Welcome to the NavList Message Boards.

NavList:

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

Compose Your Message

Message:αβγ
Message:abc
Add Images & Files
    or...
       
    Reply
    Re: Online Extended Precision Calculator
    From: Greg Rudzinski
    Date: 2015 May 4, 11:55 -0700

    Harri,

    I don't think 7 places is needed for CN (see attached example for a Sun reduction this morning).  If there were such a thing as a sextant that could measure to .001' then the extra places might be justified.

    Greg Rudzinski

    From: Harri Ojanen
    Date: 2015 May 4, 04:59 -0700

    Hello,

    Wolfram Alpha looks quite interesting, but it might not be that mature yet. I'm getting interesting results for this example. It gives the result in radians as

    0.3490658503988659153847381536977225426885743777083450912194382880342018229206898887364483139269018964 radians

    which is probably correct: it agrees with what Wolfram Mathematica gives for Pi/9, and Mathematica is a mature established product. However, Alpha prints also the following alternative results that it has computed:

    19.9999999999999988669706688890675043201776943694917992903726455566788225422415098971607513768758857°  (degrees)

    and even

    19 degrees 59 arc minutes 59.99999999999592109440800064301555263969973017047744534152400404376115206943562977870495675318852 arc seconds

    Obviously these other values that it has obtained by converting back to degrees are not correct to the requested number of decimals. Of course, if there is no other way of checking the correctness of the value in radians we wouldn't know if that is correct to 100 decimals or not.

     

    In general regarding the number of decimals that are needed: double precision is usually enough, and also often necessary, even for celestial navigational purposes. You don't need that many decimals for the final result, but the extra digits are sometimes necessary for intermediate results in order for the final result to be accurate to say 7 or 8 digits. If you don't want to worry about when you need the extra precision in intermediate steps, it's easy to use double precision always.

    An example is the cosine formula for spherical triangles. For small angles, the accuracy is halved when solving with that formula. So if you used single precision, in some cases the result would be accurate to only about 4 digits, which is not enough even for navigation. You could use the haversine formula instead, but that is inaccurate for some other angles, so basically when working in single precision you need to choose different formulas depending on the values of the angles. In general I would recommend using double precision (i.e., about 16 digits) always, then you don't have to worry about which formula to use (for celestial navigation purposes).

     

    Harri



    File:



       
    Reply
    Browse Files

    Drop Files

    NavList

    What is NavList?

    Join NavList

    Name:
    (please, no nicknames or handles)
    Email:
    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:

    Email Settings

    Posting Code:

    Custom Index

    Subject:
    Author:
    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