# NavList:

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

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Re: How Many Chronometers?
From: Frank Reed
Date: 2009 May 11, 00:34 -0700

```Geoffrey Kolbe, you wrote:
"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."

I have a hunch that we are seeing the influence of John Karl's advisor on this
book, namely Ken Gebhart. I've seen and heard Ken describe this technique in
just those terms more than once (including between sessions at Mystic last
June). He didn't invent it, of course. It's been around in one shape or form
for centuries. But Ken does like to sell the method that way.

This method of getting longitude by lunar altitudes has two problems, but
they're not necessarily more problematic than standard "lunar distance"
sights.

First, this method only works if the motion of the Moon on the celestial
sphere (in SHA and Dec). is more or less vertical at the time its altitude is
observed. Since the Moon's "horns" are nearly perpendicular to its motion
among the stars, there is a simple observational test. If the line through
the horns is within thirty degrees of horizontal, then you can safely use
this method with minimal error. Even at 45 degrees tilt, the accuracy is
reduced from 1.00 to 0.707. Since it was considered acceptable, though not
desirable, to use stars which were as much as 45 degrees out of line for
lunar distances, we should probably apply that same standard to longitude by
lunar altitudes. By contrast, if the horns are nearly vertical (consider the
Moon while it's rising, even right at due East, at the time of the "harvest
moon" in high latitudes), then the motion from a change in GMT will not much
affect the observed altitude.

Second, the horizon at sea probably shouldn't be trusted to more than half a
minute of arc. This applies mostly to sights taken at different times. If we
can observe the Moon's altitude and almost simultaneously observe altitudes
of other bodies, the lower limit on the horizon error probably can be dropped
to 0.25 minutes of arc. Measuring lunar distances, by contrast, does not have
this difficulty. On land, you can measure lunar altitudes with an artificial
horizon, and the problem of the horizon vanishes. In that case, and when the
above geometric condition for the orientation of the Moon is satisfied, lunar
altitudes are an excellent means of determining GMT using that method of
adjusting the LOPs to match as described in John Karl's book.

So we have a puzzle: why weren't lunar altitudes for longitude ever used or
recommended in practice (historically)?

-FER

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