transmitter and that of the receiver as well as the minimum cost, Cmin. We do not, at this stage, need to know anything about our control function u(r), nor do we require any of our undetermined multipliers. All we must know at this point is that our distribution function, pM = u2(r), whatever it is, is such that it makes our cost a minimum. To do this, we select any ft within reason and the correspondingX is read from our table or interpolated. Thus X is known. We can then write either Ro or Ru in terms of X. Choosing Ro, we have These three formulas are surprisingly simple. For a given fraction of power to be collected, the radii themselves are proportional to the fourth root of Ui/u0 or u0/^i as the case may be. Even more instructive perhaps is the formula for the ratio of the radii. Thus, if it costs 100 times per unit area to fabricate and put in place the transmitter as compared to the receiver, then the receiver’s radius must be 10 times that of the transmitter, provided only that we transmit with the optimum power density function. This result is independent of the power ratio. i.e., the cost of the ground antenna must be the same as the space antenna. Putting into this the explicit values of Ry and Ro, we get at once
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