Question

The light at the Earth from a certain star has an intensity of about 22×10^-8W/m². If the star emits radiation with the same power as our Sun, how far away is it from Earth? NOTE: Use 1000 W/m^2 as the intensity of the Sun at the Earth!

Answer 1

Intensity=power/area => power=intensity*area

Now, for spherical waveforms, area=4r2 , where r is the distance between source and the point where intensity is being calculated.

In the given problem, power for both the systems is same.

So,I1*A1 =I2*A2 , where I1 is intensity due to star, I2 is intensity due to sun, A1 is area for the star, while A2 is area for the sun.

So, I1*(4r1*r1) =I2*(4r2*r2)

=> I1*r1*r1 =I2*r2*r2

Here,I1 = 22×10-8W/m2 , I2 = 1000 W/m2, r2 = distance between earth and sun = 150.5 * 106 km = 150.5*109 m.

So, 22×10-8 *r1*r1 = 1000*150.5*109*150.5*109

=>r1^2 = 1000*150.5*109*150.5*109/( 22×10-8) = 1.0295568*1032

=>r1 = 1.01467 *1016 m.

So,required distance = 1.014*1016 m