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The solar constant for the earth is sum....

The solar constant for the earth is `sum`. The surface temperature of the sun is ` T K`. The sum subtends an angle `theta` at the earth :-

A

`S prop T^(4)`

B

`S prop T^(2)`

C

`S prop theta^(2)`

D

`S prop theta`

Text Solution

Verified by Experts

Let R= radius of the sun, d= distance of the earth from the sun.
Power radiated by the sun `=(4 pi R^(2))sigma T^(4)=P`
Energy received per unit areaper second normally on the earth
`=S=P/(4 pi d^(2))=(4piR^(2)sigma T^(4))/(4 pi d^(2))=(sigma T^(4))(R/d)^(2)=1/4 sigma T^(4)((2R)/d)^(2)`
Angle subtended by the sun at the earth `=theta=(2R)/d`
or `S=(sigma)/4 T^(4) theta^(2)`
Hence a and c are correct
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