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: Which calculator to use for "arctan(tan(269))"?
    From: Robin Stuart
    Date: 2017 Feb 1, 08:40 -0800


            I went back and rederived the altitude and azimuth formulas in using 3D methods (see the summary at the end of this post). The results are necessarily the same as what Lars gave but inn case it’s not clear I want to emphasize how very useful the interpretation to r is in LoP sight reductions.

    The procedure becomes:


    Pol{ [ cos(Lat) · sin(Dec) - sin(Lat) · cos(Dec) · cos(LHA) ] , [-cos(Dec) · sin(LHA) ] }

    and then

    Hc = cos-1 r and θ = Zn

    or possibly more efficiently in terms of keystrokes

    Pol{ [ cos(Lat) · tan(Dec) - sin(Lat) · cos(LHA) ] , [-sin(LHA) ] }

    and then

    Hc = cos-1( r cos(Dec) ) and θ = Zn

    There is no need for a separate calculation of the altitude!!! One proviso, as Lars indicated, is that it only gives the correct answer for objects above the horizon.


    Robin Stuart


    Summary of key results

    Define topopcentric coordinates x,y,z in which the x-axis is horizontal pointing East, the y-axis is is horizontal pointing North and the z-axis is along the vertical. Relating the global Greenwich hour and declination GHA, δ coordinates to local azimuth and altitude Zn, Hc (details on request) gives

    x = sin Zn cos Hc = -cos δ sin LHA

    y = cos Zn cos Hc= cos δ cos L - cos δ sin L cos LHA

    z = sin Hc= sin δ sin L + cos δ cos L cos LHA

    which satisfy x2+y2+z2 = 1 and hence x2+y2 = 1- z2 = cos2 Hc

    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