Is interstellar travel impossible due to kinetic energy magnitude?

  1. BitWiz

    BitWiz 64
    Gold Member

    This has been bugging me. Several respected propulsion scientists at the 2008 Joint Propulsion Conference claimed that interstellar travel within a human lifetime was impossible. The KE of a rocket traveling at a significant fraction of c would be enormous via KE=0.5 * m * v^2 and that presumably, this KE would have to come from fuel.

    Examples of KE often use a car to demonstrate that doubling the velocity quadruples the stopping distance. I get that, but though velocity is a goal in space travel, I would think acceleration is a more important energy management element in frictionless, gravity-free space.

    Then there's the difference in how cars and rockets work:

    A Chevy and a rocket are at a stop light. The light turns green . . .

    The Chevy's engine cylinders fire at equidistant points along the road; fuel usage is proportional to distance.

    The rocket is not connected to the road; fuel usage is proportional to time.

    If it's fair to plug proportions into the acceleration equation (d / t^2), then I get Fuel is proportional to t^2 for the Chevy, and sqrt(d) for the rocket, i.e:

    If we double the acceleration time, the Chevy needs four times the fuel, the rocket just twice the fuel.

    If we quadruple the acceleration distance, the Chevy needs four times the fuel, the rocket just twice the fuel.

    So my question is, is it fair to use Earth-observer-based KE to determine the fuel requirements for a rocket?

    Thanks!

    Chris
     
  2. jcsd
  3. This is correct as a low-velocity approximation. But it ignores the constant of proportionality.
    A efficiency of a rocket motor is zero at rest -- it is wasting all of its energy on the exhaust stream. It is 100% efficient when the vehicle velocity reaches the exhaust velocity. At this velocity the exhaust stream is at rest with respect to the road. Pushing on the exhaust stream is exactly as efficient as pushing on the road.

    So that's the crossover point where it might start to make sense to use a rocket.

    But there is a complication. In order to reach a vehicle velocity equal to the exhaust velocity you need to throw a significant fraction of the vehicles starting mass out the back as exhaust. If you run the motor continuously, the fraction you need to throw out the back is 1-1/e (where e is Euler's number, 2.718...). That's about 63% of your starting mass.

    In order to get to twice exhaust velocity you need to throw the same fraction out again. Now you've thrown a total of 86% of your starting mass out the back.

    If you want to get up to five times exhaust velocity you need to throw out all but 1/e5 of your starting mass. That's over 99% of your starting mass.

    This motivates the Tsiolkovsky rocket equation (http://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation)

    For any useful interstellar velocity using chemical propellants, you need an insane ratio of starting vehicle mass to payload mass.
     
  4. BitWiz

    BitWiz 64
    Gold Member

    Thanks for the reply, jbriggs.

    I ignored "k" to simplify the issue. I presume that, since we're comparing one device that uses fuel at a linear rate over time vs one on a power curve, that there is probably no k constant of "fuel efficiency" between the Chevy and the rocket where the rocket won't eventually overtake the Chevy. Is that a fair assumption?

    This is again where I'm confused. Let's say that I'm using an electric ion engine in space -- no gravity, no atmosphere, no friction. My linear mass accelerator is one meter long -- I will accelerate my propellant as single mass objects in single events for exactly one meter. The object is then ejected into space. There is no need for a nozzle.

    Further, at whatever velocity I might perceive with respect to any another object, as far as my rocket is concerned, I am at rest between propulsive events. Floating inside my rocket, as far as I and my rocket engine can tell, I'm not moving.

    I then turn on my rocket engine, and I pump a gigajoule into accelerating a single proton in my linear accelerator. Yes, this engine has great specific impulse. ;-) Is there really a difference in how much acceleration I can measure as a passenger on the rocket between one propulsion event and the next? Can't I use propellant at an arbitrary rate as long as I can pump energy into its acceleration?

    ;-) Agreed.

    Chris
     
  5. Don't forget that energy has mass. The energy equivalent of a proton at rest is about 1.5*10^{-10} joules. Sure, you can (in principle) accelerate a proton to a gigajoule, but your energy source is going to be quite a bit more massive.
     
  6. BitWiz

    BitWiz 64
    Gold Member

    You mean mass equivalent? Or are you saying that an energetic photon has mass?

    It's my understanding that propellant mass is largely arbitrary if you have a way to pump arbitrary amounts of energy into the propellant. Is this correct?

    Thanks for your reply!

    Chris
     
  7. I mean mass equivalent. A photon does not have mass. My point is that there is no way to practically achieve a specific impulse higher than that of antimatter+matter, which converts 100% of mass to radiation.
     
