faster than 830 m/sec radially, but since they are unlikely to need 1.0 km diameter ARA’s, they can tolerate larger pointing errors. The expression for the differential doppler error is (the first term of Eq. (A12)), where [], is the transmission line delay between the kth and reference elements. The phase of the kth element’s contribution to the field at r = 0 is Since it depends on the value of each v^, rather than just v , the effects of differential doppler are far more various and difficult to calculate than that of simple translational doppler. In the absence of information on the various physical properties of the ARA structure and on its attitude control system, we have no way of knowing what steady state or transient motions of the ARA are possible, and therefore, no way of applying (10). The best we can do is to calculate bounds on []. based on a reasonable bound for t, and an arbitrary [] ko 7 bound. A bound for [], which results if we assume that — [], the dimension of the ARA, and [] Let [] be the allowable phase error. Then from (10), Using the SPS as an example again, X = 0.125 m, D = 1000 m, and we shall assume 6$ = 0.1 it rad. Then
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