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100. Problem 16.69 (RHK) Assume that a geosynchronous communication satellite is in orbit at the longitude of Chicago. We have to find the direction in which the axis of a parabolic antenna has to be pointed at Chicago for receiving the maximum signal from the satellite. The latitude of Chicago is 47.50 N.
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Solution: Click For PDF Version Geometry of the situation is as shown in the diagram. We use the basic data for a geosynchronous satellite:
Using the law of cosine we will first estimate the distance of the satellite from Chicago:
Substituting the data, we find
We once again use the law of cosine for determining the angle
Substituting the data, we find
From the geometry, we note that the angle
That is the axis of the parabolic antenna should be pointed at an angle of 34.90 above the horizon in the Southern direction.
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We have
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