Consider a hypothetical planet of temperature Tp surrounded by an extensive atmosphere of temperature Ta, where Ta < Tp. The atmosphere absorbs in a narrow spectral line; its absorption coefficient is large at frequency o and very small at other frequencies, such as V: ava. The planet is observed at frequencies and . Assume and are close enough together that the Planck function does not change much between them. a) When observing at the center of the planet's disk, at which frequency, v or V, is the brightness temperature higher? Is the same true when observing near the limb, where the limb is defined as the atmosphere beyond the outer edge of the solid planet's disk? Make a sketch of the "observed" spectra. b) Repeat part (a) in the case that Ta > Tp.