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Full Impulse on my mark… engage!

by dave on September 30th, 2010

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:
  g=9.8 \frac{m}{s^2}=32 \frac{ft}{s^2}
but if you convert to light-years and such, you find:
  g=1.03 \frac{ly}{yr^2}
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 \gamma-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 (m=370 metric tons) to Gliese 581g.  The whole trip would require something like:

  • E=1.8\times 10^{25}Joules

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.

-Dave

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35 Comments
  1. Great article! I was planning a trip there myself, but now I think I might need to take some people with me to split the costs of gas.

    Gliese 581g is right in our neighbourhood when we consider galactic scales, and it wouldn’t surprise too many people if the distance between it and Earth was established as being representative of the average diffusion of habitable worlds in the galaxy. So every 20 light years or so you run into another spot capable of sustaining life as we know it.

    Yet as your article mentions, the energy requirements are beyond prohibitive, surpassing any rational estimation of how it could be done. In fact, it seems likely that these limitations could never be overcome, at least given our current understanding of physics.

    If that is the case, we should really start thinking about taking a little better care of our own home.

  2. Nice Article! Thanks Dave :)

  3. Kate D permalink

    Not to scale! Ha!

  4. 92% the speed of light, it will need more efficient spacedrive to attain very high velocities.

    • dave permalink

      True, but that’s why I’m talking about matter/anti-matter drives. My numbers are based on converting mass directly into energy.

  5. Tim Freeman permalink

    How do the numbers come out if you use a lightsail and laser, then jettison half the sail and bounce the beam off it to decelerate? That way, you don’t have to carry your fuel, but you are more vulnerable to problems at home during your trip that might deactivate the laser.

  6. Jerry permalink

    Obeying the speed of light isn’t just a good idea, it’s the law. All of relativity is based around the idea that any observer, in any frame of reference, will see the speed of light as a constant. Given this foundation, I don’t see any conceivable way that the people on the spaceship could experience traveling 20 lightyears distance in 6 years of time. That means they’d have legitimately measured their speed at over 3 times the speed of light.

    • dave permalink

      It’s because from the perspective of a moving observer, there’s not only time dilation, but length contraction as well. From the perspective of the ship, the distance appears to be less than 20.5 ly.

  7. Phillip permalink

    A friend of mine and I did this same math some years ago (after reading The Sparrow by Mary Doria Russel,) and found a problem with it.

    You’ve said that the one way trip would take 22 Earth years / 6 years for the travelers, but you also said that at 1g acceleration you would reach 1c in about a year. Wouldn’t that mean that to continue 1g acceleration you would then be going faster than the speed of light and unable to continue going any faster? Wouldn’t it end up being 1 year of max burn, x years of coasting, and 1 year of max deceleration?

    That’s what we came up with anyway. By the time you got near the speed of light, the speed at which you were throwing particles out the back of your engines would be close to the speed you were going anyway, and they would have less and less effect. At close to light speed, it would take waaaaay more energy to accelerate at 1g and that it would be essentially impossible.

    Were we crazy?

    • dave permalink

      That’s where your high school teachers lied to you. I said that after a year you’d be going relativistic speeds. The point is that on the ship, you’ll always feel like you’re accelerating at g, but from the outside, that’s not the case. F=ma is wrong, for precisely the reason you state — eventually you’d go faster than light.

      However, F=dp/dt, and p=m*v*gamma, where the “gamma factor” is 1/sqrt(1-v^2/c^2). At a constant force, you accelerate to exactly the speed I describe.

    • Chakat Firepaw permalink

      You’re not crazy, you’re just using the wrong function for velocity. V=at is the Newtonian approximation and only applies for small values of V.

      In actuality, the function is V = c * Tanh[a*T/c], where V the velocity in the origins frame of reference, T is the time on the ship and Tanh is the hyperbolic tangent function.

  8. Patrick permalink

    I was wondering, while 1g would be ideal, would we save fuel by accelerating at some level above or below 1g? I’m guessing that we don’t, since we have a 100% efficient engine, but I may be neglecting what happens with regard to mass at relativistic speeds.

    Then again, 400 kg of antimatter per kg of cargo isn’t that much more feasible than 530.

    • dave permalink

      @Patrick. Absolutely. At lower acceleration, you reach a lower maximum speed, so it requires less fuel. Of course, it takes longer to get there from both the earth perspective and _especially_ from the spaceship perspective.

  9. dr burke permalink

    Wrong! It will take less than a year to get there, IF we could
    use some large planet in its solar system, for aerobraking.

    I saw 2010 too.

    You speed into the solar system where the planet is
    located at 80%+ light speed and then use a very large planet gravity well to slow you down. It will get hot at hell, but the STL spacecraft should be able to take it.

