For an array of n identical telescopes, the rms variation in flux density is given by 4. as,= (2 mk tsys)/[ae (2 n t av)21, where n is the total number of baselines, m is a sensitivity constant (of order of unity), av is the bandwidth or frequency resolution, ae is the effective aperture of a single telescope, tsys is the system noise temperature, k is boltzmann constant (= 1.38x103 j k), and t is the integration time a). express the total number of baselines n as a function of n b). aperture synthesis images is show that then the rms brightness temperature, due to random noise, in atb= (m a tsys)/[ae , (2 n t av) ), is the synthesized beam solid angle, and a is the wavelength. where c) derived above in question b): show that the following relation is an alternative form of the equation atb (2.5 tsys dmax)/[n d (t avj'/21 where dmax is the maximum baseline of the interferometer array expressed in wavelength, av is the velocity resolution, and d is the diameter of the individual interferometer antennas. prove equation (3.17) of interferometry and synthesis in radio astronomy by 5. thompson, moran and swenson (2nd ed.) f [i', (m-cos 60] cosec 6o] isin ôolv(u', v' sin oo) exp(-j2nv'cos 8)