ENCOUNTERS BETWEEN SPS POWER BEAMS AND SATELLITES IN LOWER ORBITS Philip K. Chapman Arthur D. Little, Inc., Cambridge, Massachusetts 02140 Each Solar Power Satellite (SPS) will preempt, not only a location in geosynchronous orbit (GEO), but a large region of space (of order several hundred thousand cubic kilometers) for its power beam. If the SPS is geostationary, the beam is fixed relative to the Earth and thus rotates like the spoke of a wheel with the diurnal rotation. Other satellites in lower orbits (including those in transit to GEO) may pass through the beam, causing RFI with satellite systems or perhaps damage to sensors. In some cases, it may be necessary briefly to shut down a given SPS as a satellite approaches its power beam. If the inclinations of the orbits of both the SPS and a lower satellite are exactly zero, and if the SPS is feeding a rectenna directly on the equator, then the satellite will clearly encounter the power beam on every revolution. In the general case, in which the rectenna is at a higher latitude L and the orbit of the lower satellite has a finite inclination 1, the frequency of encounters is much less. As the power beam rotates with the Earth, it generates a conic surface about the polar axis. The intersection of this surface with an inclined orbital plane is a conic section; because of the large apex angle of the cone, the intersection will be an hyperbola except for nearly equatorial satellites. The locus of the beam intersection in the satellite plane starts at GEO altitude when the SPS passes through the right ascension of the ascending node, sweeps down to a minimum altitude (which depends on L and i) and then back up to GEO at the descending node, taking twelve hours. There is no intersection with the satellite orbital plane during the next twelve hours, until the SPS reaches the ascending node again. Since the satellite orbit, in general, has two intersections with the beam locus, there are usually only two opportunities per day for encounters between a given satellite and a given beam. Whether or not an encounter occurs naturally depends on the orbital position of the satellite at the times when these opportunities occur. The shape and orientation of the intersection locus are fixed when the latitude of the rectenna and the inclination and orientation of the lower orbital plane are given, so that beams from several SPS's, feeding rectennas at the same latitude, will follow identical paths in a given orbital plane. The longitude of the rectenna and SPS determines only the time of day when the encounter opportunities occur. The duration of the encounter of a small satellite with the beam can be up to two seconds, with large satellites taking somewhat longer — for example, if a new SPS is completely assembled in low Earth orbit (LEO) and then transported to GEO, its encounter with the beam of an existing SPS could take 3 to 4 seconds. If it is necessary to shut down the beam to avoid the encounter, or if it is occulted by a large vehicle, the duration of the outage will thus be brief. For i < L, there is a maximum safe altitude, below which a satellite will not encounter the beam: for example, a satellite launched due east from Cape Kennedy will not encounter the beam to a rectenna at latitude 35° unless its altitude is greater than 1000 km. The situation is shown in Fig. I, in which the plane of the figure is the satellite orbital plane, and the locus of the beam intersection is depicted.
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