# NavList:

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

**Re: Applications of Complex Analysis to Celestial Navigation**

**From:**Andrés Ruiz

**Date:**2009 Nov 30, 12:08 +0100

1.
The output for your examples using my source code in [NavList
10248] is:

CoP1 = 101.491917 -7.858417 28.041667

CoP2 = 147.297542 -7.810361 33.427778

Zp1 = (-0.173620, -0.853988 i)

ro1 = 0.600366

Zc1 = (-0.325224, -1.599683 i)

r1 = 1.454431

Zp2 = (-0.733942, -0.471227 i)

ro2 = 0.538132

Zc2 = (-1.213898, -0.779383 i)

r2 = 1.215208

d = 1.209394

mu = 0.218318

nu = 0.964517

Z1 = (-1.754769, -1.867588 i)

Z2 = (-0.172382, -0.153304 i)

I1 = 47.366215, -133.216088 = 47º21’58”, -133º12’58”

I2 = -64.019435, -138.352317 = -64º01’10”,
-138º21’08”

w = (0.134118, -0.355732 i) = 0.380175 e -1.210256 i

a = (0.996566, 0.082808 i)

b = (-1.934951, 0.160782 i)

mb = 1.941620

z = (0.968460, -1.842040 i)

w = (0.134118, -0.355732 i)

62.266667 38.670278 35.500000 -9.500000

Hc = 48.368899 = 48º22’08”

Z = -69.342564
= 290º39.4’

z = 0.513661

z = 0.463230

z = 0.504768

z = 0.463433

LD = 102.658496 = 102º39’31”

2.
I am working in a new release of CelestialFix.exe,
and it includes the following methods.

3.
Mathematics vs. navigation consistency

One remark Robin, for double
altitude sight you take an example from “A Treatise on Nautical Astronomy
- John Merrifield”, (see attached pdf. Page

But the important is to note that
only one of the two mathematical solutions is correct in a running fix, the one
near the initial position for taking into account the motion of the observer. (I
speak not of position or fix but mathematical solutions).

Taking this initial position near
the other intersection we obtain this solution: (-63º 33.7' -139º 27.9')

And (-64º01’10”, -138º21’08”)
should be discarded.

Of couse the fix is the solution
near the DR position.

Andrés Ruiz

Navigational Algorithms

http://sites.google.com/site/navigationalalgorithms/

-----Mensaje original-----

De: robinstuart@earthlink.net
[mailto:robinstuart@earthlink.net]

Enviado el: sábado, 28 de noviembre de 2009 22:52

Asunto: Re: [NavList 10839] Applications of Complex
Analysis to Celestial Navigation

I have put together an Excel spreadsheet that
demonstrates the use of complex numbers in calculations performed in celestial
navigation. The examples are taken from the paper Applications of Complex
Analysis to Celestial Navigation, available at
http://www.fer3.com/arc/img/110015.articlec.pdf.

Each sheet consists of three sections; Inputs,
Calculations, Results. The values of the Inputs are initially set to those that
appear in the paper, above, and confirm the results that appearing therein. The
inputs may be changed to perform the same calculations for other sets of observations.

The spreadsheet uses the Excel Engineering functions
IMSUM(), IMPRODUCT() etc. to the perform the complex number calculations. To
ensure that these are available to the system, on the Excel toolbar select
Tools>Addins and check "Analysis ToolPak".

The Excel implementation using functions IMSUM(),
IMPRODUCT() etc. to perform arithmetic operations on complex numbers means that
formulas that appear here are less compact and transparent than they are in
computer languages, such as FORTRAN, C++, PERL, in which complex numbers are a
built in native data type.

Robin Stuart

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