# NavList:

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

**Re: lunar distance analysis.**

**From:**Frank Reed CT

**Date:**2007 Jan 8, 20:30 EST

DW, you wrote:

"I believe it possible to calculate the partial of LD with respect
to

Long analytically."

Long analytically."

This came up in the context of the longitude error that results from a
given error in the measured lunar distance. I think you're thinking in terms of
a lunar line of position (as we discussed in the past three months) in which a
lunar distance observation at known GMT yields a line of position, and two lines
of position yields the observer's latitude and longitude. There may well be a
partial derivative analysis that might possibly be of use in that case. But it's
important to distinguish these lunar lines of position from a traditional
18th/19th century lunar distance analysis in which the cleared lunar distance
yields Greenwich Time. That Greenwich Time combined with a value of Local Time
from a time sight gives longitude. There's no particular complexity in this case
in calculating the rate of change of the true lunar distance and multiplying it
by the error in observed distance resulting in the error in the longitude. For
example, the rate of change of the geocentric lunar distance might be 1.2
minutes of arc in two minutes of time. If the error in the observed lunar
is 0.6 minutes of arc, then the error in the time is 60 seconds. And of course,
one minute error in time implies 15 minutes of arc error in longitude.
The rate of change of the geocentric lunar distance varies up and down a little
bit around 1.0 depending on how close the Moon is to perigee or apogee and
depending on whether the Moon is moving more or less directly toward/away from
the star. This variation is rather small in the great majority of cases, so if
you want a quick estimate of the longitude error from a given error in the lunar
distance, just multiply by 30. That is, for a traditional lunar distance
observation, an error of 0.1 minutes of arc in the observed lunar distance
implies an error of 3 minutes of arc in the resulting longitude, assuming no
errors in the clearing calculation or the almanac data.

-FER

42.0N 87.7W, or 41.4N 72.1W.

www.HistoricalAtlas.com/lunars

42.0N 87.7W, or 41.4N 72.1W.

www.HistoricalAtlas.com/lunars

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