# Relativistic Space Travel

1. Sep 14, 2004

### Minty

There have be several threads discussing aspects of space travel and how relativistic effects could be utilised to enable travel to other stars in reasonable experienced elapsed times. I want to describe and utilise such spaceships in my science fiction writing whilst resorting to as few 'fudges' as possible. Has this already been discussed (and if so where?) or could this be a suitable thread for expanding and elucidating on this concept?

TIA
Minty

2. Sep 14, 2004

### Alkatran

It may seem like 3 years to the crew, but on earth it could be 1000. That is because, according to you, you have moved across a small space over a small time and according to them you have moved over a large a space over a large time.

The idea is that once you slow down, space is no longer contracted for you and it seems that you've come farther, faster, than you actually did.

Please excuse the blatant misuses of relative speeds and contractions here. Trying to make it layman.

3. Sep 14, 2004

### Minty

Okay, I had that general impression from my laymanâ€™s grasp of relativity but I'm now looking for specifics. Perhaps I should start the ball rolling by addressing some issues I am having constructing a virtual space ship that is to be used to traverse interstellar space.

Assume we require a space ship that could travel under an acceleration of 1g, reversing the direction of acceleration at the half way point and coming to rest at some distant stellar location. During this journey travellers on the space ship will be able to benefit from time dilation with respect to an external observer. I'm sure there are equations for calculating the quantitative aspects of this effect.

The propulsion for such a space ship is open to debate but not really on topic as it is not relativistic in nature. What is relevant is the effect generated by such propulsion.

To produce constant 1g acceleration will require consumption of fuel each second to increase the velocity of the mass of the space ship (+fuel of course) by 9.8 metres per second.

At non-relativistic velocities this is all straightforward but as the velocity increases I understand relativity predicts that distance and time will dilate and mass inflate. Thus any equations involving mass, time and distance will be distorted proportionately according to an external observer.

What, however, happens within the space ships' frame of reference? Am I correct in stating that to all intents and purposes mass, time and distance act as normal without the traveller being aware any distortions?

If this is the case then we would expect that for the same expenditure of fuel the space ship will undergo an acceleration of 1g which increases the velocity of the space ship by 9.8m/s per second as measured by the traveller. Thus fuel consumption under these conditions is dictated by the elapsed time of the journey and not by any mass increase and the like (again, all within the frame reference of the space ship).

Now I have seen elsewhere on the forum discussions indicating that fuel consumption increases dramatically so what in the above is a misconception?

4. Sep 14, 2004

### Alkatran

In the ship's reference frame, the fuel consumption remains constant. In other frames it will change. This might seem like a paradox but that's what relativity is all about, looking like a paradox.

I haven't studient general relativity (or special, for that matter) but the increase in fuel consumption probably has something to do with the time dilation...

5. Sep 14, 2004

### pervect

Staff Emeritus
Probably the best place to start is

http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html [Broken]

which has a good treatment of the relativistic rocket. Accelerating at 1g will get you to the center of our galaxy in 20 years of proper time (including decceleration), and to the Andromeda galaxy in 28.

Of course, it's really really toough to accelearte at 1g for such a length of time, but you can downplay that aspect in fiction :-).

Last edited by a moderator: May 1, 2017
6. Sep 14, 2004

### Minty

pervect: thanks for the link, interesting reading. The fuel issue is discussed in terms of conservation of energy and momentum resulting in large fuel to weight ratios that probably correspond to the views expressed elsewhere; that the amount of fuel required (even at 100% mass conversion) quickly becomes unmanagable.

I'm a bit suspicious, though, that the calculations are all undertaken from the normal space frame of reference rather than the ships frame of reference.

The suggestion that the fuel be hydrogen scooped from interstellar space would appear to have merit in this context as the fuel is not part of the mass equation.

Alkatran: 'looking like a paradox' appears to the best way of describing relativity when you come at it trying to use laymans terms. As you say, a work of fiction can afford to gloss over some of the details

In Summary:

I can have my space ship, use SR equations to deduce time dilation factors and then just treat my space ship like any other ship as far as the physics goes. I need fuel to achieve 1g acceleration for the length of subjective time of the journey which becomes much easier if I use external energy sources such as scooped hydrogen. So long as I only use the ships' frame of reference everything pans out (or I can reasonably assume so for the purposes of fiction!)