  8. Chronos

    Chronos 9,874
    Science Advisor
    Gold Member

    Even using anti matter as a rocket propellant, the fuel mass required to travel to the nearest star would be about 5.6 times the payload mass and require at least 9 earth years [albeit much less for the passengers]. Of course, you need the same mass of propellant for a return voyage. And this ignores some rather nasty side effects from the matter-antimatter reaction chamber. It's clearly impractical by any technology we currently possess. I have this nagging suspicion any other intelligent life in the universe is similarly victimized by the laws of physics.
     
  9. By "nasty side effects" are you referring to long term radiation poisoning?
     
    Last edited by a moderator: Apr 12, 2014
  10. sophiecentaur

    sophiecentaur 13,396
    Science Advisor
    Gold Member

    Would you not also need to consider the energy needed to slow down at each end of the return trip? That would mean a further doubling of the overall energy requirement.
     
  11. UltrafastPED

    UltrafastPED 1,919
    Science Advisor
    Gold Member

  12. BitWiz

    BitWiz 64
    Gold Member

    I think there are a couple of misconceptions.

    First, we do not need to accelerate for the entire trip. We work to get up to a reasonable gamma, trading time for energy, and coast for most of the trip. That saves a lot of fuel, plus the fuel to accelerate that fuel. If we accelerate at about 1 g for a year of proper (passenger) time, I think we could make a γ=4. A 10 ly trip could be done in about five proper years.

    Second, we ONLY care about proper time. Earthers are not in our thoughts or frame of reference. ;-)

    Deceleration. You can refuel at the destination.

    IMO, antimatter will never be a practical propulsion fuel for the same reasons nitroglycerine isn't a good automobile fuel. The only practical fuel is water. Fuse the hydrogen (and its byproducts) and use the oxygen as the propellant. It has the additional benefits of being stable, non-toxic, relatively abundant for refueling at the destination, and a good source of water and oxygen for passengers.

    Agreed. And we'll never have a practical fusion source for space travel if we continue to rely on tritium, terawatt lasers, and 100-tonne capacitors to drive them, such as we are exploring at the National Ignition Facility. We need to develop methods of gamma ray capture for "clean" energy rather than energetic neutron capture which tears up everything (IMO).

    Of course! ;-)
     
    Last edited by a moderator: Apr 12, 2014
  13. BruceW

    BruceW 3,544
    Homework Helper

    yeah. It could be a long time before we have fusion power stations here on earth. So it would likely be an even longer time before we could get a fusion power station which is nice enough to use as part of a spaceship. So I'm guessing the scientists talking at that conference were essentially discounting fusion technology, as being something too speculative.
     
  14. We can have fusion power stations in <40 years, if it isn't killed off by politics.
     
  15. BitWiz

    BitWiz 64
    Gold Member

    Hi, Bruce,

    No, they were saying that the KE of a ship traveling at even 10% c is so large that no amount of fuel of virtually any sort could supply enough energy to produce the KE to get a passenger, the fuel, and his container to Proxima in a human lifetime.

    The issue seems to involve settled physics at such a fundamental level that I'm having trouble coaxing an alternative.

    The problem -- if there is one -- may stem from an Earth-centrism, our perceptual difficulty in excluding ourselves from the frame. Earth has no business in this -- it is not necessary for acceleration -- and without Earth, velocity and KE are undefined. Only proper, *relative* velocity exists, integrated from proper acceleration measured over proper time on the ship. So is there such a thing as proper KE, even though we are the only object in the frame?

    Externally, we can get just about any velocity (and KE) value we want by selecting the appropriate reference object. I DO care about my velocity with respect to my destination, but I do not care about the distance (irrespective of relativistic effects) required to decelerate, and distance is a fundamental unit dimension of, and argument for, the validity of KE in this issue.

    Something is out of kilter (perhaps besides the author), but I don't want to just guess. Can you help?

    Thanks!

    Chris
     
  16. Astronuc

    Staff: Mentor

    The problem of interstellar travel, besides the long distance requiring long times, is the problem of how much propellant and the energy source. A designer needs to look at the Isp (specific impulse) and specific power (kW/kg).

    One has to take the propellant and energy source with one, or utilize the solar wind or prevailing cosmic radiation. The solar wind and cosmic radiation are however tenuous.

    In chemical or nuclear thermal rocket systems, with relatively low Isp, one fires a rocket (impulse) for some short period of time to get up to a limited velocity.

