A. Show that, if the ratio of the blackbody fluxes from a star at two different frequencies (i. e., a "color") is measured, then, in principle, the surface temperature of the star can be derived, even if the star’s solid angle on the sky is unknown (e. g., if it is too distant to be spatially resolved, and its distance and surface area are both unknown).

b. Explain why it will be hard, in practice, to derive the temperature measurement if both frequencies are on the Rayleigh-Jeans side of the blackbody curve, hν >> kT.

c. For the case that both measurements are on the Wien tail of the blackbody curve, hν >> kT, derive a simple, approximate, expression for the temperature as a function of the two frequencies and of the flux ratio at the two frequencies.

d. If, in addition to the flux ratio in (c), a parallax measurement and the total flux (integrated over all frequencies) at Earth are available, show that the star’s radius can be derived.