Solar radiation?

Question:

The solar energy coming to the earth by radiation is 1340 W/m^2 when the temperature of the sun is 5800 K. If the temperature of the sun deceased by 10% then what would be the amount of solar radiation coming to the earth?

please help, thanks

Answer:
Q-dot / area = watt/m^2 = sigma [ Ts^4 - Te^4]

I = sigma Ts ^4 [1- (Te/Ts)^4]

sigma -Stefan’s constant for radiation losses/gains

It is assumed that sun radiates as perfectly black body with epsilon =1

Also, in comparison to huge temperature of sun (5800 K) small temperatute of earth can be neglected Ts>>Te so [1 – (280/5800)^4] = 0.99999999 = = = 1

I = watt/m^2 = sigma [Ts^4]

I1 = sigma [Ts1]^4
I2 = sigma [Ts2]^4

I2 / I1 = [Ts2/Ts1]^4

I2 = I1 * 0.6561

I2 = 1340 * 0.6561

I2 = 879.174 w/m^2
This is new intensity of solar radiation with 10% cut in sun’s temp.

Solar radiation?

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