Is Faster-than-Light Travel Possible with Constant Acceleration?

[peter0302]

Yeah, your last point is exactly the biggest problem, I think. You don't want to carry your fuel with you, because it's heavy, but if you don't carry your fuel with you, then your relativistic mass increases requiring more fuel anyway. Bummer!

We need to learn to harness vacuum energy...

 

[JesseM]

I actually was serious. Fission fuel lasts a very long time.

A fission rocket would require a vastly larger fuel-to-payload ratio for a 1G trip to the nearest star than the one I quoted above for a 100% efficient rocket. Quoting something I wrote on this in another post a while ago:

This page gives Tsiolkovsky’s equation for the relation between change in velocity, payload mass and initial fuel mass:

Mpayload/mrocket = exp(-delta v/exhaust velocity)

This equation is a classical one which would need to be modified if delta v were close to the speed of light, but it can give you a sense of the huge amount of fuel needed if you just figure out the mass needed to get to some small fraction of light speed, like 0.01c, where the relativistic correction shouldn't be too big. They give the exhaust velocity for a chemical rocket as 4000 m/sec, and the exhaust velocity for a fission rocket as "12,000 m/sec (for solid-core nuclear thermal with oxygen augmentation), 40,000 m/sec (for nuclear electric propulsion), 100,000 m/sec (for more exotic and theoretical forms)". Using the 40,000 m/sec figure, to accelerate from being at rest wrt Earth to traveling at 0.01c relative to Earth (again, just calculating the answer using Newtonian physics without taking into account relativity, since the time dilation factor is very small at this speed), the equation tells us the mass of the rocket would have to be about e^75 times greater than the mass of the payload, which is about 3.5 * 10^32. If you want the answer in terms of acceleration, this thread gives the equation:

accleration* time = specific impulse * ln(mass ratio)

with each type of rocket having its own specific impulse (wikipedia's relativistic rocket page mentions that specific impulse is the same as exhaust velocity)...rearranging, this should mean the mass ratio needed to accelerate at 1G for some time t would be:

e^(9.8 m/s^2 * t / specific impulse)

If we again use 40,000 m/s for the specific impulse, this becomes:

e^(t * 0.000245/s)

So, to accelerate at 1G for 3 days (259200 seconds) would require a mass ratio of e^63.5, or a total initial rocket mass about 3.8 * 10^27 greater than the payload mass. This page mentions that for an antimatter rocket you might have an exhaust velocity of 10,000,000 m/s, so plugging that into the equation would give the mass ratio as:e^(t * 0.00000098/s)

This would make 1G acceleration for a few days much more manageable, but to accelerate for 1 year (31536000 seconds) you'd need a mass ratio of e^(30.9), so the rocket would have to be about 26 trillion times more massive than the payload--that's a lot of antimatter!

 

[peter0302]

Wow. Thanks. I mean, you hear about air force fighters accelerating to many-Gs, but you don't really realize how much energy that actually requires until you consider what it would cost to reach such accelerations for a very long time.

Maybe a slingshot around the sun is the answer. :)

 

[DaveC426913]

I actually was serious. Fission fuel lasts a very long time.

Well, so was I. Your next question would ostensibly have been: 'for what size faery?' To which I would have responded 'for what type of fuel?' And there you would have had the missing element in your question.

 

[peter0302]

Every time I think the anal-retentiveness of these forums cannot get any higher, I am proven wrong.

 

[DaveC426913]

Every time I think the anal-retentiveness of these forums cannot get any higher, I am proven wrong.

"I do not sink zat means what you sink it means."

 

[JesseM]

"I do not sink zat means what you sink it means."

Well, your response was humorously pedantic, and to be pedantic myself I'll note that anal-retentive is listed as a synonym.

 

[peter0302]

HAHAH. Thanks Dr. Freud.