A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2019 Dec 26, 10:41 -0800
Herman Dekker, you wrote:
"Something got wrong in the calculation."
Yes, indeed. Your navigator broke his toe in in two places in Bermuda. He was delirious from the pain and couldn't do math so your departure was delayed by ten days...
It's now July 10, 2020. You're sailing north of Bermuda headed for New England. Your estimated position is 32.7° N, 64.9° W. The Sun has just set at 23:25 UT, and you intend to start taking sights at, or just after, 00:00 UT (so the UT date will be July 11). You have a copy of Pub.249 Vol.1 from 2015. That's close enough for this purpose (but not for clearing sights). You turn to the page for 33°N latitude...
Next you need LHA Aries, which is GHA Aries - 64.9°. For GHA Aries, we need the number of days since Sep. 21. Count 'em up: 9 for Sep, then 31+30+31 through Dec, and 31+29+31 through March, 30+31+30 through June, and 11 more to get to today's (Greenwich) date. That's 294 days total. Add one degree per day and then take back a day for every 71 days so 294°-4° gives 290°. The time is 0h UT so we don't need to add 15° per hour. The total remains 290°. That's GHA Aries. Add the negative longitude: 290-65 = 225. Thus LHA Aries is 225° to the nearest degree. Scan down on the second page for this latitude until you get to 225°. The bright stars listed are Deneb, Vega, Altair, Antares, and Spica. Somewhat fainter are Denebola and Dubhe.
You decide you're comfortable with a two-star fix. You see that Vega and Antares are almost 90° apart in azimuth, so you preset for Vega using the tabulated altitude and get its altitude easily. You do the same for Antares, and in less than three minutes you're done. It's only 00:03 UT, and you're done with sights. At this point, you crank out a two-point LOP for each star on your calculator, plot them on common graph paper, and get your fix. Easy? Too easy! You need more...
Ten or twelve minutes after shooting Antares, you decide to pick up Polaris, too. You preset your sextant to your latitude and sweep it up easily at 00:16 UT. After correcting for dip and refraction (IC=0) to get Ho, you need the Q correction. Here you realize that your 2015 edition of Pub 249 may be a little out-of-date, but you'll go with it anyway. You look up Q using LHA Aries. That was 225° at the top of the hour. It increases by 1° every four minutes, so for this Polaris sight, you enter with 229° and find that Q is +40'. Here your exceptional knowledge of nautical astronomy comes into play, and you decide to pull that back to 39.5'. You know that Polaris is approacing the pole over the next few decades, and 40 is nearly a maximum value so it ought to be a bit smaller in 2020. Add that onto the Ho for Polaris, and you have a fast double-check on the latitude from your Vega-Antares fix. You discover that the latitude is higher by 2' than your Vega-Antares fix but you're sailing due north at 6 knots so it's consistent (in a quarter of an hour, stars due north should rise just about 1.5' in that much time). And it all agrees with the GPS within a mile, too, so you're confident that everything is as it should be.
Satisfied with your fix and your Polaris check, you decide to get online and buy the 2020 edition of Pub.249. Tap, tap, tap... It will arrive before you're back on shore. Amazing what you can do in the middle of the ocean in the year 2020!
PS: There were actually two errors in the original version of this. That'll teach me to edit after setting up a scenario.