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

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Re: Nautical Almanac Method Reduction
From: Dan Allen
Date: 2000 Nov 03, 8:00 PM

```I was nicely informed that in fact I answered a different question, not the
one that was originally asked.  I apologize, but in the meantime I learned
some new things about the source of the almanac ephemeris!

In answer to the question as to how the sight reduction tables are derived,
it is the spherical law of cosines (along with the other tables for
refraction and the other corrections).  The law of cosines is:

cos(a)*cos(b) + sin(a)*sin(b)*cos(ab) = cos(c)

where

a = 90 - estLat
b = 90 - decl
ab = LHA = GHA - estLong
90-c = altitude

once the altitude is solved for, then change the variables:

b = c, c = b

and recalc to get a formula for azimuth

ab = azimuth (360-az if LHA < 180)

This all assumes that you are using degrees rather than radians...

Dan

-----Original Message-----
From  Navigation Mailing List
[mailto:NAVIGATION-L@LISTSERV.WEBKAHUNA.COM]On Behalf Of Dan Allen
Sent: Friday, November 03, 2000 2:58 PM
Subject: Re: Nautical Almanac Method Reduction

Chapter 14 of the astro.zip collection referred to below does give some
basic formulas accurate to about a half a minute of arc, but those formulas
are NOT the formulas used to come up with the Nautical Almanac.

The formulas for the Astronomical and Nautical almanacs come from the Jet
Propulsion Lab's "DE200" ephemeris.  Here is a description from a friend of
mine who works at JPL, Dr. Paul A. Finlayson:

"The real data source for the almanacs are the JPL ephemeris positions of
the Earth, Sun, Moon, and any other bodies listed in the Almanac. This data
is not obtained from formulas, but rather from a full-fidelity dynamic model
of the solar system (including relativistic effects) expressed in terms of
coupled differential equations which are numerically integrated. The final
result of this numerical integration is a massive database (which is
available on CD). Body positions (expressed in some convenient frame, such
as J2000) as a function of time are directly obtained from that data. The
values in the almanac can then be easily obtained from standard geometric
transformation formulas."

Some basic info about DE200 is here:

http://ssd.jpl.nasa.gov/eph_info.html

A detailed readme is at:

and the actual files (very large!) are here:

ftp://navigator.jpl.nasa.gov/ephem/export/

The results are extremely accurate, to less than a second of arc.  The
dataset  is HUNDREDS OF MEGABYTES in size.  Hence, DE200 and its relatives
(DE405, etc.) are sold on a CD for \$24.95 here:

http://www.willbell.com/software/jpl.htm

The datafiles must be processed by programs before they are useful.  The
source code to these programs are on the CD.  However, the programs provided
are written in FORTRAN.  You must have a FORTRAN compiler on your machine in
order to use DE200.  There are some versions that have been translated into
C as well, but they are not definitive.  If you are not a programmer fluent
in these languages, then use of DE200 or DE405 directly is IMPOSSIBLE!

Dan Allen

-----Original Message-----
From  Navigation Mailing List
[mailto:NAVIGATION-L@LISTSERV.WEBKAHUNA.COM]On Behalf Of Robert Block
Sent: Friday, November 03, 2000 9:37 AM
Subject: Re: Nautical Almanac Method Reduction

http://home.t-online.de/home/h.umland/page2.htm

Let us know how it goes.

regards

robert
S/Y Connemara
Santa Barbara

---

Can anyone tell me the formulas used to generate the numbers in both of the
Nautical Almanac Method sight reduction tables?

Gord
gord@smartt.com
```
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