Question

If a star system 30 parsecs distant is found to be broadcasting intelligent radio signals, then their news is already approximately ________ years old.

Answer 1

Answer:

97.85 years, approximately.

Explanation:

Light travels at a constant speed of 186,000 mi/seg or 300,000km/seg accross the Universe (in vacuum conditions). Radio waves are also part of the electromagnetic spectrum, and they also travel at the same speed as Light does.

A light-year is a measure of the distance that Light travels during a year, that is,  5.88 trillion miles. Light travels the same distance per year because its speed is constant, and this is an excellent property that scientists take advantage to measure distances.

A parsec is 3.26 light-years (19 trillion miles), and (a very important datum to solve this question) one light-year is 0.306601 parsec, that is, in a year Light travels 0.306601 parsec at a constant speed. The same would happen with intelligent radio signals broadcasted from a distant star system.

So, considering all these facts, it is a matter of proportions to solve this question (mostly because speed of Light is constant):

$\frac{1 year}{0.306601 parsec} = \frac{X years}{30 parsecs}$

$x =\frac{1 year * 30 parsec}{0.306601 parsec}$

$x = \frac{30}{0.306601} years$

x = 97.84704 years or,

x = 97.85 years, approximately.

In other words, Light spends 97.85 years (terrestials) to travel 30 parsecs.

Likewise, radio waves travel at the same speed, so they spend the same years (97.85 years) travelling across the Universe to be finally detected by a radiotelescope located, for instance, here, in our planet.

Finally,  the star system broadcasted intelligent radio signal with 'news' that are already approximately 97.85 years old'.