the Limitations of Intergalactic Travel

[eNtRopY]

It seems to me that the limitation of human space travel isn't time but energy. Applying Einstein's theory of relativity, we see that the time dilation effect would allow humans to travel to virtually anywhere in the universe within their own lifetime.

t' = t * gamma,

where, gamma = [1 - (v/c)2)]-1/2.

The problem of course is finding the limit of how much energy is needed to transport a human at high enough speeds for the length of the journey to become reasonable. I suppose that if there were a means of efficiently converted mass into energy then the limit is simply:

E = mfuel * c2.

The energy needed to move the ship transporting the human would of course be:

KE = mship * c2 * [gamma - 1].

So, E > KE tells us how much fuel would have to be consumed.

eNtRopY

[FZ+]

Applying Einstein's theory of relativity, we see that the time dilation effect would allow humans to travel to virtually anywhere in the universe within their own lifetime.
But I think there won't be much of an universe there when they arrive. The time they experience themselves will to t, not t'.
t' refers to the amount of time the observer (with relative velocity v) would see the ship experience with each second of their own time - in this case, the ship would be going slower than the speed experienced by the crew.

And c is still a speed limit relative to whatever destination they are looking for.

[eNtRopY]

Originally posted by FZ+
But I think there won't be much of an universe there when they arrive. The time they experience themselves will to t, not t'.
t' refers to the amount of time the observer (with relative velocity v) would see the ship experience with each second of their own time - in this case, the ship would be going slower than the speed experienced by the crew.


Sure there would be plenty of universe left to see. Remeber that although the traveller's time goes to zero, the stationary observers time is still only distance divided by the speed of light in a vacuum.

For example, in the extreme limit that a spaceship travels to Alpha Centari at the speed of light (which of course would consume an infinite amount of energy), the trip would be instaneous for the traveller but about 4.3 years for the stationary observer.

If you had a spaceship that could travel at speeds nearing the speed of light for extended periods of stationary observer time, I think the best strategy would be to look for baby solar systems and hope that by the time you get there some type of life will have evolved. Of course, the down-side to this is that you would never have the chance to see your friends or family again, as all of humanity as you knew it would be deceased before you even could think about it.

eNtRopY

[eNtRopY]

Originally posted by FZ+
And c is still a speed limit relative to whatever destination they are looking for.

No, c is constant in all reference frames.

eNtRopY

[Labguy]

On topic, but slightly off-topic, I don't think that near-c velocities will EVER be reached by any type of machine ever to be made by humans. Too much development time and way too high an energy requirement.

But, to keep the conversation going, I do think that the "effect" of c or c+ travel will be accomplished if we survive a few hundred thousand years or so. In December, 1903 the Wright brothers made their flight. Less than 66 years after that we landed on the moon. The rate of technological advancement was definitely exponential in the 20th century. Imagine going back in time to MIT in 1970 with a battery powered laptop computer. It would have easily sold for several million dollars.

If and when c+ travel is accomplished, I am convinced that it will be by some method not yet conceived, not even grazing black holes or through wormholes. The movie DUNE may not be too far off as to c+ travel. It will be by space-time "warping", folding, teleportation or some other odd method instead of building a neat ship and cranking up the power.

Any other ideas????

[Janus]

Originally posted by eNtRopY
It seems to me that the limitation of human space travel isn't time but energy. Applying Einstein's theory of relativity, we see that the time dilation effect would allow humans to travel to virtually anywhere in the universe within their own lifetime.

t' = t * gamma,

where, gamma = [1 - (v/c)2)]-1/2.

The problem of course is finding the limit of how much energy is needed to transport a human at high enough speeds for the length of the journey to become reasonable. I suppose that if there were a means of efficiently converted mass into energy then the limit is simply:

E = mfuel * c2.

The energy needed to move the ship transporting the human would of course be:

KE = mship * c2 * [gamma - 1].

So, E > KE tells us how much fuel would have to be consumed.

eNtRopY

Actuallly, the last formula you gave is just basically a modification of the formula from which E= mc² was originally derived:

E = mc²/(1-v²/c²)

Thus mc²(1/(1-v²/c²) -1) gives the value of the kinectic energy of an object moving at v.

The rub is, that in order to actually accelerate your ship through space you have to make use of a action-reaction engine.

In which case, you need to use the relativistic rocket equation

v = c *tanh(Ve/c * ln(MR))

In this case, Ve is the exhaust velocity and MR is the mass ratio (mass of the fueled ship/ mass of unfueled ship)

For a pure matter to energy conversion ship this means that we convert the fuel to photons, which we direct backwards to provide forward momentum.

