[TML] Habitable Zones

[Timothy Little]

On Sat, Nov 10, 2007 at 12:27:44AM +1100, Tim Rattray wrote:
>   L = 4 pi r^2 sigma T^4
> 
> where L is the star's luminosity, r is the distance from the center of
> the star, sigma is the Stefan-Boltzmann constant (= 5.67 x 10^ -8 W m-2
> K-1), and T is the effective temperature (in Kelvin)

The Stefan-Boltzmann constant needs to have T^-4 in the units, not
T^-1.  This would have made it much easier to work out the answer to
your following question:


> Question is, what is L measured in?  (r is in meters)

The units for L are obtained by just combining the units on the right
hand side.  Using [] to mean "units of":
 [L] = [m^2] [W m^-2 K^-4] [K^4]
     = [W]
So L is in watts.

As a standard of comparison, our sun's luminosity is estimated to be
3.83 x 10^26 W based on the mean solar constant at Earth orbit,
1366 W/m^2.


- Tim