NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: One-body fix
From: Peter Hakel
Date: 2009 Apr 28, 03:14 -0700
From: John Karl <jhkarl@att.net>
To: NavList <NavList@fer3.com>
Sent: Monday, April 27, 2009 2:59:36 PM
Subject: [NavList 8081] Re: One-body fix
> I hereby display the solutions to this "one-body fix" problem, if only as a curiosity. I expect that these have been worked out before but I haven't found them anywhere so far (references would be much appreciated). The known quantities are the GP (Dec, GHA), observed altitude (Ho), and azimuth to GP (Zn). From the navigation triangle we can calculate the LHA and then the Latitude:
>
> sin LHA = sin Zn * cos Ho / cos Dec
>
> sin Latitude = ( sin Ho * sin Dec - cos Ho * cos Dec * cos LHA * cos Zn ) / ( 1 - cos Ho * cos Dec * sin LHA * sin Zn )
>
> Peter Hakel
I don't know of a reference for Peter's second equation above. But, I
easily calculated a different one from the standard altitude and
azimuth equations:
Sin L = (cosA cosH sinH - sind cosd cosLHA)/(sind cosA cosH - cosd
sinH cosLHA).
Since both this and Peter's check out for the special case at LAN,
they're probably both OK.
--JK
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Navigation List archive: www.fer3.com/arc
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From: Peter Hakel
Date: 2009 Apr 28, 03:14 -0700
Thank you, John. The two formulae are indeed equivalent. Peter
From: John Karl <jhkarl@att.net>
To: NavList <NavList@fer3.com>
Sent: Monday, April 27, 2009 2:59:36 PM
Subject: [NavList 8081] Re: One-body fix
> I hereby display the solutions to this "one-body fix" problem, if only as a curiosity. I expect that these have been worked out before but I haven't found them anywhere so far (references would be much appreciated). The known quantities are the GP (Dec, GHA), observed altitude (Ho), and azimuth to GP (Zn). From the navigation triangle we can calculate the LHA and then the Latitude:
>
> sin LHA = sin Zn * cos Ho / cos Dec
>
> sin Latitude = ( sin Ho * sin Dec - cos Ho * cos Dec * cos LHA * cos Zn ) / ( 1 - cos Ho * cos Dec * sin LHA * sin Zn )
>
> Peter Hakel
I don't know of a reference for Peter's second equation above. But, I
easily calculated a different one from the standard altitude and
azimuth equations:
Sin L = (cosA cosH sinH - sind cosd cosLHA)/(sind cosA cosH - cosd
sinH cosLHA).
Since both this and Peter's check out for the special case at LAN,
they're probably both OK.
--JK
--~--~---------~--~----~------------~-------~--~----~
Navigation List archive: www.fer3.com/arc
To post, email NavList@fer3.com
To , email NavList-@fer3.com
-~----------~----~----~----~------~----~------~--~---
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