a ccd detector at the focal plane of a 1.0 m diameter telescope records the image of a partic- ular star. due to atmospheric seeing, the light is spread over a circular area of radius r pixels. the total number of photoelectrons over this area, accumulated during the exposure, and due to the light of the star, is nstar. meanwhile, light from the sky produces nsky photoelectrons per pisxel during the same exposure. (a) calculate the signal to noise ratio (s/n) of the photometric measurement of the star, i. e. the ratio of the counts from the star to the uncertainty in the measurement. assume poisson statistics, such that the 'noise' is the square root of the total photoelectron counts, from all sources. (b) the same star is observed with the same exposure time, with the 4.0 m mayall telescope at kitt peak. this larger telescope is also at a site with a much more stable atmosphere, and has a seeing disk radius one third as small as the telescope in part (a). find the s/n in this case. (c) assuming that the neither the star, the sky, nor the electronics are variable during the exposure, show that the s/n varies as the square root of the exposure time in the case where (i) the counts from the star are much greater than those from the sky in the seeing disk, and () the counts from the sky in the seeing disk are much greater than those from the star d) by what factor does the exposure time need to be increased on the 1.0 m telescope to match the s/n obtained by the mayall 4.0 m telescope for the cases (i) and (ii) in part (c)?