Now to decide how best to deal with collisions with energetic particles, radiation and matter whilst at relativistic speeds. Are they in fact a problem even?

What effects will a space traveller perceive when refering to the outside world, when navigating and communicating for instance?

7. Sep 14, 2004

### Alkatran

Small problem with 'scooping hydrogen': You're going REAAAALLLLY fast compared to that particle. There will be massive amounts of acceleration involved... stress on the ship... basically a BAD idea.

I have no idea what the universe would look like from the ship's point of view. If you looked almost directly ahead I suppose things would look like they weren't deep enough, but looking to the side... yeesh

The collision part is going to be a problem as well. Similar to the hydrogene problem. On the odd chance there's a comet in the way, how are you going to get out of the way? It's streaking towards you at .9c!! :surprised (that's very fast for a naked comet, yes that was a joke, there is no "naked" class of comet... lol)

8. Sep 14, 2004

### Janus

Staff Emeritus
This doesn't matter because the fuel mass calculation is for the "rest mass" of the fuel, which doesn't change for the ship's frame of reference.
Even this type of propulsion has its limitations. As you travel faster, the process of scooping up fuel creates drag on your ship. You eventually reach a point where this drag equals the thrust you can get from the fuel and the ship no longer accelerates. For example, for a fusion drive, some studies have shown that the drag at the minimum operating velocity for the scoop is greater than the thrust generated, and thus it is not self sustaining. Even the most optimistic estimates give a fusion ramjet a top speed of only a few percent of c.
If you are using the ramjet, you just have it use magnetic fields as scoops, and design them such that they clear your path at the same time.

9. Sep 14, 2004

### pervect

Staff Emeritus
The calculations should all be in the ships frame of reference AFAIK.

The fuel usage part of the equation is easy enough to derive. The best case is a "photon drive", when the exhaust is light. The most logical almost-candidate for such a drive is the beam-core antimatter rocket

http://www.islandone.org/APC/Antimatter/02.html [Broken]

but note that since this (hypothetical) design exhausts pions rather than photons, the performance will be worse in terms of mass ratio than the photon drive equations that I'll derive below.

If we use units such that c=1, we can say that with a photon drive, the exhaust energy E will be the exhaust momentum P as E = Pc, and c=1. Thus:

dp/dt = m*a = -dm/dt

where a is the proper acceleration of the ship, and dm/dt is the rate of change of mass of the ship. (Note that since c=1, mc^2 = m, so the rate of change of the mass of the ship is the same as the rate of change as its energy).

Thus a*dt = -dm/m, or ln(m) = -a*t+C, where C is some constant.

If we let m0 be the initial, fuelly fuelled mass of the ship, we can then say

m(t) = m0*exp(-a*t), where a is the proper acceleration (i.e. acceleration as measured from the ship), and t is the proper time (i.e. time as measured by the ships clock). Or if we let mf be the final (dry) mass of the ship, we can write

mass ratio = m0/mf = exp(a*t)

Since 1g is about 1 light year/year^2, we can see that we are talking about mass ratios of exp(20) or so to accelerate at 1g for 20 years even with a 100% efficient photon drive.

Another "downer" is that almost any conceivable design for a photon drive or a beam core antimatter rocket will probably melt itself into a puddle of slag long before it could reach a 1 g acceleration. If a rocket had a fueled mass of 10,000 metric tons, it would require that one convert .3 kg /second of matter to energy per second and exhaust it out the back. That's about 6 megatons/second. The beam-core design is one of the more theoretically efficient antimater drives, but it is expected to be no more than 60% efficient (because about 1/3 of the generated pions will be uncharged and will spread in all directions). That leaves a couple of megatons/second to be dissipated by a fairly small ship.

But these practical issues can be ignored for fictional purposes.

