
#1
Dec1212, 10:44 PM

P: 2

Hi, I've come across a question that I can't seem to find an equation for anywhere, it seems to exists since I have found mention of it in various papers, but none of them listed it, or at least not in a way I could understand.
The question is to find the radius of a fictional extrasolar planet, and the information we are given includes the bolometric flux of the star, what percentage it decreases by during an eclipse and the distance to the star. My question is: what equation, if any, can help me find the radius of the planet? Note: This question is asking for the planet's radius, not the radius of it's orbit. 



#2
Dec1312, 06:02 AM

P: 550

When a planet transits in front of the stellar disc, it obscures a part of it, which we observe as a reduction in brightness. That reduction is directly proportional to the relative areas of the planetary and stellar discs.
So let's say you observe an (improbable) 50% reduction in brightness during transit. It'd mean the area of the obscuring disc is 50% of the star's. Once you've got the area of a circle it's trivial to get the radius. So, [tex]\frac{L_o}{L}=\frac{A_sA_p}{A_s}[/tex] where L is the star's luminosity L_{o} is the star's luminosity when obscured A_{s} is the stellar disc area A_{p} is the planetary disc area Of course, you need to know the A_{s}. For main sequence stars it can be inferred from the luminosity, as these stars obey luminositymass and massradius relations as explained here: http://www2.astro.psu.edu/users/rbc/a534/lec18.pdf. Otherwise a measurement is in order. 



#3
Dec1312, 05:09 PM

P: 2

Thank you!



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