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Hello Martins,

Interesting Lunar which Frank subsequently solved in a much unexpected nonetheless quite brillant way.

(1) - Martin, in spite of your published and immediately usable data, I have first decided here to solve it as per our well-known non-classical manner too.

15 Jun 2024, for UT = 18h35m36.0 then TT = 18h36m45.2s, HoE = 15ft, OAT = +17°C, QFE = 1017 mb,

UT = 18:34:25.0 UT SunLL = 20°34.6'   and   UT = 18:34:35.0 MoonLL = 21°05.9'  , and with

UT = 18:35:36.0 and LD =  106°45.0' (all sextant values corrected for I.E. here).

While your true position at N 34°33'25"N / W  058°24'35" , with 2 LOP's I am getting an Observer's Position at S 34°34.2' / W 058°24.8' ,

(0.8 NM off).

Assuming then that only the Observer's coordinates obtained from the 2 LOP's are exact - i.e. not using the heights - I am getting a Sextant Distance at 106°46.274', which indicates a LD error of 1.274'. vs. 1.207' given by FER's On Line Calculator (OLC) now usable to full capacity.

From said position at S34°34.24 / W058°24.8' I then get a clock correction CT1 = -3m15.3s, i.e. a Lunar Time sight at 18h32m20.7s for LD = 106°45.0' this time. With the OLC I keep observing again a difference slightly under 4", within inside the usual range.

(2) - If I now treat this Lunar the classical way with the Heights/times and the Lunar distance/time and assuming that all 3 given angular values - i.e. both heights and the LD - are exact, I am now to compute the clock correction which minimizes / zeroizes the differences to all these 3 angles.

This method actually boils down to treating Lunars the classical way. 

I am therefore getting the following results : clock correction CT2 = -2m46.8s and Cleared Distance at 106°51.7' altogether with - cherry on the cake - the Observer's position at S34°34.6' / W057°48.6'.

In other words, under this approach, the Sun corrected height time has become UT Sun + CT2 = 18h31m38.8s (height unchanged), the Moon corrected time has become UT moon + CT2 = 18h31m48.2s and the LD corrected time has become LD UT + CT2 = 18h32m49.2s.

Obviously, CT1 and CT2 are not expected to be identical since they are derived from different "operational" assumptions explained respectively in (1) and (2) here-above.

(3) - Independent checks on the §2 results :

(3.1) - New LOP's from corrected time elements (2) here-above - keeping both heights unchanged - yield both intercepts at 0.0 NM.

(3.2) - Or alternately, feeding the OLC with the above data (2) - i.e. the "new" position at S34°34.6' / W057°48.6', the unchanged LD = 106°45.4' and "new" Lunar Distance UT = 18h32m49.2s - we get the same difference of slightly under 5" with an OLC Cleared Distance at 106°51.8' vs. 106°51.7' as indicated in (2).

Thanks for this nice drill,

Kermit