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Problem 7.41. (a) The VLA array has 27 telescopes as shown in Fig. 9a. Nine are spaced along each of three arms of length 21 km arranged like three spokes of a wheel with equal angles (120°) between the spokes. Consider an arrangement of the telescopes wherein the distances from the center on each arm scale as 1,4, 9, 16, etc. with the outermost telescopes at the end of the arms. There is no telescope at the center. (a) A brief observation is carried out of a source at the zenith. Make a Fourier-plane u ,v diagram showing the sampled points due to the inner 6 antennas only, i.e., those at radii 1 and 4, for the time of the observation. Align one spoke in the N-S direction. Hint: how many points should be in the plot? (b) If the VLA were at the North Pole observing an overhead source, how long an observation is needed to get the maximum u,v coverage with this 6-antenna configuration? Will the time differ for the 27-antenna configuration? (c) The array can operate at a frequency of 5 GHz. In this case, what is the approximate source angular size that could just barely be resolved, i.e., the smallest angular size that would appear as extended? Consider both the 6-antenna and 27-antenna cases. [Ans. 15; 4 h; ~5", ~0.3"]

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