A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
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
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.
WELCOME TO OUR "MODERN LUNARIANS CLUB" WITH FRANK, PAUL, LARS, DAVE and KERMIT
Have a Great Day and
Best Friendly Regards from
Antoine M. "Kermit" Couëtte
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