Not very fast though – only at a rate of about 3.8 cm per year. Still, this is pretty quick in astronomical terms. But how do we know this? Basically, we put a big reflector on the moon during the Apollo missions, and now we shoot giant lasers at it. We figure out the distance using the following formula:
Distance = (Speed of light × Time taken for light to reflect) / 2.
And voila! The fact that the moon gets .000001% further away every year isn’t particularly worrying at this point, but over millions of years it will definitely have an effect on tidal forces that are caused in part by the moon.