    No need to waste the last half of the trip slowing down, just go balls to the wall all the way in and let a big planet gravity well do the braking for you. Simple. And it will require less fuel to take
    along, too. Then use the fuzzy gravity of a large planet to kick
    start your return and kick in the FTL drive as an afterburner.

    Simple, even an idiot could do it.

    dr burke

    • Steve Bryan permalink

      Care to compute how many g’s you would be experiencing while decelerating from 0.8 c in a short time frame? Heat would be the least of your problems. If the ship held together and there were inhabitants they would be scraping your remains from the inside of the ship. The very best test pilots handle something like 8g’s for a very short period while fighting to not lose consciousness. Speed is a serious problem (not discussed here) but acceleration is a killer in Newtonian and relativistic physics.

    • ScottAwesome permalink

      I’m pretty sure such rapid deceleration would turn the passengers into pâté.

      • Stevok permalink

        With the energies involved at relatavistic speeds you’d be taking a real risk of turning the planet into Pate as well!

        • Glenn permalink

          Hmmm… I’m thinking tunguska incident on another planet at those speeds, just think if your aerobraking manuevers were off by even the tiniest degree. Too far out you miss and go on a dramatic and fun filled ride to the rest of the universe sans navigator who is unceremoniously booted out the airlock i.e.pirate style if it were my decision (I’m sure ripping a panel from the wall for a plank would be the least of anyone’s worries. Too close and your ship wouldn’t even touch the planet, you would vaporize before ever contacting the planet surface at those speeds. The blast wouldn’t be on the order of a planet killer I believe but you would definately leave a “boo-boo” directly below detonation point.
          Hmmm… what if that is actually what tungaska was, a failed attempt by another race to reach earth in the method we are discussing? http://en.wikipedia.org/wiki/Tunguska_event check under speculative hypothesis, the whole article is interesting reading too.

  10. dave permalink

    Incidentally, if you’re interested in the (very detailed) fuel calculations, I’ve done a post about it:

    http://usersguidetotheuniverse.com/?p=1249

  11. Tom permalink

    Nice article.. Followed most of it, quick question though..
    where do you get your figures for E = 18 x 10 ^25 J.
    By no means do I have the noggin for this kind of maths, but I find it damn interesting!

    • dave permalink

      That’s the amount released by taking 530 times the mass of the ISS and converting to energy via E=mc^2 (and thus the minimum amount of energy required to make the matter/antimatter mix in the first place). Why do we need that much energy? See my (very mathematical) post on that subject:
      http://usersguidetotheuniverse.com/?p=1249

  12. Curtis permalink

    If you only want to get people there you need a fuel ratio around 22:1, which is “better”.

  13. Joshua Gitersonke permalink

    I’m just curious here, but what happens to the space ship when it hits some space debris (large or small) at such a speed….

    Is the probability of hitting something so small it’s not factored into this journey?

    Or is there some theory that prevents the catastrophic annihilation of the ship?

    Thanks in advance if anyone can answer this.

    • dave permalink

      Very bad things. Rocks are rarer than people think, but it’s true that if you hit one at 0.996c (peak speed), it’s going to rip through the ship. Charged particles could (in principle) be deflected by a magnetic field, but neutral particles (including atoms) won’t. I should point out that by cosmic standards, a “gamma factor” of 22 isn’t that high, but it’s still not good to have that sort of exposure for 6 years.

  14. Eric Claussen permalink

    Great articles, glad I stumbled upon this site. I would propose collecting free hydrogen using some type of magnetic scoop to provide the matter component of the matter-antimatter fuel mix. I need to pull out my calculus book and brush up so I haven’t done the math. Seems like this would require less than half the amount of antimatter.

    I realize the technology doesn’t exist to do this, but I’m pretty sure we could figure it out before collecting that much antimatter. If we are around in a million years perhaps we can just cruise at warp 9.

    • Glenn permalink

      I read the calculations somewhere once to achieve that act, collecting the Hydrogen on the way. Wish I could remember where I read them, fairly certain there was a lot of fanboy presence concerning Star trek too. Those boys don’t know the meaning of “give it a rest” am I right? :)
      I think that someone had figured there just wasn’t enough “free fuel” available, one of those hopeful theories peirced thru the heart by math and astrophysics at the same time, a rather “dramatic/over the top” death on stage. Lots of flopping around and gnashing of teeth.
      And they even used the Star Trek name for the equipment, broussard collector I believe.

  15. Geoffrey permalink

    The time dilation that works on the passengers should also be working on the engine and it’s ability to accelerate (or slow down.) In fact, since the time gets stretched out, the meters per second acceleration per second, on board… woah … so the ship is accelerating at a lower rate for the passengers than for people back on Earth, or is it the other way round? Relativistic speeds are really confusing…

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