SOLVING THE ASTRONOMICAL TRIANGLE
Under favorable conditions, even a series of skillfully taken observations may show an occasional deviation from the normal gradual rise and fall. After sights showing a radical difference from the preceding or succeeding series are discarded, this should become evident, and it should be possible to judge the maximum altitude. This will probably be less than the altitude shown in one observation and more than the next below it. The result should give latitude with an error no more than 1'. This reading is considerably more accurate than could be obtained by a single sight under the conditions described.
SOLVING THE ASTRONOMICAL TRIANGLE
When you calculate and plot your line of position, you are, solving the astronomical triangle. Thirty-odd methods of arriving at solutions have been devised since the first edition of Bowditch appeared in 1802. Although the methods may vary, two basic things remain the same:
1. A single observation gives only a single Line of Position (LOP) which is at right angles to the azimuth (Zn) of the observed body.
2. To establish an LOP, the observer must observe, time, and correct the altitude (Ho). From the Nautical Almanac, the observer must determine the declination only. LHA of the observed body is 00or 360. You need only the Ho, Lat, and Dec as arguments to work out the sight.
LAN OR NOON
The noon sight, generally Called LAN (for LOCAL APPARENT NOON), is a convenient and simple element in navigation dating back several centuries. It results in a line of position which coincides with the ship's latitude. Before convenient methods of calculating the longitude were devised, many shipmasters customarily made port by running down the latitude of the desired landfall verified daily by noon sight.
Accuracy of the latitude obtained by LAN depends only upon the accuracy of the sun's maximum true altitude, and the accuracy with which its declination can be determined. When the sun is on the observer's meridian, the ship's latitude is the sum or difference of the declination and the distance the ship is north or south of the sun, depending upon certain rules .
Here are three possible situations which may be encountered in solving LAN.
(1) When the latitude is greater than the declination, but of the same name.
(2) When the declination is greater than the latitude, but of the same name.
(3) When latitude and declination are of opposite names.
