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Goldilocks planet

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west - 31 Oct 2005 07:10 GMT
Is there some sort of formula for a planet being in a "Goldilocks" orbit
like Earth?

west
Martin Brown - 31 Oct 2005 10:20 GMT
> Is there some sort of formula for a planet being in a "Goldilocks" orbit
> like Earth?

To first order the zone of habitability as we know it must include the
triple point of water on the planets surface say an average planetary
temperature range of 260-300K.

The incident solar flux per unit area at the Earth's orbit radius r is
proportional to Lsun/r^2 (approx 1kW/m^2).

To get the same incident flux on a planet at radius R with another star
of luminosity L means:

    R = r.sqrt(L/Lsun)

The tolerance band depends on the ability of the planet to lose heat by
radiation which scales as T^4. This suggests that for a viable range of
T 280+-20 (+-7%) you could have a habitable band of r_goldilocks +- 30%
or so.

Ignoring complexities of higher UV emission and very much shorter
lifetimes for the most massive stars. That leaves you with the moderate
mass stars that will live for at least a few billion years.

I guess it would be handy to live in closer orbit around a lower mass
stable slow burning star. Although you do want one that ignites properly
and gets to the main sequence and then stays there.

Regards,
Martin Brown
 
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