## Ask Ethan: Why Don’t Gravitational Waves Get Weaker Like The Gravitational Force Does?

“You have stated:

1) The strength of gravity varies with the square of the distance.

2) The strength of gravity waves, as detected by LIGO, varies directly with the distance.

So the question is, how can those two be the same thing?”

Here’s a puzzling fact for you: if you get ten times as far away from a source of gravitational waves, how much less would you expect the signal to be in your gravitational wave detector? For light, brightness falls off as the inverse of the distance squared: it would be 1/100th as bright. For the gravitational force, it also falls off as the inverse of distance squared: 1/100th the force. But for gravitational waves, the signal strength only drops as the inverse of the distance; the signal would be 1/10th the original strength.

(* – special because I had to derive this myself; nobody gives the full explanation anywhere I can find!)