There are two components to this calculation. First, the apparent magnitude of the full moon is about -12, while the sun is about -26.7.

The difference is then about 14 magnitudes, or a brightness ratio of 1 million.

Second, the moon may not reflect UV as efficiently as other wavelengths.

I have no data on this, but for simplicity, I will assume it is the same.

So, 1 second of sunlight will be equivalent to ~250 hours of moonlight.

I doubt if even albino vampires need to worry

Mike is correct as far as he takes it, and he correctly points out that one needs to know the moon's reflectivity (albedo) at ultraviolet wavelengths as well.

Not surprisingly, the moon reflects UV even more poorly than visible light (most things do!) However, there are complications. Firstly, what we call UV covers a much wider range of wavelengths than visible light (roughly four octaves rather than one, if I remember correctly), and not all wavelengths refect equally well from the moon. In fact, the longer wavelengths reflect more poorly, so one might say that the moon seen in UV would look a gloomy blue. (That is a tenuous argument, but I am just trying to convey a point by analogy!)

Now, our atmosphere lets in long-wave UV (UVA) fairly freely, medium wave (UVB) pretty stingily, and short wave (UVC, or "vacuum UV) hardly at all, ozone layer or no ozone layer. However, the shorter the wavelength, the more energetic and damaging the UV to living things. Loosely speaking UVA plays an important role in tanning, UVB plays an important role in sunburn, and UVC we usually encounter only in dangerous radiation from the likes of arc welding and germicidal lamps.

So the wavelenths that we use in tanning, the moon redirects towards us only about one tenth as generously as white light, and what it reflects of the rest doesn't get through our sky anyway.

And as for the phases of the moon...! Done much New-Moon tanning lately?

I reckon that a baby exposed to as much moonlight as possible would die of old age before getting the equivalent of a ten-minute tan. And without proper levels of vitamin D in the diet, it would never survive to old age in the first place.

Cheers,  

Jon

The moon and the earth are the same distance from the sun, the discrepancy is about 0.25%, so we may say that the earth and the moon recieve the same amount of light per square meter. Half the moon's surface area (what we see on a full moon) is about 10 trillion square meters, roughly 10% of the light hitting the moon is reflected so about 1 trillion times more light is reflected by the moon than is recived by 1 square meter of the earth on a sunny day! However, the moon is a very long way away (382million meters) and so the proportion of this that actually reaches the earth is tiny (it falls off with the square of the distance). By my reaconning the brightness of the light from the moon is in the magnitude of 1 million times less than the light from the sun, so your anwer is that moon light will probably not sustain your vitamin D levels unless you are able to spend (by the questioner's recomendations for sunlight) 10-60 thousand hours a day in the moon light.

The full moon is 500,000 times fainter than the sun.