Wednesday Lecture
Latitude by Meridian Altitude of a Star—Latitude by Polaris
(Pole or North Star)
To find your latitude by taking an altitude of a star when it is on your meridian, is one of the quickest and easiest of calculations in all Navigation. The formula is exactly the same as for latitude by meridian altitude of the sun. In using a star, however, you do not have to consult your Nautical Almanac to get the G.M.T. and from that the declination. All you have to do is to turn to page 95 of the Nautical Almanac, on which is given the declination for every month of the year, of any star you desire. The rest of the computation is, as said before, the same as for latitude by the sun and follows the formula Lat. = Dec. ± Z.D. (90° - true altitude). As when working latitude by the sun, you subtract the Z.D. and Dec. when of opposite name and add them when of the same name. Put in your Note-Book:
Formula: Lat. = Dec. ± Z.D. (90° - true altitude).
At sea, Dec. 24th, 1919. Meridian altitude Star Aldebaran 52° 36' S. HE 20 ft. Required latitude of ship.
| Obs. Alt. | 52° 36' S |
| Corr. | - 5 08 |
| ————— | |
| True Alt. | 52° 30' 52" S |
| - 90 00 00 | |
| ————— | |
| Z.D. | 37° 29' 08" N |
| Dec. | 16 21 00 N |
| ————— | |
| Lat. | 53° 50' 08" N |
Note to Instructor:
Have class work examples such as the following before taking up Latitude by Pole Star:
1. At sea, May 5th, 1919. Meridian altitude Star Capella, 70° 29' S. HE 32 ft. Required latitude of ship.
2. At sea, August 14th, 1919. Meridian altitude Star Vega, 60° 15' 45" N. HE 28 ft. Required latitude of ship.
Etc.
Latitude by Polaris (Pole or North Star)
You remember we examined the formula in the N.A. for Lat. by the pole star when we were discussing sidereal time some weeks ago. We will now take up a practical case of securing your latitude by this method. Before doing so, however, it may be of benefit to understand how we can get our latitude by the pole star. In the first place, imagine that the Pole Star is directly over the N pole of the earth and is fixed. If that were so, and imagine for a minute that it is so, then it would be exactly 90° from the Pole Star to the celestial equator. Now, no matter where you stand, it is 90° from your zenith to your true horizon. Hence if you stood at the equator, your zenith would be in the celestial equator and your true horizon would exactly cut the Pole Star. Now, supposing you went 10° N of the equator. Then your northerly horizon would drop by 10° and the Pole Star would have an altitude of 10°. In other words, when you were in 10° N latitude, the pole star would measure 10° high by sextant. And so on up to 90°, where the Pole Star would be directly over you and you would be at the North Pole. Now all this is based upon the Pole Star being in the celestial sphere exactly over the North Pole of the earth. It is not, however. Owing to the revolution of the earth, the star appears to move in an orbit of a maximum of 1° 08'. Just what part of that 1° 08' is to be applied to the true altitude of the star for any time of the sidereal day, has been figured out in the table on page 107 of the Nautical Almanac. What you have to get first is the L.S.T. Find from the table the correction corresponding to the L.S.T. and apply this correction with the proper sign to the true altitude of Polaris. The result is the latitude in. Put in your Note-Book:
To get latitude by pole star, first get L.S.T. This can be secured by using any one of the three formulas given you in Week III - Thursday's Lecture on Sidereal Time and Right Ascension. Then proceed as per formula in N.A.
Note to Instructor:
Spend rest of time in solving examples similar to the following:
1. At sea, Feb. 14th, 1919. CT 13d 21h 52m 33s. CC 1m 14s fast. In Lo. 72° 49' 00" W. IE + 1' 10". HE 15 ft. Observed altitude Polaris 42° 21' 30" N. Required latitude in.
2. At sea, March 31st, 1919. In Lo. 160° 15' E. CT 7h 15m 19s. Observed altitude Polaris 38° 18' N. IE + 3' 00". HE 17 ft. Required latitude in.
Etc.