Fig. 13. Number of sightings of antenna reflection. reflection can t>e seen only Between tnese two aates unless tnere is an appreciate longitude difference between the rectenna and satellite. If all rectennas are between 25° and 40° north latitude, a fixed observer will see all the reflections within two- week periods in the spring and summer; however, an observer north of about 24° north latitude would see no reflections at all under these circumstances. The apparent angular velocity of the sun is 2rr cos 8/86164 rad/s. Since the reflection must have the same angular velocity, the maximum contact time for a fixed observer is if the center of the spot passes his location. For an observer in the southern hemisphere who sees the reflection at the summer solstice, T could be as much as 140 seconds. The apparent diameter of the antenna from the ground is d/R rad, or from 0.024 to 0.028 mrad depending on elevation above the horizon. Since diffraction effects are negligible for a one-km aperture, the time required for the reflection to reach full luminosity will be 86164/2tt R cos 8, or between 0.33 and 0.42 seconds. By plotting the latitude extremes of the edge of the reflected spot, an approximate indication can be obtained of the number of sightings to be expected at a given location. For a typical rectenna latitude of 35°, Figure 13 shows that the reflection will be visible on about two successive nights at middle latitudes and about three nights near the equator. Comparison with Fig. 12 shows that the number of sightings varies only slightly with rectenna latitude except for rectennas above 50°, in which case observers around 60° south latitude would see the reflection for several days in succession. However, very few rectennas are likely to be located at such high latitudes. The spot moves across the earth from east to west. Figure 14 illustrates a few ground tracks for a rectenna latitude of 35°. The coverage of the spot is indicated at five-minute intervals. The track for May 1st assumes a satellite 15° east of the rectenna to illustrate the effect of a longitude differential.
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