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As the legend goes, Coca-Cola was planning on shooting lasers at the moon to project their logo. Unfortunately, the FFA said no (they didn't want planes to be blinded). I haven't been able to confirm or deny this specific legend.

My question though, is it feasible? Could you project a logo on the moon such that you can see it on the ground? How much would such a project cost?

We'll say that 10% of the moon's surface should have the logo, and be fairly visible from earth. Color is unimportant.

Is moonvertising feasible?

Note: I am not talking about etching anything in the moon. The moonvertising would only be active why the lasers are shining. It's basically a high power projector.

Note: Moonvertising during new or crescent moon is allowed.

Note: Here is a clickable picture of two dots being projected on the moon.

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This question asks for hard science. All answers to this question should be backed up by equations, empirical evidence, scientific papers, other citations, etc. Answers that do not satisfy this requirement might be removed. See the tag description for more information.

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    $\begingroup$ Related: worldbuilding.stackexchange.com/questions/26791/… $\endgroup$ – Mark Nov 11 '15 at 0:34
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    $\begingroup$ Arthur Clarke wrote a short story in 1956 called "Watch This Space". In the story a canister of gaseous sodium was to be opened on the moon as part of a science experiment. Only someone unofficially placed a stencil over the outlet, causing it to form a giant logo for a famous soft drink. $\endgroup$ – Howard Miller Nov 11 '15 at 0:42
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    $\begingroup$ Lunar Orbiter Laser Altimeter and a bit of imagination and tons of $$$$$ $\endgroup$ – user6760 Nov 11 '15 at 1:40
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    $\begingroup$ Your answer: what-if.xkcd.com/13 $\endgroup$ – FraserOfSmeg Nov 11 '15 at 3:50
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    $\begingroup$ Your description of the picture is wrong. It is a picture of the earth taken from the moon of two 2MW lasers shined at the moon. The article notes that the laser were as bright as a first magnitude star. $\endgroup$ – Gary Walker Nov 11 '15 at 14:25
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If the laser's on earth, just about impossible due to the atmosphere messing with your lasers, causing them to bloom terribly. This would make the projection on the moon be a blurry spot larger than the moon itself.
If in space, that goes away but you're left with the projection needing to be large enough that when the reflected light reaches earth it's still distinguishable as more than a bright dot on the surface. That means it needs to be projected to a size roughly the size of one of the larger mares on the moon. Technically feasible I guess, but the power requirements to make something that big that far away and have it bright enough that it reflects back to earth bright enough to be visible with the naked eye would be massive, probably so much so that even were it technically feasible to create a satellite large enough to contain the laser banks and their power source it'd be prohibitively expensive, especially considering the estimated return on investment in added sales of the product being advertised.

A more realistic scenario would have said laser be positioned in a high orbit around the earth and project its messages onto the planet through a series of blinds and stencils. If the radiation can be used to excite inert gasses in the upper atmosphere you could even create something that stays visible for some time after turning the lasers off again.
Of course aviation authorities, environmental agencies, and owners of other objects in orbit aren't going to like you. It's going to play havoc with all kind of equipment, think what happens when there's a major outbreak of solar flares causing disruption of the atmosphere...

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Painting the moon with lasers wouldn't work, as the light of the sun would overwhelm just about anything, the power needed would be prohibitive, it would only work for short amounts of time while the moon is in the sky while it's dark and in range of the laser, etc.

They'd be better off putting up a space billboard, as it would be cheaper, work during the day, and depending on what orbit it is in you could get global visibility. Everyone would hate it, but there's no such thing as bad publicity!

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