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
    Name or NavList Code:
    Email:
       
    Reply
    Re: Almanac for Computers
    From: John H Henderson
    Date: 1996 Aug 28, 12:03 EDT

    >                  Computing Position w/o a DR Position
    >
    > In principle, taking a sight reduces the possible positions you
    > might be at in 3-dimensional space to a single plane in space.
    Taking one sight put you on a cone in space (which, when it intersects
    the surface of the earth, gives you a circle.)
    > Taking two separate sights reduces it still further to the
    > intersection of two planes, which is, of course, a line. You
    > know, a priori, that your position is also on the surface of the
    > earth.  So the intersection of that line with the surface of the
    > earth yields exactly two points at which you might be.  Usually
    > one of them is ridiculous, and so you choose the nonridiculous one.
    Two sights give you two intersecting cones, which give you
    two lines at their intersection, and thus two points at the surface
    of the earth, one of which you can rule out as unreasonable.
    :
    :
    > The equations for the two planes are:
    >
    >   x_1 * x  +  y_1 * y  +  z_1 * z   =   sin(theta_1)
    >
    > and...
    I could understand this plane approach if the planes were tangent to the
    cones at your location, but there is no information from the other
    sight in each equation, so I don't know how these equations express
    the one correct plane.  Also, these planes are not tangent to the
    "sight cone" since they do not pass through the center of the earth.
    (Unless theta=0: set x=y=z=0). (Although any two planes that pass through
    the observer's location would work.)
    I just need help understanding how this expression for these planes
    is derived.
    John H. Henderson - Department of Electrical Engineering - Auburn University
                                    ----+----
      johnh@XXX.XXX/~johnh
          `---=========================(-)============================---'
                 "That's not flying...  "  that's falling with style!"
                                                      -- Woody in "Toy Story"
    
    ------------------------------------------------------------------------
    This mail list is managed by the majordomo program.
    To  from this list, send the following message
    to majordomo@XXX.XXX:    navigation
    For help, send the following message to majordomo@XXX.XXX: help
    Do NOT send administrative requests to navigation@XXX.XXX -ben
    ------------------------------------------------------------------------
    

       
    Reply
    Browse Files

    Drop Files

    NavList

    What is NavList?

    Get a NavList ID Code

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

    A NavList ID Code guarantees your identity in NavList posts and allows faster posting of messages.

    Retrieve a NavList ID Code

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

    Email Settings

    NavList ID 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