How does the radius of a star affect the temperature of a planet orbiting it?

[FunkyDwarf]

Hey guys,

Quick question:

Homework Statement

Assume the planet (from a previous question) is a perfect black body and that the only source of energy is the [neutron] star. Derive an expression for the temperature of the planet as a function of the orbit distance, star temperature and star radius.

Homework Equations

Inverse square law (I1/I2)=(d2/d1)^2
I = sT^4 (s = stefan boltzman)

The Attempt at a Solution

Ok now i know how to work out watts per m^2 at a distance, that's cool, but in terms of temperature do we really need the star radius? I did the following. I worked out the intensity at the planet distance and converted that to a temperature, but that only depended on the intial distance and the orbit distance, not star radius, unless they suppose that the former is the star radius which doesn't make sense unless we treat the source of energy as the centre of the star.

Any thoughts?

Cheers
-G

 

[Chi Meson]

A constant surface temperature would give a constant Intensity of emission at the surface, regardless of the radius of the star. The difference is that the intensity diminishes from this initial intensity as the radius goes from the radius of the star to the radius of orbit of the planet. If the orbital radius is much much bigger than the radius of the star, this becomes an insignificant difference, but it still can put into the formula.

 

[FunkyDwarf]

Sorry I am not sure i understand how the radius of the star comes into it. the only thing is intuitively if you have a larger star, at the same distance, with the same temp you're outputting more power so you'd think the planet would be hotter