## Would you pay \$70,000 for a lunar vacation?

Wednesday, January 3rd, 2018

Would you pay \$70,000 for a lunar vacation? That’s what Andy Weir estimates it’ll cost — eventually, in the 2080s, when Artemis takes place. Here are his key points, edited down:

The cheapest way to get mass to LEO (at the time of this writing) is with a SpaceX Falcon 9 booster. They charge \$61.2 million for the launch, and it can put 13,150kg of mass into LEO. So right now, that means it costs \$4,653 per kilogram.

The commercial space industry, through competition and engineering advances, will settle down to the same fuel-to-overhead ratio as the modern airline industry.

For each flight, I noted the price of each class of ticket, then worked out the take — the total amount of money the airline gets if every seat on the plane is sold at its listed cost. The fuel consumed is based on the flight duration and the fuel consumption rate of the aircraft. The cost of that fuel is based on the market price of jet fuel on the day I looked up those tickets, which was \$0.475/kg. (Actually, the price was 38 cents per liter, but I wanted price per kg and jet fuel has a density of 0.8kg/L). [...] So for the rest of this paper I’ll assume a commercial airline spends 16.5% of its take on fuel.

A passenger spacecraft would weigh the same as a passenger aircraft capable of carrying the same number of people.

The commercial space industry will use hydrogen-oxygen fuel.

The thing that matters most about rocket fuel is a property called “specific impulse.” I don’t want to bore you with physics (I’m here to bore you with economics) so I’ll just say this: specific impulse is a measure of how efficient a rocket fuel is. The higher a fuel’s specific impulse, the less of it you need to get a ship moving a given velocity. And hydrogen-oxygen fuel has the best specific impulse known. Also, it creates water as its exhaust, so there are no pollutants. And finally, it’s cheap to produce.

Right now, there are engineering limitations to using hydrogen-oxygen fuel. The main one being that it burns very hot — hotter than any engine can handle. But again, I’m assuming all these challenges get researched and solved by a profit-hungry industry.

The final piece of the puzzle is the cost of hydrogen and oxygen. This was a little harder to find. I was able to find reliable data on the 2002 price of bulk hydrogen, so I adjusted the 2002 dollars into 2015 dollars and got \$0.93/kg. As for oxygen, I used the publicly available data on what NASA pays for it — \$0.16/kg in 2015 dollars. The reaction requires one part hydrogen and eight parts oxygen (by mass), so the total fuel cost is \$0.245/kg.

Okay, we have a ship that weighs 165,500kg and we’re going to put 550 passengers on it. We’ll give them 100kg each for their bodies and luggage. That’s a total mass of 215,500kg.

The specific impulse of hydrogen-oxygen fuel is 389s (yes, the unit for measuring specific impulse is “seconds”. It makes no intuitive sense, just roll with it). To get to LEO you need to accelerate by 9,800m/s. LEO actually only requires 7,800m/s, but you lose around 2,000m/s during the ascent to air resistance and other inefficiencies.

Again, I’m skipping over the physics (Tsiolkovsky’s Rocket Equation, if you’re curious) but those numbers mean we’ll need 12.04kg of fuel for every 1kg we want to put into LEO. We want to put 215,000kg into LEO, so we need 2,594,620kg of fuel.

At our calculated fuel cost (\$0.245/kg) that means the total fuel cost for the launch is \$637,200.

Now I get to use my airline fuel overhead figure. Airlines have 16.5% fuel overhead ratio and we’re going to assume the space industry will as well. So \$637,109 is 16.5% of our total ticket take. And that means our total take is \$3,861,266.

Our ship carries 550 passengers, meaning each passenger will have to pay \$7,020.48.

According to my research, it takes a total of 5,930m/s of delta-v to get from LEO to the surface of the Moon. More physics and math happens here, but it means that for every kilogram of cargo you want to put on the lunar surface, you have to put 4.73kg of mass into LEO. 1kg of actual cargo, and 3.73kg of fuel to get that cargo to the Moon.

So what’s it cost to put freight on the Moon? Well, it would cost 4.73 times what it would cost to put the cargo in LEO. So, while it costs \$35.10 to put a kilogram into LEO, it would cost \$166.02 to put it on the surface of the Moon.

You have to get your body to LEO (\$7020), and then soft-landed on the moon. So you end up needing the same overhead – 4.73 times the LEO cost. \$33,206.87.

So let’s say you want a two-week stay. That’s a total of 28 days of expenses at \$800, so \$22,400. Round that up to \$25,000 because vacations always cost more than you expect. That plus the \$45,000 travel costs totals \$70,000.

So I ask again: Would you pay \$70,000 for a lunar vacation?