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RE : http://www.fer3.com/arc/m2.aspx?i=115707
[NavList] Re: 12 Feb 2011 Unorthodox Jupiter Lunar from a moving platform
From: antoine.m.couette---fr
Date: 20 Feb 2011 14:06

FINE TUNED RESULTS

Dear Lars, and

Hello to all

In my last reply to you Lars (http://www.fer3.com/arc/m2.aspx?i=115707) in the very last step I made an incomplete approximation about simply "shifting positions East by 10'0) which is not 'optimized' since in some 40 seconds of time the Observer's position changed due to Vessel speed.

From the previous "provisional" position earlier published on my referenced post as :

UT41 = 18h14m37.4s N46°36'.4 W002°38'.9

we already derived a UT last correction equal to -39.9 seconds of time thanks to Frank's On Line Lunar Computer.

Then we shifted both UT41 Time and Position by 10'.0 to the East, to our previous "final" result published as :

UT = 18h13m57.5s N46°36'4 W002°28'9 ,which was my last published result in the referenced post.

HOWEVER, such result in not the best one which we can get from existing data so far because we also need to take in account our Vessel motion during this -39.9 second time interval.

During 40 seconds of time, at 22 kts we covered 0.24 NM

With a Bottom Track of 135°, this translates into :

0.17 NM to the South, and

0.17 NM to the East. At a Latitude of N 46°.6, with Cos Lat = 0.687, East distance translates into 0'.25 change in Longitude towards the East.

Therefore, since we need the ship's position 40 seconds EARLIER, we need to fine tune our correction "backwards", i.e. correct our last position with :

0'.17 to the North and 0.25' to the West. (In the strict "mathematical" sense, I suspect that such kind of "quick correction" rather involves an infinite number of iterations, but let's stop here and now :-) !

From our last previous position 18h13m57.5s N46°36'4 W002°28'9, our now "Best Position" becomes :

Final (averaged) Sextant Distance UT = 18h13m17.5s N46°36'.6 W002°29'.1

Let's then compare with the Ship Navigation System position :

Ship's position at UT = 18h13m17.5s was N46°37'.0 E002°26'1

EXCELLENT RESULT INDEED : just 0.4' off in Latitude, and 3'.0 in Longitude !!! YOU ACED IT !

I think that, given the quite wonderful job you did, you really and definitely deserved a quick and comprehensive reply. This is why I decided to treat your contribution on a high priority basis, since I had time available for that.

A most hearty Triple "Ribbit" Hurray to you from Kermit, and

Welcome to the (2 member so far) "Modern Lunarians DIAMOND Club" then ! :-))

Best Friendly Regards

Antoine

Antoine M. "Kermit" Couëtte

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