Full Impulse on my mark… engage!
There has been a ton of chatter on the interwebs about yet another potentially habitable planet in the Gliese 581 system, approximately 20.5 light years from earth. This one, Gliese 581g, was discovered by the Lick-Carnegie Exoplanet Survey using Keck. Based on its size, is approximately 3 earth masses, with roughly earth-like gravity. More important still, is the fact that it’s roughly in the middle of the “Goldilocks zone“ Most everyone is focusing on the unfortunate fact that 581g seems to be tidally locked with its sun, which means that one side is blazing hot, and the other is freezing cold (and, of course, that there’d be only either day or night on each side).
But who cares? I’ll take it as read that we could live there — all of the newspapers have.
Let’s go now. How long would it take?
The Trip to Gliese 581g
I’ve explored this sort of topic a number of times before. Jeff and I do a quick calculation for Alpha Centauri in chapter 8 of the “User’s Guide.” I also did a whole piece about traveling to other star systems in my “Ask a Physicist” column.
But if you don’t want to do all of that reading, let me just sketch it out for you. Suppose you wanted to fly to 981g in smooth comfort. In that case, you’d want to accelerate at earth-normal gravity for the first half of your trip and decelerate at the same rate for the second half. I’ve made a little animated gif (mostly for talks about time travel and the twin paradox). Click to watch it:
You are going to want to accelerate at g by the way, since one of 581g’s main selling points is the earth-normal gravity. Don’t worry; you’ll get there faster than you think.
If you’ve taken a bit of physics, you probably know earth’s gravity as:
but if you convert to light-years and such, you find:
What that means it that by the time you’ve been traveling for a year (earth-time) you’re already going at relativistic speeds.
How long does it take?
I’m going to throw a bunch of numbers at you, but they’ll be in bullet points for easy reading. The upshot of all of this is that because you accelerate so quickly, you get up to near the speed of light in no time. Moreover, since you’re going so fast, the time dilation factor on the ship (the so-called -factor) is huge — at maximum time runs almost 12 times slower on the ship than back on earth.
Some details of your trip:
- Total distance: 20.5 light years
- Travel time (earth-clocks): 22.4 years
- Average speed: 92% the speed of light
- Peak speed: 99.6% the speed of light
From your perspective on the ship:
- Travel time: 6.1 years
You seem to travel so quickly because of time dilation. It really is sci-fi’s best friend.
This trip seems totally do-able! Well, not quite, but it seems feasible. People have spent of order a year on the International Space Station. We can round that up to six.
What’s to stop us from just putting a big rocket on the back of the ISS?
What’ll it cost?
Here’s how they get ya! The biggest problem in traveling to other planets is the amount of fuel that it takes to get up to relativistic speeds. I’ll grant you the existence of matter-antimatter drives which convert all of your fuel into 100% energy. Even if you have that, you still need to lug all of that fuel around. It turns out that:
- To do the trip above requires (at least) 530 times as much mass in fuel as in the ship and cargo itself.
That is very bad news. Let’s put things in perspective and imagine sending the international space station ( metric tons) to Gliese 581g. The whole trip would require something like:
Or approximately 5% of the sun’s energy output in a second. That sounds reasonable, until you realize that that tiny amount would take approximately:
- 3 million years to collect on earth if the entire surface were covered with solar panels
That, as the physicists say, is non-trivial.