There is no eclipse if 3, the angle between the solar vector and the orbit plane, is large enough (see figure IV-A-3-18). For a synchronous orbit with an eccentricity of 0.04, the minimum 3 is 8.54° at apogee and 9.26° at perigee. These must be measured at the sun's lower limb if all partial eclipses are to be avoided, and must therefore be increased by 0.27° (the sun's maximum semi diameter) to obtain the correct angle to the center of the sun. The minimum 3 is then 8.81° to 9.53°. The higher value will be used here for conservatism; the conclusions would be the same for either figure. The minimum 3 for avoidance of eclipse by other satellites is substantially less than for earth eclipses. The satellite eclipse problem need not be considered separately, therefore. It is convenient to specify the orientation of the orbit plane by the projection on the celestial sphere of the normal to the orbit plane. There will be no eclipse if the normal is at least 9.53° from the locus of points 90° from the sun. Thus, the region up to 9.53° on each side of the great circle 90° from the sun is an "eclipse zone" (figure IV-A-3-19). If the normal to the orbit plane is within this zone, an eclipse will occur; if the normal is outside the zone, there will be no eclipse. The eclipse zone rotates with the sun. Since polarity is immaterial, its period is six months (neglecting the eccentricity of the earth's orbit, which is also not pertinent to this question). The monthly movement of the zone is illustrated in figure IV-A-3-20, which represents a view from the north pole. Because of the obliquity of the ecliptic (23.5°), the motion is not symmetrical with respect to the pole. Referring to figure IV-A-3-20, it can be seen that the orbit can be kept out of the eclipse zone in two ways. The first, with the normal to the orbit plane indicated by circles, is to adjust the inclination of the orbit so that the normal always remains on the same side of the eclipse zone. The second, with the normal denoted by triangles, is to make a large plane change maneuver every six months (March and September) so as to move the orbit normal across the eclipse zone. This maneuver must be completed in less than one orbit if no eclipses whatever are to be permitted. The first approach requires relatively gradual plane changes, although the total amount is large. As shown in figure IV-A-3-20, the total plane change is on the order of 90°/year. For a mass of 82000 M.T. and specific impulse of 98 km/s, the propellant required is roughly 4 x 10® kg/year. The principal difficulty, however, is the maximum inclination of 33° (June). As noted on page IV-A-3-12, non-zero inclinations cause a large variation in the angle of incidence of the microwave beam at the rectenna, the total excursion being about twice the inclination.
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