Question

The earliest radio broadcasts on Earth were emitted about 100 years ago. Approximately where are these initial radio waves now? (Radio waves are a type of radiation, so they travel at the speed of light)

Answer 1

Answer:

100 ly are $d=9.454255\times10^{17}m$

Explanation:

The speed of light is, by definition (we define this and derive a definition of distance from there nowadays), c=299792458m/s. We want to know, at this speed, how much distance the radio signals travel in 100 years. Since each year has 365 days (not a leap one though), each day has 24 hours, each hour has 60 minutes and each minute has 60 seconds, the number of seconds in a year will be (365)(24)(60)(60)=31536000, so the distance traveled by the waves in 100 years will be:

$d=vt=(299792458m/s)(100)(31536000s)=9.454255\times10^{17}m$, which, of course, are 100 light years.