Finding an Extrasolar Planet's Radius

[crocvox]

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.

 

[Bandersnatch]

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,

$$\frac{L_o}{L}=\frac{A_s-A_p}{A_s}$$

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 luminosity-mass and mass-radius relations as explained here: http://www2.astro.psu.edu/users/rbc/a534/lec18.pdf.
Otherwise a measurement is in order.

 

[crocvox]

Thank you!