Planet Insolation

Can someone give me a planetary insolation equation that uses the luminosity of the star, and the distance of the planet? I can't find any that make sense. L / d^2 doesn't seem to work either.

Also, what about an equation that takes into account the radius of the star?

I'm not sure if it's what you're asking but a radius relation for the star is that I know for luminosity:


L_Star=(Teff_Star/Teff_Sun) ⁴ x (R_Star/R_Sun)²

Where Teff is effective temperature of the star (Teff_Sun=5870 K) and R is radius (R_Sun=1).

For example, you wanna get Sirius' luminosity:


L_Sirius=(Teff_Sirius/Teff_Sun) ⁴ x (R_Sirius/R_Sun)²

L_Sirius=L_Star=(9940/5780) ⁴ x (1.71)²=25.6 L_Sun


Then, if you wanna also get the habitable zone for the star, you just get the square root of the luminosity and that's all:

HZ_Sirius=√L_Sirius

HZ_Sirius=√25.6= 5 AUs

I'm looking for an equation for planetary insolation (i.e. a measure of how much energy a planet receives from its star, relative to Earth, or measured in watts per square metre).

Sirius_Alpha wrote:

I'm looking for an equation for planetary insolation (i.e. a measure of how much energy a planet receives from its star, relative to Earth, or measured in watts per square metre).

I = L / R^2 (inverse-square law)

I = the insolation. This is equivalent to the sun apparent brightness, i.e. how bright it appears when viewed from the planet.

R = the distance between the planet and the sun.

L = the sun's luminosity, i.e. how much light it gives out.


from Creating an Earthlike Planet:
http://www.cix.co.uk/~morven/worldkit/index.html#astro-sun

If the planet is on an eccentric orbit, the orbit-averaged flux is given by

f = L / (4πa²) * 1/√(1-e²)

where L is luminosity of the star, a is semimajor axis, e is eccentricity, given in SI units - if you are working in units scaled to the Earth/Sun system (i.e. solar luminosity, AU, flux relative to Earth's), you can drop the 4π.

Derivation of the factor involving eccentricity is fairly straightforward but requires somewhat better mathematics rendering than is available here

This formula works too:
I = (r² * sigma * T^4)/d²; where I is the insolation in W/m², r is the radius of the star in meters, T is the temperature of the star in kelvin and d is the semi-major axis in meters.

Bye

Sedna