Question

Assume (unrealistically) that a TV station acts as a point source broadcasting isotropically at 3.2 MW. What is the intensity of the transmitted signal reaching Proxima Centauri, the star nearest our solar system, 4.3 ly away? (An alien civilization at that distance might be able to watch X Files.) A light-year (ly) is the distance light travels in one year._______W/m2

Answer 1

Answer:

$I=1.5\times10^{-28}W/m^2$

Explanation:

The intensity is related to the power and surface area by $I=\frac{P}{A}=\frac{P}{4\pi r^2}$. We need to calculate the surface area of a sphere of radius r=4.3ly.

Since 4.3ly is the distance light travels in 4.3 years at 299792458m/s, we can obtain it in meters by doing:

$r=vt=(299792458m/s)(4.3\times365\times24\times60\times60s)=4.1\times10^{16}m$

So we have:

$I=\frac{P}{4\pi r^2}=\frac{3.2\times10^6W}{4\pi (4.1\times10^{16}m)^2}=1.5\times10^{-28}W/m^2$