is the maximum allowable relative radial velocity of the elements. Such large relative velocities would be most unusual for any spacecraft. b) Aberration Error The transverse component, [], of the ARA relative to the pilot source produces pointing error We shall call this error "aberration" because it is essentially the same phenomenon as astronomical aberration: the small annual oscillation in the apparent position of stars due to the Earth’s orbital motion. Eq. (12) is just twice the astronomical value, as one might expect from the fact that retrodirectivity is a two way light path process, while the light from a star reaches the Earth by a direct, one way, path. In Figure 11, we assume that the spacecraft carrying the ARA moves with uniform velocity, v, with respect to the pilot source. Eq. (12) is obtained by applying the coordinate transformations of special relativity twice: first to obtain the angle of incidence of the pilot signal with respect to the ARA, and second to obtain the angle of incidence of the retrodirected signal with respect to the pilot source. The exact result of the calculation (see Appendix B) includes terms of order [] and higher, which are dropped to obtain (12). Aberration error is negligible for geosynchronous satellites. For the 1.0 km diameter ARA of the SPS, the maximum allowable error, .56 x 10^-5 radians, would be exceeded only by
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