Starship Math: Are the Stars Our Destiny?

Once again I have drifted off thinking about the size and scale of space--the things in it and the distances between them--and once again have brought pen and paper, math, and a spreadsheet to bear on the question: are the stars in our destiny, or is the notion of physically reaching them (in person, at least) beyond the available realities?

With all of the science fiction stories devised to get their characters to other stars not only within their lifetimes, but sometimes within a few paltry days, it’s easy to think of interstellar travel as something we might eventually get around to, given the technology, time, and money. We just need to figure out how warp drive or hyperspace work, and how to exploit them, and we’re off!

But putting teleportation and wormhole expressways and their ilk on the shelf labeled, “Cool, but probably just fancy” for a moment, what are the Newtonian-Einsteinian requirements to get us to, say, the nearest known extrasolar planet, which orbits the star Epsilon Eridani, 10.4 light years away from us? It’s a gas giant planet larger than Jupiter and orbits well beyond its star’s habitable zone, but it’s a planet after all, and we star-seekers just love planets.

Now the math that will get us there. I had to assume a mass for our would-be starship, conservatively chosen as 2000 metric tons, or about the weight of the Space Shuttle. In reality that’s far too small a ship for any human interstellar journey, unless the crew are all frozen. And keep in mind, my calculation does not take into account the weight of any fuel we need to carry with us. I’m also choosing a top cruising (coasting) speed of one-tenth the speed of light, or 30,000 kilometers per second. A tenth light speed is pretty darned fast, but not so fast that we need to worry much about relativistic mass—that is, the increase in the spaceship’s effective mass when traveling a significant fraction of the speed of light.

If our engines can produce thrust sufficient to accelerate our 2000 ton spaceship at a rate of “1 gee”, or one Earth-gravity equivalent (~10 meters per second, per second), then to achieve a velocity of one-tenth light speed we’ll need to run those engines for about 35 days, non-stop. We should assume our engines are powered by nuclear fusion or even antimatter reaction (possible future technologies that today present technical challenges, but which aren’t on that shelf of sci-fi fancy).

The energy required for this 1-gee, 35-day engine burn of our 2000 ton spaceship is about 900,000,000,000,000 (yes, 900 trillion) MegaJoules, or 250 trillion kilowatt-hours. That’s the same amount of energy required to launch 20 million normal Space Shuttle flights to low Earth orbit, or almost twice the world’s annual energy consumption. And that’s just to get this little ship accelerated to cruising speed. We’d need another like amount of energy to slow it down to its destination in the Epsilon Eridani system.

As for how long the trip would take, forgetting the 35 days spent getting up to speed and the 35 days spent slowing down again, traveling 10.4 light years at one-tenth the speed of light would take 104 years, one way. (Although, moving at a tenth light speed, the trip would only feel like 103.5 years due to relativistic effects.)

What about the weight of fuel required to do the job? Forget normal rocket fuel; we’d need the energy contained in about 20 billion tons of it just to get to cruising speed—and that doesn’t take into account the mass of the fuel itself, which would also need to be accelerated. Two-thousand ton spacecraft + 20 billion tons of fuel = not practical.

If our engine is powered by hydrogen fusion, we may only need about 3000 tons of fuel (and I’m assuming our fuel is also our propellant—the mass we need to fling out of the engine to accelerate the ship by reaction force; probably not a conservative assumption, in reality).

And if we could use antimatter as our fuel, as does the Starship Enterprise, releasing energy by mixing equal parts antimatter with normal matter, we could carry in our fuel tanks as little as 5 tons of the stuff (plus, I think, 5 tons of normal matter to react with) to achieve cruising speed.

And of course double the fuel amounts if you plan to come to a stop at your destination, 104 years from now.

In summary: tiny cramped ship, 20 tons of antimatter/matter fuel to pack the necessary 500 trillion kilowatt-hours of energy, and 104 years to delivery you to the fabulous Epsilon Eridani system with its one known super-Jupiter sized planet. Anyone interested? Or should we leave space travel to the robot crowd....