a variation in power density on the rectenna and consequently a variation in power output. This is illustrated in figure IV-A-3-4, which presents output as a function of time and rectenna latitude for an eccentricity of 0.04. This eccentricity is thought to be an achievable peak value (with suitable initial conditions) and has been used for the following analyses. The plots assume an SPS designed for 5 GW rectenna output at 40° latitude in a circular orbit. Total variation in output is roughly 100 MW from maximum to minimum, or about 2 percent. The variation is greater at higher latitudes. The azimuth and angle of incidence of the microwave beam also vary and influence the power density distribution over the rectenna. The effect appears to be minor for small longitude differences between satellite and rectenna (but not for large differences: see "Longitude Offset" below). Orbit eccentricity has two effects, essentially independent, on transmitting antenna motion. In a circular orbit, the antenna would rotate continuously at constant angular velocity about an axis perpendicular to the orbit plane (POP). However, the varying orbital velocity of the SPS and the resulting daily oscillation in longitude require a deviation from constant velocity about this axis. The departure from uniform motion is shown in figure IV-A-3-5. Peak angular acceleration of the antenna is about 4.8 x 10“10 rad/s2 for an eccentricity of 0.04, zero inclination and rectenna latitude of 40°; it is approximately proportional to eccentricity and varies only slightly with latitude. The second effect of eccentricity on antenna motion is a variation in elevation angle above the orbit plane, caused by the variation of the satellite radius vector; the amount is illustrated in figure IV-A-3-6 for an eccentricity of 0.04. The amount of variation is greater for higher rectenna latitudes and for higher eccentricities. For 40° latitude and 0.04 eccentricity, maximum angular acceleration is about 5.2 x 10-H rad/s2. Collision avoidance may be the most important problem with eccentric orbits. Relative to a coordinate system fixed in the earth, a satellite in an eccentric synchronous orbit follows an approximately elliptical path whose major axis is 4ae, where a is the semimajor axis of the orbit (42164 km) and e is the eccentricity. It follows the same path relative to a satellite in a stationary (synchronous, zero-eccentricity, zero-inclination) orbit. If 112 satellites are distributed uniformly between the longitudes of Maine and Oregon, the average separation is 0.5° of longitude or 368 km at synchronous altitude. If the difference in eccentricities of two adjacent satellites was as much as 0.0045, their orbits would intersect. Since the expected eccentricity of the SPS orbit is
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