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The corrections are necessary because Polaris orbits in a small circle around the pole. When Polaris is at the exact same altitude as the pole, the correction is zero. At two points in its orbit it is in a direct line with the observer and the pole, either nearer than or beyond the pole. At these points the corrections are maximum. The nofollowing example illustrates converting a Polaris sight to latitude.
At 23-18-56 GMT, on April 21, 1994, at DR Lat. 50°23.8' N, λ=37° 14.0'W, the observed altitude of Polaris () is 49° 31.6'. Find the vessel’s latitude. To solve this problem, use the equation:
where is the sextant altitude () corrected as in any other star sight; 1° is a constant; and , , and are correction factors from the Polaris tables found in the Nautical Almanac. These three correction factors are always positive. One needs the nofollowing information to enter the tables: LHA of Aries, DR latitude, and the month of the year. Therefore:
The first correction, ,isa function solely of the LHA of Aries. Enter the table column indicating the proper range of LHA of Aries; in this case, enter the 160°-169° column. The numbers on the left hand side of the correction table represent the whole degrees of LHA ; interpolate to determine the proper correction. In this case, LHA was 162° 03.5'. The A0 correction for LHA = 162° is 1° 25.4' and the correction for LHA = 163° is 1° 26.1'. The correction for 162° 03.5' is 1° 25.4'.
|(162° 03.5')||+1° 25.4'|
|(L = 50°N)||+0.6'|
|Observed Altitude||49° 31.6'|
|Latitude||N 49° 58.5'|
|Tabulated GHA (2300 hrs.)||194° 32.7'|
|Increment (18-56)||4° 44.8'|
|DR Longitude (-W +E)||37° 14.0'|
To calculate the correction, enter the correction table with the DR latitude, being careful to stay in the 160°- 169° LHA column. There is no need to interpolate here; simply choose the latitude that is closest to the vessel’s DR latitude. In this case, L is 50°N. The correction corresponding to an LHA range of 160°-169° and a latitude of 50°N is + 0.6'.
Finally, to calculate the correction factor, stay in the 160°-169° LHA column and enter the correction table. Follow the column down to the month of the year; in this case, it is April. The correction for April is + 0.9'.
Sum the corrections, remembering that all three are always positive. Subtract 1° from the sum to determine the total correction; then apply the resulting value to the observed altitude of Polaris. This is the vessel’s latitude.