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: Bris Sextant Math.
    From: Alexandre Eremenko
    Date: 2005 Oct 31, 20:18 -0500

    Dear John,
    My math estimate from the observationbs is that
    the two angles between the adjacent glass panes are
    about 5.2d and 6.5d.
    
    (The rest of this message is pure math.
    I apologise to the list members who don't like it.
    Just skip it then).
    
    Here is the theory of the Bris sextant. The ray from the Sun to your eye
    experiences on its way an even number of reflections.
    Two reflections are equivalent to a rotation
    by twice the angle between the two reflection planes.
    (This is a theorem we teach in our linear algebra courses;
    the ordinary sextant
    is based exactly on this theorem: the ray from the Sun experiences
    exactly two
    reflections, one in the Index mirror and another in the Horison mirror).
    
    Now we have 3 mirrors. Say 1, 2, 3. Let the angle between 1 and 2 be A/2,
    and the angle between 2 and 3 be B/2. (The mirrors are enumerated in
    the natural order, from the Sun to your eye, for example.
    
    Consider first the three bright Suns.
    They correspond to the rays which experience 2 reflections.
    The possible combinations of 2 reflections are
    (21), (32) and (31).
    The angles of deflection are A, B and A+B.
    
    Now consider the dim Suns. They correspond to the rays
    experiencing 4 reflections.
    There are 8 combinations of 4 reflections possible,
    (2121), (2132), (2131), (3232), (3231), (3121), (3132), (3131).
    Some of them will produce the same angles. (These Suns
    will look slightly brighter).
    The possible angles of deflectio of the ray are only 5:
    2A, 2B, 2A+B, 2B+A and 2A+2B.
    Now, assuming without loss of generality, that A
       
    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