We are given that Vega has a magnitude of zero on the AB system, so 0 = -2.5 log(f) - 48.60 where "f" is the flux, in ergs per second per sq.cm. per Hz. We can solve for f: erg f = 3.63 x 10^(-20) ----------------- sec * sq.cm. * Hz Each photon has frequency of roughly 5.5 x 10^(14) Hz, so the energy of each photon is E = h f = 3.64 x 10^(-12) erg The V-band has a width of 9 x 10^(13) Hz. We can compute the number of photons per second per sq. cm. of collecting area like so: photons erg 1 photon ------------- = 3.63 x 10^(-20) ---------------- * ------------------ sec * sq.cm. sec * cm.sq. * Hz 3.64 x 10^(-12) erg * 9 x 10^(13) Hz = 8.96 x 10^(5) photons / (s * sq.cm.) The telescope has a radius R = 7.5 cm and so a collecting area A = pi * R^2 = 176.7 sq.cm. We can expect to collect photons ---------- = 1.74 x 10^(8) photons / s sec If we need 9 million photons to reach our goal, then the exposure time will have to 9 x 10^(6) photons exptime = ----------------------- = 0.05 seconds 1.74 x 10^(8) photon/s