Why would the spectral analysis take a long time? Once the light hits the sensor array, characterization of the spectra should be done in seconds, I would think. A reading of the total EM spectra for the objects should quickly reveal atmospheric or other elemental composition, temperature and other interactions with the system's star. With a starship the size of a large building, even imaging the planets to get a quick measure of size and distance shouldn't take long at all, in my opinion.
"In the nightgown of the sullen moon, How the windows lean into the room, In the nightgown of the sullen moon."
-They Might Be Giants