LHA and the Astronomical Triangle (Part Two)

Pub. No. 249, Volume 1

Volume 1 of Pub. No. 249 deals solely with the solution concerning selected stars and is considered separately from Volumes 2 and 3. Volume 1 provides complete worldwide coverage from pole to pole for each degree of latitude. The LHA of Aries is listed in 1° increments from latitudes of 0° to 69° North and South inclusive. From 70° through 89° of latitude, the meridians are so close together that it is only necessary to tabulate the values of the LHA of Aries in even 2° increments. There are two pages devoted to each whole degree of latitude between latitudes 69° N and 69° S inclusive. From there to the pole, only one page is devoted to each whole degree of latitude. The three stars marked by diamonds on each page provide sets for fixing purposes that are favorably situated in altitude and azimuth.

 

The entering arguments are the assumed latitude and the LHA of Aries (to whole degrees). At any one time, the navigator has the choice of the seven listed stars for that latitude plus Polaris. The names of the stars are in capital letters if the star is of first magnitude or brighter; the second magnitude stars are printed in small letters. The names of the stars are listed every 15° of LHA of Aries (every 30° in the polar latitudes). For the time the navigator expects to make an observation, commonly called a shot, they look up the GHA of Aries and apply the approximate longitude to get a whole degree LHA of Aries. The navigator then enters Pub. No. 249, Volume 1, with the latitude closest to the dead reckoning (DR) latitude and the LHA of Aries to select the stars that will be shot.

Figure 9-5. Enter tables with LHA Aries and latitude.

Figure 9-5. Enter tables with LHA Aries and latitude. [click image to enlarge]

Since single celestial observation results in only one LOP, it is necessary to shoot two or more bodies to obtain a fix. Suppose the navigator wants to shoot at approximately 0230 Greenwich Mean Time (GMT), he or she looks up the GHA of Aries (in the Air Almanac) and finds it to be 196°. The DR position for this time is 31° 48′ N, 075° 26′ W. A quick calculation shows the LHA of Aries is approximately 121°, and the closest latitude is 32° N. Notice in the portion of the tables reproduced in Figure 9-5 the available stars at this position are Alkaid, Regulus, Alphard, Sirius, Rigel, Aldebaran, and Capella. Using Sirius, a shot is taken at 0231 and the Ho obtained is 37° 50′.

GHA Aries for 0230 GMT 196° 06′
Correction for l minute 15′
GHA Aries for 0231 GMT 196° 21′
Closest longitude to DR for whole LHA
(assumed longitude)
W075° 21′
LHA Aries for 0231 GMT 121°

The closest whole degree of latitude is 32° N; therefore, it is used as the assumed latitude. The assumed longitude is selected as the closest point, resulting in an LHA of Aries that is a whole degree (no minutes). The Hc of Sirius is listed as 37° 40′. The Zn is 205°.

 

The second shot was taken at 0234 using Regulus, the Ho being 55° 30′. A new DR position could be obtained for 0234 GMT, but the 0230Z DR position will suffice for this determination of Hc and Zn.

GHA Aries for 0230 GMT 196° 06′
Correction for 4 minutes 1° 00′
GHA Aries for 0234Z 197° 06′
Closest longitude for whole LHA
(assumed longitude)
W075° 06′
LHA Aries for 0234Z 122°

The assumed latitude is still 32° N and, in this case, 075° 06′ W is the assumed longitude since this is the closest longitude to the DR longitude that results in the LHA of Aries being a whole degree. The Hc of Regulus is listed as 56° 19′, and the Zn is 119°. The various corrections that must be applied, as well as the plotting of the fix, are discussed later.

Postcomputation Method

The steps in the precomputation method are as follows:

  1. Determine the GHA of Aries for the time of observation from the Air Almanac.
  2. Assume a position as close as possible to the DR position at the time of the shot so the latitude and LHA of Aries in whole degrees may be determined.
  3. Turn to the page in Pub. No. 249 for the assumed latitude and, opposite the LHA of Aries, select the stars to be shot. In making the selection, assume the LHA of Aries will change 1° every 4 minutes of time.
  4. Shoot the body and record the time, Ho, and name of the body.
  5. Obtain the GHA of Aries for the time of the observation, and apply the assumed longitude to determine the LHA of Aries.
  6. Turn to the pages for the assumed latitude and, opposite the LHA of Aries in the column headed by the name of the star, find and record the Hc and Zn.
 

Pub. No. 249, Volumes 2 and 3

Volume 1 consists of tables of Hc and Zn for selected stars. Because the Dec and SHA of each star change slowly, these tables may be used for many years with only small corrections. The Dec and SHA of a nonstellar body change rapidly, making a permanent format similar to Volume 1 impossible for the sun, moon, and planets.

Volumes 2 and 3 have Dec tables adequate for determining the Hc and Zn of any celestial body within the Dec range of 30° N to 30° S. They are intended primarily for use when observing nonstellar (solar system) bodies. Volume 2 provides latitudes between 39° N and 39° S, and Volume 3 provides for latitudes from 40° N or S to the poles.

Provision is made for observed altitudes from 90° above to 3° below the horizon (7° from latitudes 70° to the pole). In view of refraction and of possible long intercepts, the tables are actually extended 2° below these limits.