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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Antoine Couëtte
Date: 2022 Jun 20, 10:22 -0700
Hello Dave,
So, after your ealier quizz this year, you just did it again on the very same subject as it looks.
I have come up with an "improved solution" when compared to the one I earlier submitted to your first quizz.
(1) - First, I am starting exactly as before : computing the 3 D intersection curve(s) of a sphere and a cylinder. Nothing magic if you a have suitable software program to that end.
(2) - Then I am to draw on a paper sheet both immersion and ermersion curves. Whatever the coordinates chosen, an intersection shows up as an intersection. This is why here I am simply choosing plain 2D rectangular coordinates.(see attachment).
As you can see on this attachment, I am manually hand drawing / deriving an Oberver's approximate position at N40°12' / W074°30'
(3) - Now I am just setting aside the previous hassle of accurately drawing lines on a sheet of paper. I am now simply using only computations.
Starting from an(y) approximate position, I am computing :
3.1 - Occultation and emersion times for this position
3.2 - The same (i.e. immersion and emersion times) for a position exactly 1° North of 3.1
3.3 - The same for a position exactly 1° W of 3.1
(4) - Using position 3.1 as a local coordinates center - i.e. showing as (0, 0) - I am computing the intersections on its parallel and on its meridian of the 2 isochronic lines : Line (1) for the requested imersion time (here 02h20m08.1s) and Line (2) for the requested emersion time (here 03h05m30s).
(5) - The intersection of Lines (1° and (2) defines an improved Observer's position. Check for immersion and emersion times from this updated position and iterate as necessary.
Results are :
Initial Position (AP1) as earlier indicated at : N40°12' / W074°30' for which imm. UT = 02h20m50.4s and em. UT = 03h05m12,6s
Second position (AP2) at : N40°39.464' / W074°34.045' for which imm. UT = 2h20m05.9 s and em. UT = 03h05m31.8s
Third position (AP3) at : N40°37.9' / W 074°34.1 for which imm. UT = 02h20m08.3 s and em. UT = 03h05m29.9s ( vs. benchmark values at 02h20m08.1s and 03h05m30.0s).
No need to further iterate.
Submitted position is at N40°37.9' / W 074°34.1
Probably (hopefully ?) within a couple miles of the actual position (vicinity of NYC in NJ).
I am now going to take a look at the results published here by other colleagues.
Best Regards,
Antoine M. "Kermit" Couëtte
