Gliese 581c is the first Earth-like extrasolar terrestrial planet discovered. It

Question

Gliese 581c is the first Earth-like extrasolar terrestrial planet discovered. Its parent star, Gliese 581, is a red dwarf that radiates electromagnetic waves with poser 5.00x10^24W, which is only 1.30% of the power of the Sun. Assume the emissivity of the planet is equal for infrared and for visible light and the planet has a uniform surface temperature. Identify (a) the projected area over which the planet absorbs light from Gliese 581 and (b)the radiating area of the planet. (c) If an average temperature of 287K is necessary for life to exist on Gliese 581c, what should the radius of the planet's orbit be?

Explanation / Answer

(a) projected area of the planet absorbs light from Glise = r^2 Here r = radius of the planet (b) The radiating surface area of the plannet = 4r^2   (c) The intensity rcieved by the plannet   I_in   = Power / 4R^2 .............(1) here R = distance between the plannet and the star at steady state P_ in   = P _ out e * I_in * (r^2) = e(4r^2) *T^4 Here e = emmissivity   = Stefan's boltz mann constant   = 5.67*10^-8   W / m^2 . K^4 I_in = 4T^4 ...............(2) From equation (1) and (2) Power / 4R^2 = 4T^4 R   = sqrt ( P / 16T^4 ) Temperature = 287 K power = 5.0*10^24 W plug the all values we get   the radius of the orbit R = 1.6 * 10^10 m

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