# NavList:

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

**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 To: NAVIGATION-L@LISTSERV.WEBKAHUNA.COM 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: http://ssd.jpl.nasa.gov/iau-comm4/README 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 To: NAVIGATION-L@LISTSERV.WEBKAHUNA.COM Subject: Re: Nautical Almanac Method Reduction download astro.zip at 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? Thanks in advance. Gord gord@smartt.com