Welcome to the NavList Message Boards.


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

Compose Your Message

Add Images & Files
    Re: DIY long-term almanac for calculators
    From: Paul Hirose
    Date: 2018 Jan 23, 13:32 -0800

    I modified my Monte Carlo test program to compare the low accuracy Sun
    ephemeris algorithms from Umland ("Short Guide to Celestial
    Navigation"), Meeus ("Astronomical Algorithms"), and the USNO
    (http://aa.usno.navy.mil/faq/docs/GAST.php and
    In celestial navigation we are really interested Greenwich hour angle,
    not right ascension, so my error statistics include GHA, declination,
    and semidiameter. The "dir" column is the total error in direction due
    to the GHA and declination error. I also calculated error in Greenwich
    hour angle of Aries, since that's necessary to reduce star observations.
    The "gold standards" are the JPL DE431 ephemeris and IAU 2006/00B
    precession / nutation / sidereal time routines, implemented in my
    SofaJpl fundamental astronomy DLL.
    All values in the table are the root mean squared error in minutes of
    arc after 10,000 tests at random times in the 21st century.
    GHA  dec  dir   SD   GHAA
    .22  .13  .33  .006  .19   Umland
    .29  .12  .30  .002  .00   USNO 1
    .29  .12  .30  .002  .01   USNO 2
    .29  .12  .30  .002  .01   USNO 3
    .22  .06  .22  .001  .01   Meeus 1
    .22  .06  .22  .001  .00   Meeus 2
    Umland's formulas are the simplest. His GHAA expression does not correct
    for Δψ (nutation in longitude), whereas the other routines apply the
    correction. Curiously, his Sun GHA is as good as any method despite the
    greater error in GHAA.
    The USNO says the squared term in their GMST expression "can be omitted
    in most applications." That's #2, and #3 is the result with the still
    simpler "alternative formula" in which GMST is a linear function of UT1.
    My Meeus implementation is from the "low accuracy" section of his "Solar
    Coordinates" chapter. It is more elaborate than the other routines. In
    #2 I used more precise expressions from his Nutation chapter for the
    angles Δψ and Δε. The difference is hardly noticeable.

    Browse Files

    Drop Files


    What is NavList?

    Join NavList

    (please, no nicknames or handles)
    Do you want to receive all group messages by email?
    Yes No

    You can also join by posting. Your first on-topic post automatically makes you a member.

    Posting Code

    Enter the email address associated with your NavList messages. Your posting code will be emailed to you immediately.

    Email Settings

    Posting Code:

    Custom Index

    Start date: (yyyymm dd)
    End date: (yyyymm dd)

    Visit this site
    Visit this site
    Visit this site
    Visit this site
    Visit this site
    Visit this site