In order to project something on the moon to have it visible during a full moon, you'd want the projection to be at least as bright as the sunlight hitting the full moon (about 1 kW per square metre).
In order to have a readable logo you'd probably need it to cover at least, say, 1% of the moon's visible surface area (about 9 million square km).
So that's 9e12 * 1000 * 0.01, or about 9e13 watts, which happens to be about fifty times more power than is produced by all the power plants in the world put together.
It wouldn't have to be visible to the naked eye. For Coke's purposes it would be enough for it to show up in highly magnified photos. And once the logo gets smaller you can project it into the shadow of a crater rim. You'd want to put a small logo next to a crater anyway, since otherwise it wouldn't look moony enough in a magnified shot.
...this feels alarmingly like what I do in my day job.
Hmm. I think they actually had it in mind to have it visible to the naked eye. Imagine a perfectly round, full moon with the coke bottle right in the center. I think that's what they were going for.
Okay, so what about projecting on to a new moon instead? You'd need a lot less brightness; aside from not having to be brighter than the sun, it's naturally darker at night with a new moon...
In order to project something on the moon to have it visible during a full moon, you'd want the projection to be at least as bright as the sunlight hitting the full moon (about 1 kW per square metre).
In order to have a readable logo you'd probably need it to cover at least, say, 1% of the moon's visible surface area (about 9 million square km).
So that's 9e12 * 1000 * 0.01, or about 9e13 watts, which happens to be about fifty times more power than is produced by all the power plants in the world put together.
So I'm thinking that's a no.