The spectrum of reflected light from a planet question.

[BERGXK]

Is the spectrum of reflected light of a planet the same as the spectrum of the star near it but just less in magnitude? Like when you do B(Lambda;T) for it you just multiply that answer by the albedo?

 

[mgb_phys]

No it depends on the surface of the planet and the atmosphere (if any)
eg. Mars and Jupiter appear a lot redder than the sun.

A rocky object like the moon is 'grey' to a first approximation so you can just use the albedo.

 

[BERGXK]

Thanks for the quick reply. I still don't quite get it though. Plancks Spectrum gives an intensity of light at a certain wavelength and temperature right? For a star you can chose the wavelength and calculate the temperature if you assume the star is a blackbody. But how would you do this for a planet? The planet has both emitted and reflected light contributing to its Planck spectrum.

I have a problem on my HW that asks me to compute the brightness of the planet relative to the star at certain wavelenghs 450nm 700nm and 2.2um. It asks me to consider both the starlight reflected off the planet and the backbody light emitted from the planet. When i first started this problem I just did B(lambda;Temp of planet)/B(lambda;Temp of star) for all the wavelengths and compared to see what was higher in each case. But this doesn't take into account the reflected light of the planet right? The reflected light and the emitted differ by a factor of albedo and 1-albedo. So my question is can i just do
((B(lambda;Temp of planet)*(1-a)) * (B(lambda;Temp of star)*a)) / B(lambda;Temp of star) to compare total brightness of planet to that of the star?

 

[mgb_phys]

The blackbody emission from a planet at 300K with a radius of 3000km is pretty insignificant compared to a star at 6000K with a radius of 700,000Km. You can use the Stefan–Boltzmann law to work it out. At the short wavelengths you are given the planet emits hardly anything.

To a simple approximation you can then work out from the solid angle, the fraction of the solar radiation hitting the planet and assume some albedo. You can also approximate the planet to a 2d disc facing the sun.

I was trying to explain why some planets are coloured due to the rock on their surface or the gases in their atmosphere.