The ramjet proposal, BTW, is a possible source of additional mass for the ship, as you point out, but it has drawbacks. Remeber that the interstellar medium is coming in towards you at hyper-relativistic velocities, and when gamma >> 1, most of the incoming energy will be due to the velocity of the interstellar hydrogen, only a small fraction of it (the energy flux) will be due to the rest mass of the hydrogen.

You'll probably have to sweep it out of the way to avoid being thorougly fried but it'll be hard to turn a "net profit" in terms of the rocket's energy budget.

Last edited by a moderator: May 1, 2017
10. Sep 15, 2004

### Minty

Hmm, it would seem that all in all the fuel issue is not one that can be resolved simplistically. I'll write some software and get some simulations running to see how it hangs together.

I may have to decide between fudging the science to get useful journey times or falling back on the ark ship principle and accept a different on-board culture from that I was trying to build a plot around. Still, thats part of the fun in writing this stuff

Thanks to all for their contributions to date.

Minty

11. Sep 29, 2004

### chifos

how bout a ship powerd by eletromagntic waves (light radio ways ect...) this might work if the proton has momentem because if we do this the ship can go nearly at the speed of light you guys might aready heard about the space ship or satilite the will spin around the sun as all the proton are hit the ship it speeds up the ship then finally the ship will go fast enough to get out of the suns gravity after that it back to good old fuel to make the ship turn or stop there is my version of the ship be powered by lights all this ship need is eletricity and fuel
P.S the ship should be made out of a refletive materale so it wont aboserve the light to turn it into heat

12. Apr 20, 2011

### pip1974

Just ran into this thread, I know it's a bit old but there are some misconceptions here about what the space ship will experience in terms of particles coming towards the spaceship. The only relevant quantity is the acceleration of the ship, not it's velocity relative to the origin. Remember at any point you can turn the engines off and the space ship can be considered to be stationary in it's own frame of reference which is jut as valid as any other. It may be moving away from earth at an incredible speed but it's just as valid to say earth is moving away at that speed. Which means that hydrogen atoms or any other particles crashing into the spaceship are of no more or less concern than the same thing happening if it was orbiting earth.
Also, travelling at speeds near the speed of light wouldn't look any different to any other speed from your spaceship window, even if you look sideways! It's exactly the same in fact as not moving at all - just like any other speed. No matter how fast you go, light reaching you from any direction still comes towards you at the speed of light.

13. Apr 20, 2011

### cosmik debris

No this is not correct, if you are traveling at high speed you may run into clouds of interstellar gas or other matter. The kinetic energy of the atoms or sub-atomic particles will smash through the hull of your ship or generate x-rays and/or gamma rays from the materials in the hull. Whether you view this as the matter traveling at relativistic speed or your ship doesn't alter the kinetic energy relationship between the two.

14. Apr 20, 2011

### JesseM

It's true that you can consider either frame to be at rest, but the point is that there is an interstellar medium which is more or less at rest relative to the galaxy, so while the basic laws of physics are the same in every frame, if you are traveling at relativistic speed relative to the galaxy then in your frame there will be huge numbers of hydrogen atoms moving at relativistic velocities, much more so than in the rest frame of the Earth.

15. Apr 20, 2011

### DaveC426913

You are mistaken.

Yes, you can consider yourself stationary if you choose, but that only works in a figurative vacuum. In reality, you cannot ignore that

1] you are now being pelted with interstellar gas and dust that is moving at relativistic velocities,
2] every star in the galaxy is hurtling toward/past/away from you at relativistic velocities, they will be extremely compressed in their direction of travel (as will the entire galaxy),
3] All those stars and the light from them will exhibit very high doppler shifts, upshifting in front of you and downshifting behind you,
4] Same goes for any other freefloating EM radiation. It will be hardened coming toward you and softened going away.
- all things you would not experience in Earth orbit where your velocity wrt the surrounding galaxy effectively zero.

The idea that relativity implies you can consider yourself at rest is idealistic; in reality there are lots of ways you know you are moving and lots of effects from moving.

[ EDIT: Doh! Beaten twice! Press Save, THEN edit!]

Last edited: Apr 20, 2011