How can you calculate the power intercepted by a planet from a distant star?

[haki]

Hi,

I found one very interesting physics problem but I have no idea how to solve it.

Lets say we have a star with radius R and the surface temperature T. Now we wish to know, what is the ratio between the total power output of the star and the power that the distant planet receives from that star. The planet has a radius r and the distance between the center of the objects is d. We idealise the problem and say that both object have e=1.

I know that the trick is in the Stefan's law. I can calculate the power output of the star by

P=Stefan's constant*area of a spheare of radius R*temperature of star T on the 4th power,

now the funny thing is how can you calculate how much of that power is intercepted by the planet?

Any help would be apprichiated.

 

[haki]

Got an idea. Maybe the correct way to go is by saying that the ratio

area of a spheare of radius d(distance from the two object) / half the area of the spheare of radius r(radius of the planet) = total output of the sun / power gotten by the planet?

 

[Astronuc]

Assume the power P of the star is isotropic, i.e. same in all directions.

At the distance R from the star, i.e. the radius of the planet's orbit, the flux, \Phi (power per unit area) = P/(4\piR²).

If the planet has radius r, then the fraction of power intercepted is simply the product of the power and the ratio of the areas, or the product of the flux and area subtended by the planet, i.e.

\Phi * \pi\,r^2