To determine how much fuel we need to attain any given velocity, we re-arrange the formula to read

MR = etanh-1(v/c) * c/Ve

If Ve = c and we measure v is units of c we can reduce this to:

MR = etanh-1v

To reach .6c you would need a mass ratio of 2 (1 gram of fuel for every gram of payload.)

for .9c, a mass ratio of 4.259
.99c ---------------------- 14.1
.999c--------------------- 44.7
.9999c------------------- 141.4

Etc.

And that's assuming 100% efficiency; every photon produced in the reaction captured and directed straight backward.

[Janus]

Another point:
The mass ratios given in my last post only concern achieving the given velocity in the first place. You will also need to decelerate once you get to your destination.

That mean's in order to come to a stop from .999c you need 140.1 g of fuel for every gram of ship and cargo.

This compounds the problem, because this fuel is part of the payload you have to accelerate up to .999c in the first place. This means it actually takes 19628 g of fuel for every g of payload you actually want to deliver to the end point of the trip, if you are not just planning on doing a fly-by at .999c.

For actual intergalactic travel, consider the following example:

Andromeda is the nearest galaxy at 2,000,000 ly. Let's assume a 3 yr trip. (2yrs accelerating and decelerating and one year coasting.)

This means you would need to attain a velocity of 0.9999999999998749999999999921875c
for the coasting period.

To attain this Delta v you would need a mass ratio of 4000000. This is the mass ratio you would need to decelerate at the end.

Thus you would need 1.6*1013 g of fuel per gram of payload to complete the trip, or just about the mass of Deimos for every 100 kg of payload ( including the empty mass of the ship itself).

[schwarzchildradius]

if mf = mass of the fuel and ms = the mass of the ship, arent you forgetting that the fuel needs to be accelerated? seems like you need a dms/dt in there somewhere, but I ran through it anyway:
mfc2 > msc2(γ-1)
say you were to accelerate mass ms which must include mf at 9.8 m/s2 for a year (3.1563E7 sec)
Alexander's equation for finding relativistic velocity under constant acceleration was:
v = c tanh (at/c)
tanh a combination of exponentials of (at/c)
I found v=2.322E8 m/s or 60% c after 1 year of acceleration, γ = 1.5793
so the mass of the fuel has to be at least 58% the mass of the fuel + ship by
mf = ms(γ -1) if all the mass of the fuel is converted into energy.
and it gets worse from there (infinitely) as you approach c.

[eNtRopY]

Originally posted by schwarzchildradius
if mf = mass of the fuel and ms = the mass of the ship, arent you forgetting that the fuel needs to be accelerated?

No, I didn't forget that.

mship = mfuel + munfueled ship

I was just presenting some very general equations, and I didn't feel like typing out all the details.

eNtRopY

[eNtRopY]

Originally posted by Janus
Thus you would need 1.6*1013 g of fuel per gram of payload to complete the trip

Okay, that's the number I was looking for.

eNtRopY

[eNtRopY]

Does anyone know to what speed a ship could be accelerated if one were to slingshot the schwarzchild radius of a black hole?

eNtRopY

[Integral]

Originally posted by eNtRopY
Does anyone know to what speed a ship could be accelerated if one were to slingshot the schwarzchild radius of a black hole?

eNtRopY


For a body traveling with respect to, say your Black Hole, there are 2 possible non capture orbits. You are either parabolic or hyperbolic, in either of these the velocity of approach = velocity of exit. You gain NO velocity simply by passing near something.

Ok, what is the slingshot that we hear about near Jupiter. The velocity a satilite picks up as it passes near Jupiter is Jupiters ORBITAL velocity. This is the slingshot, not the mere fact that you pass nearby. Thus, the exit velocity of something passing near a BH would depend on the velocity of the BH, with respect to what?

[huxxar]

"If and when c+ travel is accomplished, I am convinced that it will be by some method not yet conceived. It will be by space-time "warping", folding, teleportation or some other odd method instead of building a neat ship and cranking up the power"

I tend to agree with you. I am also thinking that while superluminal is one prerequisite for inter planetary or inter galactic travel, perhaps the nature of our bodies and spacecrafts needs modification. While most physicists will probably laugh at what I am about to suggest, I think we need to convert our physical forms into energy or some type of zero mass substance before long range interstellar travel can take place. That will not only take out the kinetic energy problem as we approach c, but also drastically increases our life span to perhaps a few million years.

I have come across the "Negative Energy" phenomenon postulated by Paul Dirac but didn't really understand it. I wonder how a body of negative energy will behave at c or near c. Perhaps the physicists among us can shed some light on this matter?

[The Dagda]

I think the only way that c will be exceeded is by sidestepping it. Ie bending space, so the distances become closer, hyperspace sounds a little out there but can we bend space so much it "breaks"? if we could get a light year down to a thousandth or a millionth of a light year by bending the space in between, then maybe we'll effectively travel distances faster than would be possible at c or greater. Mind you what do I know, we may in 1 million years just beam ourselves there. Who really knows...