The Earth receives over all frequency band about 1.5 kW/m^2 of power from the su
ID: 1654877 • Letter: T
Question
The Earth receives over all frequency band about 1.5 kW/m^2 of power from the sun. (a) The Earth-Sun distance is 150 Gm, how long does it take the sunlight to reach the Earth? (b) The Earth radius is 6400 km, what is the total power received by the Earth? (c) Assume the Sun's mass is 2 times 10^30 kg which converts to radiation according to mc^2 at 1 percent efficiency, how long can the Sun radiate at the present level? (d) The Sun radiates 10^-20 w m^-2 Hz^-1 at 3 GHz. Assuming constant power level over 1 GHz bandwidth, what is the Pointing power density and the corresponding electric field amplitude?Explanation / Answer
(a) distance d = 150 Gm = 150 x 109 m
Speed of light c = 3 x 108 m/s
Time required for power to reach from sun to earth
t = d/c = 150/3 x 109-8 s = 500 s
Or t = 8 min 20 seconds
(b) radius of earth = 6400 km
Shadow area of earth = pi x r2
= 3.141529 x (6.4 x 106)2 m3
= 1.285 x 1014 m2
Power density = 1.5 kW/m2
Total power received = 1.285 x 1014 x 1.5 kW = 1.92 x 1014 kW
(c) 1% of mass 2 x 1030 kg = 2 x 1028 kg
Energy E = mc2 = 2 x 1028 x 3 x 108 x 3 x 108 J
= 18 x 1044 J = 18 x 1041 kJ
Present rate = 1.92 x 1014 kW
Hence time = 18/1.92 x 10 27 = 9.32 x 1027 s
(d) as given power density = 10-20 W/m2Hz
For 3 GHz range
Poynting flux = 10-20 x 3 x 109 W/m2
= 3 x 10-11 W/m2
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