# NavList:

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

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Longitude by altitudes. was Re: How Many Chronometers?
From: George Huxtable
Date: 2009 May 8, 10:47 +0100

```I have switched the threadname to make it more relevant

Geoffrey Kolbe wrote-

"List member John Karl, in his book "Celestial Navigation in the GPS Age",
has a nice little section on page 73 entitled Time from a Lunar LOP and a
Star Fix. The essence of the method is the LOPs from a number of star fixes
will cross neatly at a given point on the chart, but that point will in
error in longitude due to the error in the chronometer. The longitude error
in a lunar LOP will be slightly different due to the faster motion of the
moon across the sky. The trick then is to adjust the time so that all LOPs -
including the lunar LOP - cross at the same point. The amount of adjustment
required gives the error in the chronometer.

I had not seen this described before and thought it quite neat."

"Hi folks, yes indeed this method also discussed in "Self Contained
Celestial Navigation" by John Letcher Chap 17 pgs 96-105. Pretty neat
indeed."

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

A sceptic  writes-

This reappears in our columns from time to time, and was proposed, 40 years
or so ago, by Francis Chichester, in an article entitled "longitude without
time", or something similar. It has two serious snags, which tend to be
glossed-over by its proponents.

Consider, first, the standard lunar distance method, which is perfectly
valid in principle, but has its own serious drawbacks, as follows-

1. The biggest problem is its inherent inaccuracy. Every minute of error in
the measured distance gives rise to about 30' of error in longitude.
2. Corrections for parallax and refraction are very demanding and need to be
3. The observation itself can be tricky because the sextant has to be used
in an unfamiliar way. It call for much practice and high precision.

The alternative way that Chichester, Karl, and Letcher, and perhaps many
others, propose to do this job, is basically by measuring the ALTITUDE of
the Moon and in some way comparing it with what that altitude should be from
a position determined by altitudes of other bodies. Any difference relates
to an error in the presumed time, and therefore in the longitude.

Because this involves only the familiar process of measuring altitudes, it
avoids drawback 3, above. It calls for quite a lot of calculation, but that
too is familiar stuff, so it avoids most of drawback 2. However, everything
still needs to be done to very high precision, because the result depends on
small discrepancies between different altitude measurements. But this method
has drawbacks of its own, which may explain why it has never caught on.

1. Except in or near the tropics, the Moon's changing altitude is less
affected by its changing position with respect to the star background, of
about half a degree an hour. Near Moon's meridian passage, it's hardly
affected by it all, so measuring Moon's altitude becomes a rotten way to
determine the Moon's motion against the stars. At high latitudes, and low
Moon declinations, the effect of the Moon's motion against the stars, on the
altitude, is never more than a fraction of that half a degree an hour,
because the Moon is never rising or falling vertically, but only at a
shallow angle. So the inherent weakness of a lunar observation for time, its
insensitivity, calling for such extreme precision in observation, becomes
amplified when measured by means of altitude, except in special
circumstances. On the other hand, measurements of the lunar distance
directly, with respect to Sun or star, are always in line, or nearly so,
with the actual motion of the Moon, so the full sensitivity of half a degree
an hour (or near) are achieved.

2. The inherent error in a normal sextant observation is not so much in
establishing the position of the object itself, but in assessing the true
line of the horizon below it, especially from the deck of a vessel. Horizons
are seldom straight sharp lines. Dip may vary from one day to another.
That's why a lunar distance has the potential for such high precision in
measured angle, because it doesn't involve the horizon at all (except for a
subsidiary, and insensitive, correction). In the Moon-altitude measurement,
errors in determining altitudes of Moon and other-bodies combine, and can
amount to a few arc-minutes, each minute giving rise to a longitude error of
at lease 30', and in some circumstances much more.

So, if anyone tries to persuade you of the virtues of such a method, look at
their arguments with a leary eye before taking such claims at face-value. To
be fair, John Karl does mentions some of these difficulties. But his
example, on page 77, must be in error when he states- "..also we see that
the Moon's altitude only changed by 31.3' in an hour (about 0.5' per
minute)". That's the rate of change of motion of the Moon with respect to
the stars, not the rate of change of altitude, which will be much greater.

George.

contact George Huxtable, at  george@hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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