    In the case of nuclear electric or antimatter systems, the thrust (low) is employed more or less continuously to achieve high velocity. At some velocity, one would coast, as is the case with short impulse propulsion. Near the destination, one has to turn around and decelerate.

    The problem with Alcubierre drive is still the energy source. What energy density is required to warp space, and what would be the local pressure? Could any physical object survive intact?
     
  17. BruceW

    BruceW 3,544
    Homework Helper

    I don't think that's what they were saying. More likely is that they were saying it was not possible with technology in the near-future. (thus excluding things like fusion generators which could fit nicely on a spaceship).

    We should be able to work out an example. Using the (relativistic) Tsiolkovsky rocket equation (as jbriggs mentioned), if we have an exhaust velocity of c (which I guess would be the case if we were using matter & antimatter propulsion, or using some other propellant that we can somehow propel out the back of the spaceship at near light speed). Then to get our spaceship to a velocity of 10% speed of light, then we only need an amount of fuel of mass roughly 10% of the mass of the payload. (the fact that both fractions are the same is a coincidence, by the way). So anyway, this would be a very ideal rocket. But the point is that it is definitely possible, if we had the right kind of technology.

    Well, I think it is true that the KE of the spaceship would be so large, that current technology cannot provide enough energy. I think that is what they meant. But I'm guessing too. I wasn't at this conference. Although it does sound like an interesting one :)

    p.s. no, there is no such thing as proper KE. But the KE of the rocket, according to the Earth is an important quantity, because the rocket initially has the same velocity as the earth, this means the KE of the rocket according to the Earth was initially zero. That is why the KE of the rocket, according to Earth is an important quantity.

    p.p.s. also, we must assume the earth represents an inertial reference frame, which it doesn't really, because it is in orbit around the sun. So really, we should talk about the KE of the rocket according to the sun. (Which is more or less an inertial reference frame, since our rocket will not be going across the galaxy, it is only going to the nearest star)
     
    Last edited: Apr 12, 2014
  18. I suspect the way we will travel to the stars (and I firmly believe we will) is to drop the "in a human lifetime" constraint. Large, self-sufficient colony ships with 1000's of inhabitants that travel at ~1% of the speed of light and require 100's of years to travel between stars appear quite feasible.
     
  19. sophiecentaur

    sophiecentaur 13,396
    Science Advisor
    Gold Member

    Why would anyone fund a project like this?
    1. It would be totally altruistic - in favour of the travellers and at the expense of 'the rest of us'.
    2. Governments have difficulty thinking much further ahead than the time of the next election. A project like this would take decades or even hundreds of years.
     
  20. I didn't say it was going to happen any time soon. A project like this is probably centuries to millennia in the future. As we progress as a species, especially as we move off of the Earth and out into the solar system, we can expect economic growth to continue, so that the resources required could be within reach of a large group of people. Why did people fund the Mayflower? Why is there a group planning on colonizing Mars? What is the alternative? Huddle here on the Earth until the sun swells up and incinerates us all?
     
  21. BitWiz

    BitWiz 64
    Gold Member

    The complaints were based on a combination of tech and energy -- but "never" is a long time to discount tech advances. There are summary references to the 2008 AIAA conference that can be extracted with Google. One source for the gritty details is here (http://arc.aiaa.org/doi/abs/10.2514/6.2008-5121), but not for the faint of heart. A good article appeared in Wired on 8/19/08, but is no longer accessible online (though Google still finds it -- go figure).

    If our propellant has mass, I think we can (theoretically) pump energy into it up to the limits of our supply and tech, even if it's a single proton, and still get an "equal but opposite" reaction. The proton would gain mass as we push it closer to c, and I'm not sure that relativistic Tsiolkovsky takes this into account.

    I made a point of stating that the propulsion system accelerated propellant over a distance of a single meter to simplify the KE of the propellant. "Distance" is a variable relativistically, and I would think a propellant cranked up to a high gamma will see a correspondingly shortened path through the accelerating field. You mentioned later that there is no "proper KE," but I wonder if our accelerated proton would agree with its KE measurement by a shipboard observer, not to mention an Earth-based observer.

    As you can imagine, it created quite a stir in the SciFi community. Suddenly, every outer space opera had the scientific validity of "second star on right, and straight on till morning," regardless of the sincerity of the author.

    I suspect KE is important for concepts such as storing potential energy in Earth's gravitational field, but once we're beyond the overwhelming magnitude of a nearby field, aren't we storing and harvesting potential energy in the gravitational fields of every mass object in the Universe? When we're several parsecs from Sol, why do we care about our KE with respect to Sol? ;-)

    Thanks very much for your reply, Bruce!

    Chris
     
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