Planet Temperatures in multiple star systems?

Evil Dr Ganymede · Post #1by **Evil Dr Ganymede** » 07.09.2003, 23:38

Hopefully this will be easier to answer than my atmospheres questions...

I'm wondering how one can calculate blackbody temperatures for planets in multiple star systems. I know the BB temperature equation is:

Tb = [278.3 * (L^0.25)]/(D^0.5)

(where L is luminosity in Sols, D is distance in AU). But how do you incorporate the effect of another star at a varying distance in there? It's definitely not just a case of calculating separate Tb's using the L and D of each star and adding the results together. And I don't think it's a case of adding or averaging the L and D values before taking the roots...

Let's say we have a planet orbiting an G2 V star (luminosity: 1 sol) at 1 AU, with a K0V star (luminosity: 0.3 Sols) orbiting the G2V at 5 AU (I think that's stable...). So the K0V companion varies between 4 and 6 AU from the planet. How do I determine by how much the companion raises the BB temperature of the planet?

Any ideas?

Post #2by **granthutchison** » 08.09.2003, 00:36

You need to be able to add the radiant fluxes from the two stars before converting to temperature. Recast your equation by raising both sides to the power 4:

"Flux" = 278.3^4 * L / D^2

Plug in L and D for your central star. Do the same for your companion at max distance. Add the two results together. Then take the fourth root of the total to convert back to temperature. Now do the same thing again, this time with your companion at minimum distance. You now have a temperature range for your orbiting body.

(I've put "flux" in inverted commas there because it's really flux over sigma - but the sigma cancels out as you convert back and forth, so there's no point in having it in the first place ...)

I make it 278.9 to 279.6K, which seems reasonable, since the added energy from the K-type is only 1% of the flux from the central star. The temperature of the planet only needs to increase by 0.2% to compensate for that.

Grant

Evil Dr Ganymede · Post #3by **Evil Dr Ganymede** » 08.09.2003, 02:07

Bonzer. I was just perplexed about what to do with the varying distance... Thanks again!

ajtribick · Post #4by **ajtribick** » 08.09.2003, 20:47

If there were three stars would I just have to add up the to-the-fourth equation results and fourth-root just like the two-stars situation?

Post #5by **granthutchison** » 08.09.2003, 22:21

chaos syndrome wrote:If there were three stars would I just have to add up the to-the-fourth equation results and fourth-root just like the two-stars situation?

Yes.

Grant