Ads on the moon?

So I was twittering about this company that claims to want to put advertising on the moon by imprinting patterns in the lunar dust with a rover of some sort. At first I was just shocked and/or pissed that anyone would think this was a good idea. But then I started thinking about whether such an idea was even possible. After all, for something to be visible to the naked eye on the moon, it's got to be really big. For example, the Mare Crisium is a basin on the moon that's usually visible to the naked eye, and it's 176,000 sq. km.

So just how big would we be talking here? Let’s do a little calculation...

Here are some basic data:

• A 9 x 9 pixel grid is the minimum size needed to accommodate all roman characters.
• The surface of the moon is about 376,351,000 meters from the earth’s surface.
• Human visual resolution (assuming 20/20 vision) is 60 arcseconds. The Hubble’s resolution is 0.05 arcseconds, for comparison).

So, what we’ll want to answer is, how big would a pixel have to be on the moon for someone to see it? Then multiply that area by nine to get an idea of the area we’d have to work in to display a single letter.

Firstly, an object really needs to be twice the theoretical size to be properly resolved, so that means we’ll put the working human visual resolution at 120 arcseconds.
The formula to determine the angular size of an object based on it’s physical size and distance is pretty simple:

	d/D x 206265 = α

So now we just do some simple algebra,solving for d:

	d/376,351,000 x 206265 = 120

In this case d = 218,951 meters or about 219km. That means a person could, theoretically, be able to see a spot on the moon if it was 219 kilometers in diameter. (FWIW, the smallest thing on the moon the HST can see is 96.1 meters, and the human eye's resolution is far lower). So multiply our 219km pixel by 9 and you get 1971 km. In other words a letter would have to be 1971 km tall to be visible to the naked eye and distinguishable as a letter rather than a dot. How long would it take to imprint a letter that big? (By comparison the total surface area of the moon is 3.793 × 10^7 km)

The web site claims a pattern would be made with the raised tread of lunar rover wheels. The lunar rover used by the Apollo missions was 2.3 meters wide, so, assuming the rover could travel at 50 kilometers per hour (again, being extremely optimistic in imaging a fast rover that doesn't exist yet) then:

219km/50 = 4.4 hours to travel the hieght of the letter.

Now let's assume the letter is equally wide:

219,000m/2.3 m = 95217 trips 

That means:

95217 * 4.4 = 418,956 hours

Or 49 years. For a letter. I think this project is bogus, or a hoax. That said, I did these calculations pretty fast, so if you see a mistake, let me know.

EDIT: 49 years is probably not fair, because that's how long it would take to fill an entire letter grid. But of course a letter is not going to fill the whole grid. Let's say, on average, a roman character occupies 50% of it's grid space. That's still 25 years. And that's not accounting for the complex pathways that would need to be calculated for the rover to render the letter which would assuredly involve the rover going over the same area twice in some cases.

EDIT: I edited this post a bit more for clairty and added some additional links.