Imagine you are trying to detect a Jupiter-like planet located 7.5E11 m from a Sun-like star. At what wavelength is the peak of the planet's Planck blackbody intensity function (assume the planet is a perfect blackbody)?
Radius of Planet r = 7E7 m
Radius of Star R = 7E8 m
Temp of Star = 5800 k
Luminosity of Star = 3.8E26 J/s
Stefan-Boltzman law j = σT^4
Total Incident Flux (σ T^4 r^2) /distance^2
The Attempt at a Solution
Now, my professor gave me the equation for Stefan's law. He then gave us the task of determining the incident flux upon the planet given by the star on the planet. If the planet is a perfect black body, then the planet will absorb and then emit all this energy. I can go through the steps to show you how I determined the Total Incident Flux equation. But I believe that it's correct.
The problem I am having now is how to change this emission to a wavelength. I feel like I need a nudge in the right direction. Do I need to rearrange Planck's law and solve for wavelength at the temperature of the planet?