Question

Suppose that the sun were hotter (and therefore bluer) than it is, so that wavelength of maximum emission were 0.400 um instead of 0475 um. Find the resulting change in the equilibriunm emitting temperature of the Earth, assuming that the albedo stays the same. For simplicity, assume here that the sun's emission obeys Planck's function. Hint: Start by combing equations (6.3) and (6.5) (Petty, 2006) in order to find the ratio of the new solar constant to the present value S. Then use this to derive a simple expression for the new equilibrium temperature as a function of the present value and the two wavelengths.

equation 6.3

2898 μm

equation 6.4 , $\sigma = \widehat}$ stefan boltzman constant

Answer 1

If wavelength of maximum emission is 0.4 $\mu$m then the surface temperature is

2898μ m 2898 7245K 0.4

The intensity of sun received at Earth's distance I =

$\frac{4\pi R_{s}^2\sigma T^4}{4\pi d^2}$

Where d = 1AU =1.496*10¹¹ m, R_S = 6.96*10⁸ m

Therefore I = 3381.364 Wm^-2

_al do

Thus

JUI-albedo. ยู่3381 5671 10-3)-31962K T) 45.67 *10-8 319.62K