July 26, 2013

## What is the brightness (B) of polaris, in watts per square meter, as observed from earth?

The north star (Polaris) is 4.1X10^18 meters away from Earth and has a luminosity (L) of 8.7 X10^29 watts. Ignoring the effects of the atmosphere what is the brightness (B) of polaris, in watts per square meter, as observed from earth?

OK! This looks like a challenging one, so I am going to have to sharpen my pencil, roll up my sleeves, get my good pair of scissors out (since i like to cut and paste), & put on my hard thinking cap on

concerning a star’s brightness, i normally describe it in terms of magnitude. Nonetheless, apparently it is fairly easy to measure a celestial object’s brightness or its luminosity, as observed from the earth with CCDs and other analytical instrumentations one can find in any astro-laboratory. But let’s pretend just for one moment that those instruments are not available. Based on the data you provided, i can use a well-known relation in order to answer your Q:
Luminosity of Polaris (L) = Apparent brightness of Polaris (B) (4pi) distance of Polaris from earth (D)^2
are you following any of this?
So brightness in terms of Watts per meter squared is 8.7×10^29 W/(12.57)(4.1×10^18 m)^2 or approximately 4.12 nW/ m^2
=P