SOLVING THE ASTRONOMICAL TRIANGLE (PART 2)
Each of these cases has a different rule, and you can't do much else but try to memorize each of them.
The value "Z" in the LAN problem is obtained by subtracting the corrected altitude (Ho) from 90°: in other words, "Z" (for ZENITH DISTANCE) always equals 90° minus the corrected altitude (Ho).
RULES FOR SOLVING LAN
The situation where latitude is greater than the declination but of the same name is called CASE 1, and the rule for that case is:
Lat. = dec. divided by Z
Let's see how a problem would be solved under Case1, before taking up the other two rules.
Example:
Both ship and sun are in north latitude, and the ship is farther north than the sun. Consequently, latitude is greater than declination, and both have the same name. Corrected altitude (Ho) is 60°; declination, 20° N.
True altitude of zenith always 90 degrees
Corrected altitude (Ho) -60 degrees
Z (always 90-the Ho 30 degrees
Declination 20 N degrees (the rule for this case is,Lat.=dec.+Z)
Latitude 50 N degrees
Case 2: Declination greater than latitude but of the same name. This would be the case if the ship were SOUTH of the sun's G. P., but still in north latitude. The rule for case 2 is:
Lat. = dec - Z
Example:
Both ship and sun are in north latitude, and the sun is farther north than the ship. Consequently, declination is greater than latitude, and both have the same name. Corrected altitude (Ho) is 76°, declination,- 23° N.
True altitude of zenith always 90 degrees
Corrected altitude (Ho) 76 degrees
Z (always 90 -the Ho 14 degrees
Declination 23 N (the rule for this case is Lat. = dec - Z)
Latitude 9 N degrees
In this case the resulting latitude would, of course, have the same name as the declination.
Case 3: Latitude and declination of opposite names. The rule for this case is:
Lat. "Z" - dec.
Eample:
Both ship and sun are in opposite latitudes, and the ship is north and the sun is south. consequently, declination is greater than latitude, and both.have the same name. Corrected altitude (Ho) is 26°; declination, 23° N.
True altitude of zenith always 90, corrected altitude (Ho)26 "Z" (always 90 - the Ho) Declination 23° N (the rule for this case is; Lat. = Z - dec)
Latitude 41 N degrees.
Subtract the declination from "Z", and give the resulting latitude the same name as declination
you can't memorize the above cases, just add or subtracted the declination from "Z" to get your DR latitude.
I don't try to memorize these case, I have made up a form and just fill in the blanks. The form will be published titled: LOCAL APPARENT NOON (LAN) SIGHT FORM.
