# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: LOP's without DR Position
From: Bruce J. Pennino
Date: 2015 Feb 27, 13:20 -0500
Hello:  I’m going to  use a subtitle – Position without St. Hilaire (simultaneous equations)

I’ve stared at the figure in  Page 101 in John Karl’s book (CN in GPS  Age) more time than I want to admit. This figure shows sighting two bodies simultaneously and finding location. The equations are are on Page 102. From my math background  it seems to be a variation on simultaneous equations: 2 equations/2 unknowns, 3 equations 3 unknowns, etc.  I had the thought a while back that the 50 minute daily shift of the moon could provide another “known” piece of information. I then tried to use the equations and develop a unique solution without iterative attempts . Could not do it.   Here is the simple thought: The  person/ship  is not moving. I assume that latitude is known from a noon sight . But I think latitude and even time could be unknown.   I assume we have a watch (might be incorrect) but we could use it as a time piece to plot Hs for the moon versus time on two successive days.

If you plot the Hs of the moon on two successive days there is a 50 minute (more or less) shift. At the same time on two days the Hs is generally  different.  For example on day 2 when the moon is ascending, Hs is smaller than at the same time on day 1.  But there is a time on day 2 when the increasing Hs curve (below the day 1 Hs curve) intersects the descending day 1 Hs curve and the day 2 curve Hs exceeds  the day 1 plot of Hs.  It seemed to me the intersection point of the 2 curves ( a unique value of Hs at that particular time) would ease a simultaneous solution by providing  an Hs and time(if watch is correct).  I could not “make it work”, but it was interesting. Basically it is algebraic manipulation of standard CN sight reduction  equations.

Regards to all.

Bruce

From: John Karl
Sent: Thursday, February 26, 2015 10:26 PM
Subject: [NavList] Re: LOP's without DR Position

Robin,

Well, I thought of it myself while I was writing the book.  Since it's a pretty obvious solution to the two-LOP problem, I can't be the first one to write it up.

The interesting obsevation is that it requires solutions to five equatioins, while computing St. Hilaire for a two-LOP fix requires four solutions of the same type equations, PLUS DRs, straight-line approxmations to the LOPs, and plotting.  So the one extra equation yield a pretty good return...

And Kermit, Thanks for your note.

John K.

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