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    Re: Friendly challenge : Jupiter Lunar Exercise 09 Feb 2011
    From: Antoine Couëtte
    Date: 2011 Feb 23, 01:00 -0800

    RE : http://www.fer3.com/arc/m2.aspx?i=115722
    [NavList] Re: Friendly challenge : Jupiter Lunar Exercise 09 Feb 2011
    From: hojanen---fi
    Date: 22 Feb 2011 22:02

    Good Morning Harri,

    So you live in the Helsinki area, so cold now ....
    I'v been there quite a few times, including lately to renew my B757/767 qualification on the FINNAIR Simulator next to the Holiday Inn Vantaa Airport ...

    That's a small world !


    Thank you very much for your contribution to our "”Friendly challenge: Jupiter Lunar Exercise 09 Feb 2011” published in http://www.fer3.com/arc/m2.aspx?i=115625.

    Your solution (Let's call it "Solution HO") is the same in essence than a solution (Let's call it "Solution A/F") earlier published under the title " 115633.one-solution-to-the-jupiter-.pdf" as an appendix to http://www.fer3.com/arc/m2.aspx?i=115633 which must have escaped your attention.


    Both HO (Step 1) and A/F (PRELIMINARY STEP) use averaged values, which is also a common starting point used by all other solutions Contributors.


    The main and only difference between HO and A/F comes from their respective "Starting Watch corrections" as follows :

    HO (Step 1) uses the 15h45m "approximate watch error as given in the original description", while

    A/F (PRELIMINARY STEP) uses the even more global approach since it assumes that the TOPOCENTRIC Lunar Distance is equal to the GEOCENTRIC Lunar Distance, which permits to assume that UT41 = 17h12m52.2s, and which is also equivalent to assuming that Watch time correction is 15h05m34.8s .


    HO (Step 1) then gets a first Fix "somewhere near 46.6°N 1.5°E, which is inland France. Ok so far, since the exact time is not yet known." , while

    A/F (STEP 1b) gets a first fix as " Initial Position 1 : UT14 = 17h12m52.2s N 46°17'.2 E 011°42'.0 " which is even further to the East given its initial assumed Watch error value.


    HO (Step 2) computes a correction to the Jupiter-Moon Distance according to the precepts of John Karl's Book, to derive a " watch error of 917s to be added to the original estimate " , while

    A/F (STEP 1C and STEP 1d) computes a correction to the Jupiter-Moon Distance according to the results given by Frank E. Reed's On Line Lunar Computer, to derive an additional Watch "correction of +0H54m23.2s to UT", with this latter 3263.2 second correction quite understandably more important than the 917s derived in HO.


    HP (Step 3) computes a new position with the "Improved Watch" which is " estimated (visually) at 46.7°N, 2.5°W ". Such intermediate position is used (Step 4) as an AP " in a standard St Hilaire calculation. It gives a fix at 46°42.8'N 002°27.8'W. ", while

    A/F (STEP 2a and STEP 2b) also computes a new position with the "Improved Watch" and derives an " Updated Position 2 : UT24 = 18h07m15.4s N 46°43'.1 W 002°23'.6 ".


    HO (Step 3) indicates that " Repeating the lunar time calculation with the same data gives 0s as the watch error, which suggests the 917s is sufficient.

    Thus arriving at fix 46°42.8'N 002°27.8'W
    Additional watch correction 917s = 15min 17s
    Total watch correction: 15h 45m 00s + 15m 17s = 16h 00m 17s " , while

    A/F (STEP 2c) repeats the Lunar Time Calculation with FER's OLC and gets the following result : " We then find a correction of +0h00m08.0s to UT".

    Since A/F does not find a 0s additional watch error, it continues the same iteration. STEP 3a and STEP 3b derive the following new fix : " Updated Position 3 : UT34 = 18h07m23.4s N 46°43'.1 W 002°25'.4 "

    From such "Updated Position 3" , A/F (STEP 3c) repeats one more (and last) time the Lunar Time Calculation with FER's OLC and gets the following result : " We then find a correction of +0h00m03.6s to UT". (See NOTE 1 hereunder), which is simply then transformed into a plain shift to the " last Longitude by 0'.9 to the West ", and concludes with :

    " UT of Sextant Average Distance = 18h07m27.0s , and Observer's Position at this time was N 46°43'1 W 002°26'2 " . Total watch correction is not indicated per se here, but it is equal to 18h07m27.0s - 2h07m17.4s = 16h00m09.6s.


    As we can see the results from the HO and the A/F solutions are extremely close.

    We also notice the very fast convergeence of the algorithm used here.

    NOTE : Given the very fast convergence rate of the here-above algorithm, we may very well have an error in A/F "Updated Position 3". Look at the sequence : 3263.2 seconds of time, 8.0 seconds of time ... 3.6 seconds of time as derived from "Updated Position 3" . Not to really worry about : a good and solid iteration algorithm will always put you back onto a rightly converging track (see quite similar remark in http://www.fer3.com/arc/m2.aspx?i=115712


    One of the beauties with "solid" iterations such as these ones is that if in one of them you happen to go "off-track" - within certain limits though - next iteration, if performed 100% correctly, will put you back onto a different nonetheless rightly converging path !

    Isn't that beautiful ? :-)



    Dear Harri, certainly it is quite rewarding to hear that you had lots of fun devising/deriving your solution here.

    Hopefully you will soon have a nice Spring and Summer so that for my upcoming B757/767 License Renewal in July I can again enjoy your absolutely wonderfully tasteful Wild Raspberries when walking between the Holiday Inn and the FINNAIR premises.



    Have a Great Day and

    Best Friendly Regards from


    Antoine M. "Kermit" Couëtte

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