The Ansari X-Prize for the first reusable private craft to reach “the edge of space,” 100 kilometers above the earth, was won in 2004 by Burt Rutan's SpaceShipOne. The cost? Three years of research and $25 million.

That same year, George W. Bush's Vision for Space Exploration gave NASA sixteen years to get back to the moon, with startup costs alone of $16 billion. Is government inefficiency to blame? What makes the private program so much more efficient than the government one?

The answer probably isn't free-market efficiency; it's fuel efficiency.

On earth, your car gets a certain number of miles to the gallon. If you want to go twice as far, you need twice as much fuel. But space travel doesn't work that way. Rocket fuel usage is governed by something called the Tsiolkovsky rocket equation, which says that the amount of fuel needed grows exponentially as you try to make a rocket go faster.

In layman's terms, the equation says that miles-per-gallon makes sense only if you've got very few gallons. If a significant chunk of your spacecraft's weight is fuel—as it will be until the rise of interplanetary gas stations—you need to start taking the weight of that fuel into account. The fuel cost of the ten-thousand and first mile you travel against gravity is the little bit of fuel you use traveling that last mile, plus the huge amount of fuel you used dragging that bit of fuel around for ten-thousand miles.

If you fitted a rocket onto a Pontiac Firebird, you'd need 500 gallons of rocket fuel to get it to the edge of space, but 20,000 gallons to take it to the moon.

Let's put some numbers on this. Without fuel, SpaceShipOne weighed about 1,000 kg. For a single-stage rocket with standard propellant, Tsiolkovsky's equation tells us that we'd need around 500 kg of fuel to take those 1,000 kg to "the edge of space." But having gotten that far up, we won't have enough fuel to prevent falling right back down.

To actually sustain low earth orbit indefinitely (what the space shuttle does) a 1,000 kg vehicle would need nearly 10,000 kg of fuel. To get to the moon, it would need 30,000 kg of rocket fuel - for a payload of only 1,000 kg. If you fitted a rocket onto a Pontiac Firebird, you'd need 500 gallons to get it to the edge of space, but 20,000 gallons to take it to the moon.

This is the dark underbelly of compound interest, the phenomenon that makes long-term investing so effective. It’s the final years of a long term investment that make most of the money, and the final legs of a space voyage that cost the most fuel. As private spacecraft travel further from earth, the size of the vehicles will need to increase dramatically. That's one reason private efforts to get to the Moon will need Vision-style billions, not the mere millions that powered SpaceShipOne.

Yet the private sector has been here before. Crossing barren expanses in a premodern age, desert caravans would pack months worth of food and provisions—the caravan equivalent of rocket fuel. If the caravan needed to go just a tiny bit further, they'd have to drag the supplies for that final leg around for months, making the initial trip that much more exhausting. But it could be done: Ibn Battuta, the 14th century citizen-explorer, criss-crossed Arabia by foot, horse, and camel, covering 100,000 kilometers—a third of the way to the moon!

The proud history of private exploration, and some notable improvements in transportation, should give hope to latter-day Battutas.

Erez Lieberman is a graduate student at Harvard and MIT. He is co-author of "City of Salt" and "The Apollo Prophecies" (both Aperture Press), with Nicholas Kahn, Richard Selesnick, and Sarah Falkner. His scientific research has appeared in journals including Nature.

Image credit: Photo by Michael Pereckas