Temperature derived from ratio of blackbody radiation

[xSilja]

Homework Statement

Show that 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).

Hint:
Remember that the quantity we measure is a flux on the surface of Earth. This will depend on (omega) and distance of a star. Flux in the formula for Stefan-Boltzmann's law is the flux on the surface of a star.

This problem is from Astrophysics In A Nutshell by Dan Maoz.

Homework Equations

$F=σT^4$

The Attempt at a Solution

No clue. It seems like no matter how I do ratios the temperature cancels out.

 

[Simon Bridge]

You only have Stephan-Boltzmann's law there - you also need to factor in the distance to the star (see "hint") and the formula for blackbody radiation (from main question).