================================================
contact George Huxtable by email at george---.u-net.com, 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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