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maximum; that is, when the observer and the subpoint are separated by 90o. Since the earth's radius is
tiny compared to the infinite distance to the stars, the angle p is very small. For the sun, angle p is a
negligible 9 seconds of arc or 0.15 NM. Observed altitudes from either the artificial or celestial horizon
are practically the same.
8.14.2. The bubble in a sextant or artificial horizon is most used by navigators. As in a carpenter's level,
a bubble indicates the apparent vertical and horizontal. With the bubble, the navigator can level the
sextant and establish an artificial horizon parallel to the plane of the celestial horizon. Figure 8.16 shows
that the plane of the artificial (bubble) horizon and the plane of the celestial horizon are parallel and
AFPAM11-216 1 MARCH 2001 211
separated by the earth's radius. Compared to the vast distances of space, the radius of the earth is
inconsequential. Thus, the artificial horizon and the celestial horizon are nearly identical.
Figure 8.15. Parallax.
Figure 8.16. The Two Planes Are Parallel.
8.15. Observed Altitude. The distance of the observer from the subpoint and a body's Ho are related.
(Figure 8.17). When the body is directly overhead, the Ho is 90o, and the subpoint and the observer's
position are collocated. When the Ho is 0o, the body is on the horizon and the subpoint is 90o (5,400
NM) from the observer's position (See Figure 8.18, where C is the center of the earth, AB is the
observer's horizon, and S is the subpoint of the body). Since the sum of the angles in a triangle equals
180o, the angle OX is equal to 180o – (Ho + P). The sum of the angles on a straight line equals 180o, so
angle OXC is equal to Ho + P. The horizon AB being tangent to the earth at O is perpendicular to OC, a
radius of the earth. Thus, angle OCX equals 90o (Ho + P). The preceding discussion showed that angle P
is negligible, so this angle becomes 90o – Ho. The arc on the surface subtended by the angle OCX at the
center of the earth is arc OS. This arc then is equal to 90o – Ho.
212 AFPAM11-216 1 MARCH 2001
Figure 8.17. Measure Altitude From Celestial Horizon Along Vertical Circle.
Figure 8.18. Finding Observed Altitude.
8.15.1. The distance from the subpoint to the observer is the zenith distance or co-alt and is computed
using the astronomical triangle described in Chapter 9. Basically, the zenith distance equals 90o minus
the Ho (Figure 8.19). The figures are then converted to NM by multiplying the number of degrees by 60
and adding in the odd minutes of arc.
Ho = 37o26'
therefore, co-alt = 90o – 37o26'
therefore, co-alt = 52o34'
Zenith Distance = (52o x 60) + 34'
Zenith Distance = 3,154 NM
Zenith distance is the radius of the circle which becomes the celestial LOP.
AFPAM11-216 1 MARCH 2001 213
8.15.2. This circle is called the circle of equal altitude (Figure 8.20), as anyone located on it will view an
identical Ho. Now that you can determine the distance to the subpoint, you must next find the direction.
Figure 8.19. Co-Altitude and Zenith Distance.
Figure 8.20. Constructing a Circle of Equal Altitude.
214 AFPAM11-216 1 MARCH 2001
8.16. True Azimuth (Zn). The direction to a body from an observer is called Zn. A celestial body's Zn
is the true bearing (TB) to its subpoint. The Zn is the angle measured at the observer's position from true
north (TN) clockwise through 360o to the great circle arc joining the observer's position with subpoint,
as illustrated in Figure 8.21. If you could measure the Zn when you measure its altitude, you could have
a fix. Unfortunately, there is no instrument in the aircraft which will measure Zn accurately enough.
Except in the case of a very high body (85-90 degrees), if you observe a body with a Ho of 40o and you
mismeasure the Zn by 1 degree, the fix will be 50 NM off.
Figure 8.21. Relationship of True Azimuth to an Observer.
8.17. Celestial Fix. Since you cannot normally fix off a single body, you will usually need to cross two
or more LOPs. The fix position is the intersection of the LOPs. A celestial LOP is a circle as shown in
Figure 8.22. When two celestial LOPs are plotted, they intersect at two points, only one of which can be
your position. In practice, these two intersections usually are so far apart that dead reckoning removes
all doubt as to which is correct.
AFPAM11-216 1 MARCH 2001 215
Figure 8.22. Celestial Fix With Two Bodies.
216 AFPAM11-216 1 MARCH 2001
Chapter 9
COMPUTING ALTITUDE AND TRUE AZIMUTH
Section 9A— Introduction
9.1. Basics. This chapter discusses the procedures and some of the tables used to compute a celestial line
of position (LOP). Some of the tables used to resolve the LOP, including the Air Almanac, were
　
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