Respuesta :
Answer:
4.34 K
Explanation:
The % is not given by usually by January the solar flux varies from 3.2 to 3.5%. We can take 3.4% as a good estimate for this case.
The solar flux S, arriving at the outer edge of the atmosphere, is represented by the solar constant of [tex]1370 W/m^2[/tex] . We are assuming that the solar flux varies by ±3.4 percent as the earth moves in its orbit. If we do the operation 1370*0.034=46.58, then the margin for the solar flux would be [tex]Solar flux =1370 \pm 46.58 W/m^2[/tex] .
From theory we have an expression for the energy absorbed by Earth and is given by [tex] S\pi R^2 (1-\alpha)[/tex] and we have also a formula for the energy radiated back to space by earth given by [tex]4\sigma \piR^2 T^4[/tex], according to the Stefan-Boltzmann Law.
For this case the energy absorbed by Earth needs to be equals the energy radiated back to space since we assume a balance of energy, so we can set equal the two quantities of energy like this:
[tex]S\pi R^2 (1-\alpha)=4\sigma \piR^2 T^4[/tex].
And if we solve for the temperature we have this:
[tex]T=[\frac{S(1-\alpha)}{4\sigma}]^{1/4}[/tex]
We need to do another ssumptions for example the average albedo for Earth constant, [tex]\alpha=0.3[/tex]. The Stefan-Boltzmann Constant is  [tex]\sigma=5.67x10^{-8}W/(m^2 K^4)[/tex]. Â
Since we have a variation [tex]S=1370\pm 46.58 W/m^2[/tex] we can do operations in order to find the possible change of temperature, like this:
[tex]T=[\frac{1323.42W/m^2(1-0.3)}{4*5.67x10^{-8}W/(m^2 K^4)}]^{1/4}=252.806 K[/tex]
[tex]T=[\frac{1416.58W/m^2(1-0.3)}{4*5.67x10^{-8}W/(m^2 K^4)}]^{1/4}=257.143 K[/tex]
So the possible variation on this case is 257.143-252.806 K=4.34 K
