Will We Reach the Stars? A Physicist’s Analysis (Part I)

If you watch any science fiction at all, you probably take it for granted that humans will be traveling casually from one star system to another in the not-too-distant future. (At least, I’ve always taken it for granted.) And why shouldn’t you? There’s good precedent for science fiction becoming reality; just look at any of the latest military, medical, and communications technology. But in light of the physical requirements of interstellar travel, should we really expect to reach the stars some day?

To answer this question, let’s examine what it would take to travel to the nearest star, Proxima Centauri.

First, consider the distance. Even though it’s our closest neighbor, Proxima Centauri is a whopping 4.24 light-years away from us. Traveling that far would be equivalent to circumnavigating the globe (at the equator) one billion times. If you flew the space shuttle at its maximum speed, it would take you 164,000 years to get there. Over five thousand generations of humans would be born and die on the shuttle during your trip!

No problem, you say. We’ll just have to go a bit faster than that.

Okay. Let’s decide on a speed, then. First, we need to know how long we want the trip to take. I, for one, would like to get there within one generation and still have some time to spare. So let’s say ten years. That’s a long time, but hey, this is a pioneering trip. I mean, how long did it take Columbus to reach America? (Five weeks.)

So ten years it is.

All right. Now that we know both the time and the distance, we can calculate the required speed. That’s just distance divided by time, right?

Well, not quite. The number that we have for the distance (d) to Proxima Centauri was measured in the Earth’s frame of reference, whereas the amount of time (t) that the trip takes will be measured in the ship’s frame of reference (i.e., we want the traveler to age ten years). If we take into account relativistic effects, the required speed is given by:

Plugging in the distance to Proxima Centauri for d and ten years for t (and the speed of light for c), we find that we will have to travel at 39% of the speed of light.*

Okay. So what?

Well, the next question is how we will accelerate the ship up to this speed. Specifically, we need to know how much energy it will take. For this, we need the ship’s mass in addition to its speed.

To get a reasonable estimate of our ship’s mass, let’s suppose that we’re traveling in something like the space shuttle (which is really too small for a ten-year journey, especially if your mother-in-law is on board). Without its usual two million kilograms of fuel (who needs fuel, anyway?), the shuttle weighs a trifling 75,000 kg.

Armed with knowledge of our ship’s speed and mass, we’re now ready to calculate the amount of energy we need. Don’t worry; this won’t hurt. Remember the ol’ kinetic energy formula from high school? No? Well, it doesn’t matter. That formula isn’t valid at high speeds, anyway. We need to use the relativistic formula for kinetic energy, which is this:

After we plug in our numbers and wait for the dust to clear, we find that the amount of energy required is … drum roll please …

In case you’re wondering what the hell a joule is (which is especially likely if you were educated in America), I’ll just put this number in perspective by telling you that this is the amount of energy that the largest power plant in the world (the Three Gorges Dam) produces in 820 years.

It’s time for some reflection, I think.

Even if we could pack the largest power plant in the world onto the space shuttle without adding to the shuttle’s mass, it would still take us 820 years just to reach the desired speed. And we haven’t even considered how we’re going to slow down once we arrive at Proxima Centauri!

Granted, there are little tricks we can use to get an energy boost here and there. The most obvious is what’s known as a gravitational assist, which would involve flying our ship by a planet in such a way as to steal some of the planet’s gravitational energy.

The Voyager 1 probe executed at least one gravitational assist. Launched in 1977, it’s the first human-made object to leave our solar system. But even after over 36 years of travel time, including a boost from a gravitational assist, it has only traveled 1/2100 of the distance to Proxima Centauri. The full distance will take another 75,000 years or so.

Thus, even clever tricks such as gravitational assists probably won’t be enough for our purposes. And so it looks like traveling to another star — even the nearest one within our own galaxy — won’t be that easy. In fact, we’re likely never to be able to do it at all.

You might say that I’m being overly pessimistic. After all, we can surely expect some technological advancements in the future. Won’t they make interstellar travel possible?

Perhaps. We’ll consider some of the possibilities in my next post.

*For those of you familiar with relativity, this corresponds to gamma = 1.086.