Precession and Nutation

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.

Figure 9-9. Earth’s axis wobble.

Figure 9-9. Earth’s axis wobble.

 

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 90° 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 90° 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 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 that otherwise appear fixed in space.

Figure 9-10. Precession of the equinoxes.

Figure 9-10. Precession of the equinoxes.

 

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.

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.

Figure 9-11. Nutation changes the declination.

Figure 9-11. Nutation changes the declination.

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.

 

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 Hc and Zn 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.

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.

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.