The final topic to be described in this section is the LEO SunTower-Relay link geometry, with ReflectArray relay satellites placed either in MEO or GEO. Figures 4-10 and 4-11 illustrate typical variations of the range and direction angles as a function of time over a single day. Maximum range of this link is determined by Earth occultations that occur about 55% of the time for MEO or 27% for GEO relays. Direction angles vary widely and quasi-periodically as would be expected from the relative motion of the two orbiters, although the maximum angular rates are not excessive - about 6°/minute for MEO or 4°/minute for GEO. If there were no beam pointing constraints, then the ST-Relay link would be visible for 651 minutes/day (MEO) or 1052 minutes/day (GEO), in this example. However, with the specified constraints of a fixed orientation of the transmitter array pointed along the ST orbit normal, and a 30° electronic beam slewing limit, the link visibility decreases to only 175 minutes/day (MEO) or 238 minutes/day (GEO). When averaged over the manifold of orbit orientations and initial positions, the calculated duty cycle values are 136 minutes/day (MEO) or 221 minutes/day (GEO). Since the ReflectArray relay satellite does not have energy storage capability, there must also be congruence (time overlap) between the ST-Relay and Relay-Ground Site visibilities. Hence, for MEO relays in particular, there is a further contraction of the total power beaming operability of a single SunTower/Relay pair. The way this is handled on a average basis in the Space Segment model is indicated by the following expression: Figure 4-12 Ground Contact Time for Various SSP Orbit Concepts where Ate and Nep are the ground contact time and number of equivalent daily passes defined earlier, and Kr is the fraction of the day (duty cycle) that the ST-Relay link is operable. Taking the 13° N latitude
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