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9.10.7. This completes the solution for the Dec tables. Keep in mind this solution is computed after the
observation. Because of the speeds involved in air navigation, we will explain a way to compute the
solution before the shot in the next chapter.
Section 9C— Precession and Nutation
9.11. Basics. The earth's axis does not maintain a fixed direction in space. Actually, the earth is like a
slow running gyro that is wobbling. There are several separate patterns that the wobble makes. Some of
those patterns have short cycles, while others take hundreds of years to complete. Two of the many
patterns are shown in Figure 9.9. One involves small nodding motions while at the same time
completing a larger circular path. You must use a correction called precession and nutation to account
for these variations in the apparent position of the stars. This correction is applied only to celestial LOPs
determined with Pub. No. 249, Volume 1.
226 AFPAM11-216 1 MARCH 2001
Figure 9.9. Earth's Axis Wobble.
9.12. Precession. Because of the equatorial bulge, the attractive forces of other solar system bodies,
principally the moon, are unbalanced about the center of the earth. The imbalance is directed toward
aligning the equator with the plane of the ecliptic. However, the rotation of the earth transforms this
force into an effect acting 90o away in the direction of rotation—a precessional effect. The result is that
the poles travel in a conical path westward around the ecliptic poles, as shown in Figure 9.10 (the point
90o from the ecliptic). Consequently, the points of intersection of the equator with the ecliptic, or the
equinoxes, travel in a westerly direction along the ecliptic. This travel is called precession of the
equinoxes, and it amounts to approximately five-sixths (5/6) of a minute (50.26") annually. The
equinoxes complete one revolution along the ecliptic in approximately 25,800 years. The equator is used
as a reference for Dec and its movement, due to precession of the equinoxes, causes slight changes in the
celestial coordinates of the stars, which otherwise appear fixed in space.
9.13. Nutation. As the relative positions and distances from the earth to the sun, moon, and planets vary
so does the rate of precession. The only variation of importance in navigation is nutation. Nutation is a
nodding of the poles, one oscillation occurring in about 18.6 years.
AFPAM11-216 1 MARCH 2001 227
Figure 9.10. Precession of the Equinoxes.
9.13.1. In Figure 9.11, you can see that if the stars remain fixed and the equinoctial moves up and down,
the Dec of these bodies is changing.
9.13.2. Nutation, being approximately perpendicular to the ecliptic, has an appreciable influence on Dec.
It is caused by complex gravitational forces among the sun, moon, and earth because the moon's orbit
does not always lie in the plane of the ecliptic. The change in Dec of the celestial bodies caused by the
resulting wobble of the earth's axis is called nutation.
9.14. Position Corrections. Because of precession and nutation, Hc and Zn for a star are accurate only
at the instant, or epoch, at which the LHA and Dec for the computations are correct. A position obtained
at any other time with that Hc and Zn requires a correction. Pub. No. 249, Volume 1, contains Hcs and
Zns calculated for an epoch year (midnight, 1 January, of that year) so, if the volume is used in any other
year, the resultant position must be corrected. The precession and nutation corrections are combined and
given in Pub. No. 249, Volume 1, Table 5.
9.14.1. Entering arguments for the table is year, latitude, and LHA of Aries, and the correction is
presented in the form of a distance and direction to move the fix. The tabulated values show the
distance, parallel to the ecliptic, between the observer's position in the year of the fix and the position in
the epoch year at the latitude and LHA of Aries.
228 AFPAM11-216 1 MARCH 2001
Figure 9.11. Nutation Changes the Declination.
9.14.2. Directions for using Table 5 are printed in the introduction of Pub. No. 249, Volume 1. One
point needs emphasis here: The table is to be used only for observations plotted with the aid of Volume
1, never in conjunction with Volumes 2 or 3.
9.15. Summary. This chapter has dealt with the astronomical triangle and how the Pub. No. 249
volumes you use in resolving the astronomical triangle. We've discussed obtaining solutions involving
celestial bodies using Pub. No. 249, Volumes 1, 2, and 3. Succeeding chapters will discuss plotting of
the celestial LOPs and techniques of precomputation.
AFPAM11-216 1 MARCH 2001 229
Chapter 10
CELESTIAL PRECOMPUTATION
Section 10A— Introduction
10.1. Basics. Celestial precomputation is neither new nor revolutionary. The tables necessary to do
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