An astronomer named william herschel was one of the first people to try and map the structure of our galaxy in 1785 (believed to be the entire universe at that time). he did this by assuming that all stars had the same absolute magnitude and then counted how many stars he could see in each direction on the sky. he put this together to draw*a map of our galaxy suppose that you are a modern william herschel and you are looking at a visual ccd image. this ccd image has a field of view of 10 arcminutes by 10 arcminutes. now a few assumptions: o all stars have the same absolute magnitude as the sun (4.8) the density of stars is uniform (assume one star per 25 pe3) assume that this ccd image has an exposure time that allows you to see stars with apparent magnitudes of 20 and brighter (a) how far away is the most distant star you see? b) how many stars with magnitude between 19 and 20 do you expect to see in your image? c) how many stars with magnitude between 13 and 14 do you expect to see in your image? (d) make a plot of the luminosity function φ(m) vs m, so that φ(m) shows the number of stars in the frame with magnitude between m an