Lasers, space, ET and long-distance communication oh my!

So the other day the article 'No extraterrestrial laser pulses detected from KIC 8462852, SETI reports' came out and I got a little curious about how wide a laser's beam would be by the time it got here. 

First we need to figure out how quickly a laser spreads as it travels a distance, fortunately someone else already did this work. The Lunar Laser Ranging experiment let's me know that a laser shined from earth is about 6.5 kilometers wide.

  • IC 8462852 is approximately 454 parsecs from Earth
  • The moon is about 238,900 miles from Earth
  • A parsec is 19,173,511,600,000 miles
  • 1 parsec is 80257478.4429 x farther than the moon
  • KIC 8462852 about 36,436,895,213.1 farther than the mooon

So a beam from a laser similar to the on used for the Lunar Laser Ranging Experiment, sent at us from something 454 parsecs away would be something like 236,839,818,885 km wide/147,165,440,629.8467 miles wide. Or 1 parsec away would be 521,673,609.879 km wide/324,152,952.929.

That means the beam from that a hypothetical laser from KIC 8462852 would be 1583.1x wider than the distance from the earth to the sun by the time it got to us!

Ahem. But wait, there's more!

Let's take something from my problem with time travel, the fact that the Earth is moving through the solar system, the solar system through the galaxy and the galaxy through the universe, essentially in different directions. 

Ok so 1 parsec is 3.26156 light years, and that system is about 454 parsecs away meaning that light has been traveling about 1481 years to get to us which means our solar system has moved 557,863,080,000 miles through our galaxy in the 1481 years since the hypothetical laser left KIC 8462852, which means if it was truly aimed at us they'd have to be thinking where we'd be in 1481 years as light travels straight (ignoring very large gravity sources curving it) and wouldn't be rotating around the galaxy. There's likely also some variation in speed of our star and KIC 8462852 traveling through our galaxy.