The last expression shows the symmetry that exists between the ground and space antennas; interchanging the indices gives the same result. The formula, so to speak, cannot tell which antenna is on the ground and which is in space. Distribution function of the space antenna To obtain the optimum value of u(r), we must now calculate the X/s and XW1, or rather, as will be seen presently, a certain set of ratios of these quantities. We first recast the equation for u so that Ro does not appear explicitly. We note that This normalizes the abscissa of u since our variable here is r/Rv, i.e., 0 < r/Rt < 1. Since X = X^p) has already been determined, only the X’s remain to completely define u. As noted previously, the X/s are contained in a set of homogeneous simultaneous linear equations. We may write them in matrix form as
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