Re: Habitability of Gliese 876c & d



Logan Kearsley wrote:

figure out the angle of a line tangent to both the surface
of  the sun and the planet, and use that to calculate
exactly what fraction of the planet is lit at once


  Yep, but you also have to account for the angle of incidence, which
now will vary in quite a complex way across the lit
more-than-a-hemisphere. It's usually that point at which I throw up
hands and go back to doing something productive :-).



Maybe I'll ask a mathematics professor about it. Oughtn't you be able to
simply figure out the average angle of incidence and use that to get the
average temperature?

Dandelin spheres are a good model to use when thinking of insolation of a planet
http://clowder.net/hop/Dandelin/Dandelin.html
http://en.wikipedia.org/wiki/Dandelin_spheres

Two discrete spheres (in this case sun and planet) generally define two tangent cones.

What I call "the fat cone" forms an hour glass between star and planet. Any point on the part of the planet within this hourglass can see the entire star. That is, the sun is completely above the horizon.

What I call "the thin cone" connects star and planet with a lamp shade.
Any point on the planet within the lamp shade can see at least part of the sun.

A viewer outside of the hour glass but within the lamp shade will be viewing a sunrise or sunset. He can see part of the sun but part is concealed by the planet's horizon. I'll call this the sunrise/sunset band.

The insolation of the planet within the hour glass isn't hard to figure. You find the solid angle it subtends as seen from the star's center, call this solid angle a. Insolation = a/(4 pi steradians) * star's total output.

However the insolation of the sunrise/sunset band is harder. I still haven't thought of a way to do this.





--
Hop David
http://clowder.net/hop/index.html

.

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