Once again we are dealing with finding latitude from a noon sight. This is the most reliable means of checking north/south position and the easiest application of celestial navigation. The noon sight was the method most commonly employed by the navigators of the 19th and early 20th centuries. The math is simple, and the tables required are few. The only downside to this method is if the sky is overcast at the time of LAN. There are other methods that allow for this possibility, most notably the Ex-Meridian altitude shots, which we will deal with in a later problem. For this problem, though, we will reduce the Hs to Ho, find the declination and then use the time-honored formula: Lat = Ho ï¿½ 90 degrees = Zenith Distance +/- Declination. Letï¿½s go to the problem!
Capt. Braden is at DR position 40 degrees 56 minutes N by 71 degrees 50 minutes W. It is May 15, and the Height of Eye is 15 feet. The sextant has an Error of 4 minutes On the Arc, and Braden takes an Upper Limb sight of the sun, and the Hs is 68 degrees 31.4 minutes.
What is the time of Meridian Passage in GMT?
To find the answer, we go to the daily page of May 15. Meridian Passage of the sun for that day is 11 hours 56 minutes. LMT. We go next to the Arc/Time conversion pages in the rear of the NA to convert longitude into time. We convert 71 degrees 50 minutes to 4 hours 44 minutes plus 3 minutes 20 seconds. We add this combined time (4 hours 47 minutes 20 seconds) to the time of the Meridian Passage of 11 hours 56 minutes, and get the time for Meridian passage at our longitude at 16 hours 43 minutes 20 seconds.
We next have to reduce the Hs to Ho. We have to factor in Height of Eye, Index Correction and the 3rd correction for semidiameter, refraction and parallax:
Hs 68 degrees 31.4 minutes IE- 4.0 minutes Dip- 3.8 minutes App alt 68 degrees 23.6 minutes 3rd corr- 16.2 minutes Ho 68 degrees 07.4 minutes
IE- 4.0 minutes
Dip- 3.8 minutes
App alt 68 degrees 23.6 minutes
3rd corr- 16.2 minutes
Ho 68 degrees 07.4 minutes
The important items to remember while doing this exercise are: Make certain you look up the right column for either Upper or Lower Limb sight of the sun on the inside front page of the NA in order to determine the 3rd. corr. Also, if the sextant error is On the Arc, then it is subtracted in the reduction; thus, the +4 minutes Index Error is subtracted when doing the math.
Now we need to find the latitude. We go to the daily page and look under the Sun column for 1600 hours on May 15. We are using 1600 hours because that is the time of the Meridian Passage in GMT. Declination of the sun for that time is N 19 degrees 03.1 minutes. We look at the bottom of the page and note that the d corr is 0.6 minutes. This means the sun is moving in a north/south direction at 0.6 minutes every hour. We have to decide which way the sun is moving. Since this is before the summer solstice, we know that the declination of the sun is still increasing, so we know that we have to add the value of the d corr. We find this number by going into the Increments and Corrections pages at the rear of the NA, to the 43-minute page. Under the v or d tables, we see that a d corr of 0.6 minutes converts to a correction of 0.4 minutes. We add this to our declination and get the following:
Dec: N 19 degrees 03.1 minutes + 0.4 minutes Dec: N19 degrees 03.5 minutes Now we are ready to get our latitude: 90 degrees = 89 degrees 60.0 minutes -Ho 68 degrees 07.4 minutes ZD 21 degrees 52.6 minutes Dec + 19 degrees 03.5 minutes Lat = 40 degrees 56.1 minutes
+ 0.4 minutes
Dec: N19 degrees 03.5 minutes
Now we are ready to get our latitude:
90 degrees = 89 degrees 60.0 minutes
-Ho 68 degrees 07.4 minutes
ZD 21 degrees 52.6 minutes
Dec + 19 degrees 03.5 minutes
Lat = 40 degrees 56.1 minutes
We add the declination because, based on our DR, that is the only thing we can do. If we subtracted it, we would be nowhere near our DR, and we assume — as we must — that we have been keeping a reasonable DR.