equinox; you then have the star located on the timediagram. Let’s say it is the star Vega, whose SHA isapproximately 81°. Figure 15-9 shows Vega located onthe time diagram.Itis easy to see herethat the GHA of Vega must beequal to the GHA of the vernal equinox plus the SHA ofVega (or GHAEL%%, = GHAr + SHAVqa. In this example,the GHA of Vega is 81° plus 45°, or 126°.Now let’s use the time diagram to explain somemore facts about nautical astronomy.Local Hour Angle (LHA)Local hour angle (LHA) is the name given to theangle of arc (expressed in degrees, minutes, and tenthsof minutes) of the celestial equator between the celestialmeridian of a point on the celestial sphere and the hourcircle of a heavenly body. It is always measuredwestward from the local meridian through 360°.Let’s work this problem of LHA on a time diagram.Say you are at longitude 135° from M towardGreenwich which means, of course, that Greenwichwill be shown east of M. Think it over for amoment—you are to the west of Greenwich; therefore,Greenwich is to the east of you.Now that we know where Greenwich is and whereyou are, let’s figure the LHA of the sun as it is shown infigure 15-8.Figure 15-10 shows us that the sun is 90°west of Greenwich. We know that the LHA is alwaysmeasured westward from your location meridian(M) tothe hour circle of the body (in this example, the sun).Therefore, the LHA here is the whole 360° aroundminus the 45° between the sun’s hour circle and M. This45° may be found by inspecting figure 15-10 or bysubtracting 90° from 135°. Let’s think this over—we are135°W of Greenwich; therefore, G is 135° clockwisefrom us. The sun is 90°W or counterclockwise from G.The difference is the 45° we mentioned. Subtract this45° from 360° and we get 315°, the LHA.Look again at figure 15-10. As you can see, the sunis east (clockwise on the diagram) of your local meridian(M). Now let’s suppose that you are at the samelongitude (135°W), but the GHA of the sun is 225°instead of 90°. The time diagram will appear as shownin figure 15-11. ‘The sun is now west of your meridian(M). The LHA is always measured westward from thelocal celestial meridian to the hour circle of the body.Therefore, the LHA is the 90° from M to the sun’s hourcircle.Here are two general rules that will help you infinding the LHA when the GHA and longitude areknown:Figure 15-10.-LHA on the time diagram.Figure 15-11.-LHA with the sun west of your celestial meridian.1. LHA= GHA– AW (used when longitude is west)2. LHA = GHA + kE (used when longitude is east)In west longitude it may be necessary to add 360°to the GHA before the subtraction can be made. In eastlongitude, 360° is subtracted from the LHA if it exceedsthis amount. Be sure, however, to check the accuracy ofyour work by referring to a time diagram. It offers agraphic means of obtaining the data you need.As an illustration, suppose the GHA of the sun isand the longitude is 79°15’05”E. Sincelongitude is east, you use formula 2 above. Transposingto solve for the LHA, you have15-13

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