# Is interstellar travel impossible due to kinetic energy magnitude?

1. Apr 11, 2014

### BitWiz

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. Apr 11, 2014

### jbriggs444

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.

3. Apr 11, 2014

### BitWiz

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

4. Apr 11, 2014

### Khashishi

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.

5. Apr 11, 2014

### BitWiz

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?

Chris

6. Apr 12, 2014

### Khashishi

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.

7. Apr 12, 2014

### Chronos

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.

8. Apr 12, 2014

### HomogenousCow

By "nasty side effects" are you referring to long term radiation poisoning?

Last edited by a moderator: Apr 12, 2014
9. Apr 12, 2014

### sophiecentaur

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.

10. Apr 12, 2014

### UltrafastPED

11. Apr 12, 2014

### BitWiz

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
12. Apr 12, 2014

### BruceW

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.

13. Apr 12, 2014

### Khashishi

We can have fusion power stations in <40 years, if it isn't killed off by politics.

14. Apr 12, 2014

### BitWiz

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

15. Apr 12, 2014

### Astronuc

Staff Emeritus
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?

16. Apr 12, 2014

### BruceW

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
17. Apr 12, 2014

### phyzguy

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.

18. Apr 12, 2014

### sophiecentaur

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.

19. Apr 12, 2014

### phyzguy

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?

20. Apr 13, 2014

### BitWiz

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? ;-)

Chris

21. Apr 13, 2014

### sophiecentaur

I know people have a romantic notion about space travel and the parallel is often quoted with early exploration on Earth. However, the big difference is that exploration has always been done incrementally and there is no essential difference between sailing across an ocean (particularly if you island hop) and sailing along the coast. The Pilgrim Fathers were going nowhere that hadn't been visited before. Also, they funded themselves and were ripped off by the people they bought their ships from.
You make the assumption that we will "progress as a species". Civilisations tend to have a cycle of development - this is what History tells us. I think it is naive to imagine it will be different for our current culture. We are on a knife edge all the time. The simplest microbe could bring the present 'civilisation' down on its knees, as could a visit from an asteroid or just some loony group of extremists. If you are talking big numbers for developing advanced technologies then you also have to talk big numbers for the arrival of catastrophe.
As far as the Earth is concerned, this is of no consequence. Just a few viable surviving organisms is all that's needed for a civilisation to appear again. I do not regard that as a failure - it's just something we can expect to happen to humankind, eventually.

Btw, the group is not seriously planning to colonise Mars. The best they can hope for is to survive for a while and then come back in one piece. (What kind of an eejit can say he'd like to die on Mars?) I think it's a shame they can't direct their finances to some humanitarian project that would be better value and is more likely to succeed. The project isn't Science - it's a self-indulgent exercise by people who can afford it.

22. Apr 13, 2014

### BruceW

It does take that into account. That's why it's called the relativistic Tsiolkovsky equation :) If you think about it intuitively, the rest mass of the fuel you carry on board only needs to be very small, to give a huge amount of momentum to the spaceship, as long as you expel the propellant at close to the speed of light. Of course, the problem is that our technology is most likely not able to do such a thing. But this comes back to the statement that our technology is not nearly advanced enough to allow for interstellar space travel. This is different than the statement that it is not possible even in principle.

I'm not sure what you mean here. For sure, there is no absolute KE. The kinetic energy for an object with non-zero rest mass is simply $m_0(\gamma -1)$ So this is certainly dependent on the frame of reference which we use to describe the KE of the object, since gamma is for sure dependent on the frame of reference.

yeah, thanks for making this thread :) Uh, the KE with respect to sun is important because the sun is effectively the inertial reference frame that the spaceship initially has zero velocity according to. (I'm completely ignoring any gravitational fields, by the way). So, I'm assuming that we can get the rocket out of the gravitational field of the sun, then from there we have a rocket whose velocity is approximately zero according to the reference frame of the sun, and from there we can use the Tsiolkovsky rocket equation to work out how much fuel we need to make the journey. Also, I'm assuming there is zero effect from the gravitational fields of other objects, which should be approximately true. Unless we slingshot the spaceship past Jupiter, or do something similar, then this will mean we need to carry even less fuel than in the calculation I did before.

23. Apr 13, 2014

### phyzguy

I suspect the people on this project do seriously intend to colonize Mars. Perhaps not on the first try, but eventually. We all die eventually; why do you think dying on Earth is better than dying on Mars? I think that if I died on Mars feeling that I had helped mankind spread off of the Earth out into the solar system, I would consider it a life well lived.

24. Apr 13, 2014

### sophiecentaur

I can understand the romance of such an idea - at first sight. But there is not the remotest similarity between travelling to another planet and the 'wild frontier' on Earth. People tend to confuse the two.
How many generations of Curiosity could one premature human trip pay for? Sending people is little more than a vanity project. Now - if there were a military interest involved, that would change everything.
I think we will have to disagree about this. The practicalities of it all are highly interesting though.

25. Apr 14, 2014

### BruceW

I like romantic ideas. But maybe money could be better used to fight poverty. But again, economics is not a zero sum game, so I think maybe it is not so simple. Also, space research can help technology.

edit: In either case, interstellar travel for humans is not practically possible in the near future. Or at least, that seems to be the case to me. I don't really know much about this stuff.