NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Interesting challenge
From: Peter Hakel
Date: 2012 Aug 5, 19:08 -0700
From: Lu Abel <luabel@ymail.com>
To: Navigation <NavList@fer3.com>
Sent: Sunday, August 5, 2012 11:41 AM
Subject: [NavList] Interesting challenge
From: Peter Hakel
Date: 2012 Aug 5, 19:08 -0700
Lu,
This page from my website:
http://www.navigation-spreadsheets.com/lops.html
refers to three methods relevant to your friend's question. Here are the references:
1a. lops.xls: (3-D flat geometry)
James A. Van Allen, An Analytical Solution Of The Two Star Sight Problem Of Celestial Navigation, Navigation 28 (1), (1981).
1b. two_body_fix.xls: (2-D spherical geometry)
John Karl, Celestial Navigation in the GPS Age, pp. 78-79
2. many_body_fix.xls: (a least-squares-based technique with the intercept method under the hood)
Nautical Almanac, 2010 Commercial Edition, pp. 282-283
Methods 1a and 1b are equivalent. Usually they yield two distinct mathematical solutions. No "assumed position" is needed in either case.
Method 2 gives one location. Assumed position is one of the inputs. Two, three, or more sights can be entered on input.
Peter Hakel
This page from my website:
http://www.navigation-spreadsheets.com/lops.html
refers to three methods relevant to your friend's question. Here are the references:
1a. lops.xls: (3-D flat geometry)
James A. Van Allen, An Analytical Solution Of The Two Star Sight Problem Of Celestial Navigation, Navigation 28 (1), (1981).
1b. two_body_fix.xls: (2-D spherical geometry)
John Karl, Celestial Navigation in the GPS Age, pp. 78-79
2. many_body_fix.xls: (a least-squares-based technique with the intercept method under the hood)
Nautical Almanac, 2010 Commercial Edition, pp. 282-283
Methods 1a and 1b are equivalent. Usually they yield two distinct mathematical solutions. No "assumed position" is needed in either case.
Method 2 gives one location. Assumed position is one of the inputs. Two, three, or more sights can be entered on input.
Peter Hakel
From: Lu Abel <luabel@ymail.com>
To: Navigation <NavList@fer3.com>
Sent: Sunday, August 5, 2012 11:41 AM
Subject: [NavList] Interesting challenge
When celestial navigators draw a LOP, it's usually by the altitude-intercept method, ie, "here's where I think I am, but where would I have to be to see get this Ho?"
A friend asked me the following: "If I know my [great circle] distance from three points on earth, can I determine my location?" Of course one can. But beyond getting a globe and using dividers or a string to draw arcs of the proper distance on it, is there a mathematical/paper-and-pencil way of determining latitude and longitude? I guess the celnav equivalent would be determining location from three sights (or each of the two possible positions from two sights) with no assumed position.
Lu
