Dear 100 Hour Board,
If the moon were made of cheese, how much milk would it take to produce that quantity of cheese?
Dear Mr. Morton,
Oh boy, am I excited for this. I've kept myself and the other writers waiting on this answer for the past 97 hours, so let's get right to it!
First of all, there are a couple of different ways to interpret your question. When you say "that quantity", do you mean the mass of the moon or the volume of the moon? Well, I'm going to answer both of those questions. Also, what kind of cheese? When someone says that the moon is made of cheese, most people think of Swiss cheese, because of the holes, but there are so many different types of Swiss cheeses, so I'm going to pick Emmentaler, which is the cheese that most "Swiss cheese" is modeled after.
The mass of the moon (according to Google) is 7.34767309 x 1022 kg. According to Fundamentals of Cheese Science, you can get somewhere between 9 kg and 12 kg of Emmentaler cheese for every 100 kg of milk. If we pick the midpoint of those numbers, that's 10.5 kg of cheese for every 100 kg of milk. If we divide the mass of the moon by that ratio, we get 6.99778390 x 1023 kg of milk. The density of milk is approximately 1.03 kg/L, and there are 3.78541 liters in a gallon, so that is equivalent to 1.7947765 x 1023 gallons. In standard notation, just for emphasis, that's 179,477,650,000,000,000,000,000 gallons of milk.
The volume of the moon will take less cheese, but the calculations will be slightly more complicated, so bear with me. The volume of the moon is 2.197 x 1022 L. The density of Swiss cheese happens to be pretty close to the same as that of milk, 1.03 kg/L, so we can convert our 10.5 kg cheese/100 kg milk factor to 10.5 L cheese/100 L milk. So it takes 2.092381 x 1023 L (5.5274883 x 1022 gallons) of milk to make a ball of Swiss cheese the size of the moon, right? Well, no. See, the whole point of Swiss cheese is that it has holes, and I haven't factored in the porosity of the cheese. Some scientists measured the volume of the holes (technically called eyes) in Emmentaler cheese using CT scans and found that the relative eye volume cheese with the strongest eye formation was about 3.47%. So, since Swiss cheese is only about 96.53% cheese, we'll factor that into our calculated volume and get 2.019775 x 1023 L (5.3356845 x 1022 gallons) of milk.
Finally, let's put this into perspective. The Holstein is the highest-producing dairy cattle in the world. Every year, the average Holstein cow produces 2674 gallons of milk per year, and most of the more than 9 million dairy cows in the United States are Holsteins. It would take all the cows in the USA more than 2 trillion years to make enough milk to make a ball of Swiss cheese the size of the moon, and over 7 trillion years (more than half the age of the universe so far) to make enough milk to make a ball of Swiss cheese with the same mass as the moon.