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(or aircraft's altitude) is approximately the center of the universe.
8.2.2. Ptolemy proposed the celestial concept of the universe in AD 127. He said the earth is the center
of the universe, and all bodies rotate about the earth from east to west. In the relatively short periods of
time involved with celestial positioning, you can assume that all bodies on the celestial sphere rotate at
the same rate. In actuality, over months or years, the planets move among the stars at varying rates.
8.2.3. Establishing an artificial celestial sphere with an infinite radius simplifies computations for three
reasons. First, since the terrestrial and celestial spheres are geometrically similar, every point on the
198 AFPAM11-216 1 MARCH 2001
celestial sphere has a corresponding point on the terrestrial sphere and; conversely, every point on the
terrestrial sphere has a corresponding point on the celestial sphere.
8.2.4. Second, the celestial sphere's infinite radius dwarfs variations in the observer's location. An
infinite radius means all light rays from the celestial body arrive parallel, so the angle is the same
whether viewed at the earth's center, on the surface, or at the aircraft's altitude.
8.2.5. Third, the relationships are valid for all bodies on the celestial sphere. Because the moon is
relatively close to the earth, it must be treated differently. With certain corrections, the moon still
provides an accurate LOP. This will be addressed in Chapter 10.
8.2.6. Because the celestial sphere and terrestrial sphere are concentric, each sphere contains an equator,
two poles, meridians, and parallels of latitude or declination. The observer on earth has a corresponding
point directly overhead on the celestial sphere called the zenith. A celestial body has a corresponding
point on the terrestrial sphere directly below it called the subpoint or geographic position. At the
subpoint, the light rays from the body are perpendicular to the earth's surface. See Figures 8.1 and 8.2.
8.2.7. Consistent with the celestial assumptions, the earth and the celestial meridians don't rotate. All
bodies on the celestial sphere rotate 15o per hour past the celestial meridians. The moon moves at
approximately 14.5o per hour.
Section 8B— Motion of Celestial Bodies
8.3. Basics. All the celestial bodies have two types of motion, absolute and apparent. Apparent motion is
important to navigators. Apparent motion is the motion of one celestial body as perceived by an
observer on another moving celestial body. Since apparent motion is relative, it is essential to establish
the reference point for that motion. For example, the apparent motion of Venus would be different if
observed from the earth or the sun.
8.4. Apparent Motion. The earth's rotation and revolution causes the apparent motion of the celestial
bodies. Rotation causes celestial bodies to appear to rise in the east, climb to a maximum height, then set
in the west. All bodies appear to move along a diurnal circle, approximately parallel to the plane of the
equator.
8.4.1. The apparent effect of rotation varies with the observer's latitude. At the equator, the bodies
appear to rise and set perpendicular to the horizon. Each body is above the horizon for approximately 12
hours each day. At the North and South Poles, a different phenomenon occurs. The same group of stars
is continually above the horizon; they neither rise nor set, but move on a plane parallel to the equator.
This characteristic explains the periods of extended daylight, twilight, and darkness at higher latitudes.
The remainder of the earth is a combination of these two extremes; that is, some bodies will rise and set,
while others will continually remain above the horizon.
8.4.2. The greater the northerly declination of a body, the higher it appears in the sky to an observer at
the North Pole. Polaris, with a declination of almost 90o, appears overhead. Bodies with southern
declination are not visible from the North Pole.
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Figure 8.1. Celestial Points and Subpoints on Earth Have the Same Relationship.
Figure 8.2. Elements of the Celestial Sphere.
8.4.3. A circumpolar body appears to revolve about the pole and never set. If the angular distance of the
body from the elevated pole is less than the observer's latitude, the body is circumpolar. For example,
the declination of Dubhe is 62o N. Therefore, it is located at an angle of 90o – 62o from the North Pole,
or 28o. So, an observer located above 28o N will view Dubhe as circumpolar. Although Figure 8.3 uses
the North Pole, the same characteristics can be observed from the South Pole.
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Figure 8.3. Some Bodies Are Circumpolar.
8.4.4. If the earth stopped rotating, the effect of the earth's revolution on the apparent motion of celestial
　
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