Local hour angle (LHA) is the name given to the angle of arc (expressed in degrees, minutes, and tenths of minutes) of the celestial equator between the celestial meridian of a point on the celestial sphere and the hour circle of a heavenly body. It is always measured westward 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 toward Greenwich which means, of course, that Greenwich will be shown east of M. Think it over for a moment—you are to the west of Greenwich; therefore, Greenwich is to the east of you.

Now that we know where Greenwich is and where you are, let’s figure the LHA of the sun as it is shown in figure 15-8. Figure 15-10 shows us that the sun is 90° west of Greenwich. We know that the LHA is always measured westward from your location meridian(M) to the hour circle of the body (in this example, the sun). Therefore, the LHA here is the whole 360° around minus the 45° between the sun’s hour circle and M. This 45° may be found by inspecting figure 15-10 or by subtracting 90° from 135°. Let’s think this over—we are 135°W of Greenwich; therefore, G is 135° clockwise from us. The sun is 90°W or counterclockwise from G. The difference is the 45° we mentioned. Subtract this 45° from 360° and we get 315°, the LHA. Look again at figure 15-10. As you can see, the sun is east (clockwise on the diagram) of your local meridian (M). Now let’s suppose that you are at the same longitude (135°W), but the GHA of the sun is 225° instead of 90°. The time diagram will appear as shown in figure 15-11. ‘The sun is now west of your meridian (M). The LHA is always measured westward from the local celestial meridian to the hour circle of the body. Therefore, the LHA is the 90° from M to the sun’s hour circle.

Here are two general rules that will help you in finding the LHA when the GHA and longitude are known:

In west longitude it may be necessary to add 360° to the GHA before the subtraction can be made. In east longitude, 360° is subtracted from the LHA if it exceeds this amount. Be sure, however, to check the accuracy of your work by referring to a time diagram. It offers a graphic means of obtaining the data you need.

As an illustration, suppose the GHA of the sum is 327°44'24" and the longitude is 79°15’05"E. Since longitude is east, you use formula 2 above. Transposing to solve for the LHA, you have

This is over 360°, so you subtract 360° from the 406°59’29" The result is 46°59’29".

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