Planet Insolation

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?

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Sirius_Alpha

Number of posts : 3658
Location : Earth
Registration date : 2008-04-06

Re: Planet Insolation

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

LStar=(TeffStar/TeffSun) 4 x (RStar/RSun)2

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

For example, you wanna get Sirius' luminosity:

LSirius=(TeffSirius/TeffSun) 4 x (RSirius/RSun)2

LSirius=LStar=(9940/5780) 4 x (1.71)2=25.6 LSun

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:

HZSirius=LSirius

HZSirius=25.6= 5 AUs

Edasich
dM star

Number of posts : 1545
Location : Tau Ceti g - Mid Latitudes
Registration date : 2008-06-02

Re: Planet Insolation

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).

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Sirius_Alpha

Number of posts : 3658
Location : Earth
Registration date : 2008-04-06

Re: Planet Insolation

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

jbjerk
Micrometeorite

Number of posts : 13
Registration date : 2009-11-19

Re: Planet Insolation

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

Last edited by Lazarus on 20th November 2009, 6:44 pm; edited 2 times in total (Reason for editing : oops dropped a factor of 4pi)

Lazarus
dF star

Number of posts : 2979
Registration date : 2008-06-12

Re: Planet Insolation

This formula works too:
I = (rē * sigma * T^4)/dē; where I is the insolation in W/mē, 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

Sedna
Planetary Embryo

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