Planet Insolation

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Planet Insolation

Post by Sirius_Alpha on 2nd May 2009, 10:27 pm

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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Re: Planet Insolation

Post by Edasich on 3rd May 2009, 7:00 am

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
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Re: Planet Insolation

Post by Sirius_Alpha on 3rd May 2009, 11:42 am

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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Re: Planet Insolation

Post by jbjerk on 19th November 2009, 4:01 pm

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
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Re: Planet Insolation

Post by Lazarus on 19th November 2009, 5:03 pm

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 Sad


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)
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Re: Planet Insolation

Post by Sedna on 20th November 2009, 4:57 pm

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

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