the earth equatorial plane undefined) will attain a maximum I of 14.7 degrees after 26.5 years. However, the last row shows that an orbit with initial I =7.3 degrees and initial = 0 has a constant orientation in space. For e = 0, the satellite longitude A remains constant but the latitude varies between +/- 7.3 degrees each day. (2) The Solar Pressure Effects The solar pressure effects depend upon the area and weight of the satellite. The results of this section are consistent with the area and weight data stated elsewhere in this document. The effects of solar pressure are very complex to analyze and the studies are not yet complete. However, the significant effects are a growth in eccentricity, e, and a rotation of the line of apsides. In the idealized case, e = 0, but the solar pressure causes an increase in this value to 0.068 in the first year. During the first few years, there is a periodic oscillation in e between 0 and 0.068. However, numerical studies indicate that for certain initial conditions there is a long term growth of the mean value of e. Further studies should reveal whether this growth in e is truly secular (increasing without bound) or is simply a longer periodic motion. It also appears that the maximum e can be reduced by choosing an intermediate initial value of e and a suitable perigee location. This possibility also requires more detailed study. The principal result of the periodic (one year) variation in eccentricity is a daily longitude oscillation AX about the mean value of the longitude X. For small I (up to about 10 degrees), ax = ±2e (radians); for e = 0.068, the variation in longitude is +/- 7.87 degrees. (3) Equatorial Ellipticity Effects This perturbation arises from the fact that the earth is not symmetrical about its spin axis. A slice of the earth perpendicular to the spin axis has an elliptical shape. This corresponds to the J?2 tesseral term in the earth's potential expansion. Mathematically the problem has four stationary solutions. Two of these solutions are stable and two are unstable. The stable solutions represent points above the equator at about 120°W and 60°E on the minor axis of the equatorial ellipse; the unstable solutions represent points at 30°W and 150°E (see figure IV-A-3-2) on the major axis of the equatorial ellipse. If at a stable point initially, a satellite will tend to remain; if disturbed somewhat it will librate about the stable point. The period of libration is a function of the initial displacement from the stable point (see figure IV-A—3—3). For example, a displacement in longitude of 60° from a stable point results in a libration period of about 1000 days.
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