A Star's Power Output at 11 Light Years Away?

[cattons3]

1. A star at a distance of 11 light years from the Earth provides us with a power per unit area of 1.7x10^-12 W m^-2. Calculate the power output of the star.



2. 1ly=9.4608x^15 m therefore 11ly=1.040688x10^17 m



3. How do you work it through? I've never understood these questions involving power per unit area and over a distance :/

Thanks in advance.

 

[gneill]

Assume that the star's energy is being radiated uniformly in all directions. If you were to draw a Gaussian surface around the star, it would intercept all of the star's energy. Note that it wouldn't matter at what distance the surface was drawn, it would intercept all of the star's radiated energy.

Now, suppose that Gaussian surface was a sphere centered on the star with the Earth located on that Gaussian surface. You're told that 1 square meter of that Gaussian surface intercepts a power of 1.7 x 10^-12 W. How much would the whole sphere intercept?

 

[cattons3]

Thanks very much i haven't come across the term 'Gaussian surface' before but i completely understand now.

If you take the distance between the star and the Earth as the radius of the sphere and calculate its surface area, then one square meter is receiving 1.7x10^-12 Watts of power so overall the star has a power of 1.7x10^-12 times by the surface area to provide that amount of power per square meter.

cheers