These two equations have essentially the same form and they suggest that, in some sense yet to be determined, one function may simply be a multiple of the other. If equation (62) is substituted into equation (63), or equation (63) is substituted into equation (62), the same integral equation results for u^r) and y^p,^). We can then conclude that y and u are proportional, or equivalently their squares are proportional: 4. NUMERICAL RESULTS In this section, some general results of this investigation are presented in non- dimensional form plus selected calculations for particular cost ratios and fraction of power collected to that transmitted. In addition, some cost comparisons are made between the optimum distribution and the well-known truncated Gaussian distribution. From the computer program, we show the functional relation between p and X in Table 1. In this report, we will perform all calculations with two representative ratios of the cost coefficients, namely, Accordingly, we will not evaluate the minimum cost in absolute terms, but only as the minimum cost per unit ground antenna cost, i.e., Cmln/a0- This is sufficient for comparison purposes. Furthermore, we will assume the frequency of transmission to be 2.45 x 109 Hz and the product of the wavelength A and the geosynchronous distance z will be taken as Az = 4.380 x 10® meters2. For all the detailed calculations, we will always assume 95% of the transmitted power is collected. Thus /3 = .95 and, for the optimum case, X = 3.5203. Other values of /3 are used in this paper only when the nondimensional optimum distribution function is considered. It is perhaps worth
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