Would it be possible to burn an image on to the surface of the moon?

Lunar soil is made out of rock and dust, with some glasses. Because of this, any laser would have to be powerful enough to heat the sands and other particles such that they melt together. Another option is to vaporize sections of lunar dust, uncovering the color of the rocks below.

Some technical difficulties include the refraction of Earth’s atmosphere, which could bend the laser beam and send it off target. Even though the refraction may only be at a one-degree angle, over the distance of space this results in the laser being off target by a considerable amount. However, we have successfully hit targets on the moon with lasers, such as when we hit a reflector placed by an Apollo mission.

Any laser powerful enough to melt rocks with be powerful enough to melt the laser apparatus that is creating it, unless we find a way to prevent this.

As far as math involved, we would have to be able to calculate the exact distance, location, and velocity of the moon so that we can calculate the correct angle at which to fire the laser.

If the image (when viewed from Earth) is to look correctly, it has to appear as if it were painted on a flat surface. However, the moon is spherical. This would mean that we would have to calculate how to project the image in a way that would counteract the distortion of the moon. The act of projecting the laser actually does some of the math for us. By making the image look correct from Earth, it would look horrendously distorted from lunar orbit.

@PhiNotPi Real nice answer, thanks.

What do you think of the idea of using not so powerful lasers, however have several of them all coordinated to target the same spot?

@poisonedantidote That could work. However, it does bring in an additional difficulty, in that all of the lasers must point at the exact same place.

If you had one very powerful laser that aimed a few feet off target, the result would be unnoticeable from Earth due to the great distances involved. However, if you had two lasers that aimed a few feet off target from each other, the result is that it is possible that no image would be burned at all.

Perhaps if we had a very large number of lasers, that chances are at least enough of them are hitting the target that an image does get burned (actually melted).

Another option it simply pointing the laser at a particular spot for longer. This can only work if the heat is not radiated away too fast so that the temperature can build up to the needed amount. One problem in this is that doubling the exposure time will (probably more than) double the amount of time needed to make the image.

Much easier, I think, to build a team of robotic vandals and ship them to the Moon.

I could just imagine seeing Trump’s mug up there looking at us.

Well there’s skidmarks on uranus.

Me and my friend has this conversation the other day, we think we should emboss our RE teachers face on it.