# NavList:

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

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Re: Latitudes by lunar distance. was: Lunars with and without altitudes
From: Dave Walden
Date: 2006 Nov 26, 14:23 -0800

```Apologies for the lack of documentation in the code.  Like many/most
engineers and scientists, I find the work fun, the report writing less
so.  I realized that if I didn't "just send it", I'd probably
move on and never come back to write it up more properly.  So again,
apologies, and I'm more than happy to provide any

The previous post is a place to start on Maxima documentation.  A
reference I find useful is Michael Clarkson, DOE-Maxima Reference
Manual, ver5.9, Aug 2002.  (Try google for macref.pdf)

%i10 is the usual equation for cleared lunar distance (Cotter p212
bottom following "From which:") I actually took it, with the fairly
widely used notation, from, "Josef de Mendoza y Rios", Recherches
sur les principaux Problemes de l'Astronomie Nautique, p79, as
discussed earlier.  In FORTRAN (and radians):

D=acos(
(cos(d)-sin(a)*sin(h))*(cos(A)(cos(H))/(cos(a)*cos(h))+sin(A)*sin(H))

Where, D is cleared distance, d is observed, a is apparent moon
altitude, A is true moon alt, h is apparent star/sun/planet altitude, H
is apparent star alt.

Using the Nautical Almanac algorithm for position from intercept and
azimuth by calculation p282, I get W69-33, N38-40.  I purposely used
Nautical Almanac precision.  I will repeat with ephemeris values.

On SD, I may have mistakenly used 16.2 for one star and 16.1 for the
other.  I meant 16.1.  This is the Nautical Almanac value.  It agrees
to the nearest 0.1' for 30 to 60 degrees to the more precise value in
this case.  Again, more precision is possible.

On refraction, that is indeed the method I used.  I stopped at one term
because it gave accuracy consistent with other choices.

On parallax, yes the issue is the "backwards" correction.  See for
example, John Brinkley, Elements of Astronomy, 1819, pg 319.   (Google
books, full text)

On earth shape, yes I neglected it for this calculation.  Could be

Next topic, eliminate need for AP.  Approach, solve for equation of
cone in space on which observed lunar distance is found.  Find
intersection of cone with sphere (earth) ((or flattened sphere)).
Repeat for second cone/star.  Intersection of two lines on sphere is
position.  (Unless one or both stars are very close to the moon, there
will only be one such intersection.)  I think I'm still a few days
away.  Anyone done it?

Sorry, what computer "basic" matter?

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