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The recent discovery of HD85512b only 36 light years from Earth has promising attributes to harbor life. Assuming we want to travel there, we cannot instantaneously jump to light speed, (StarTrek euphemisms aside), we'll have to accelerate the conventional way by building momentum.

Now, how long would it take to first reach the speed of light at a rate of acceleration that wouldn't kill the occupants of the spacecraft ? (We can't continuously accelerate at 4g's for prolonged periods because it would eventually kill you from physical stress.) Secondly, then given the time to accelerate to the speed of light, how long would it then take to travel the remaining distance and reach our new utopia ?

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I just tried a naive Newtonian calculation that involves accelerating at $g$ for half the trip, then turning the ship around and decelerating at $g$. I ended up going faster than light, so this must be a relativistic calculation. In short, you could probably get close to $c$, in which case the journey would take a smallish multiple of 36 years. –  Warrick Sep 14 '11 at 7:53
    
You didn't allow time for re-fuelling and oil changes and so on. I predict those things will at least double your transit time and that isn't allowing for construction and whatnot. I recommend you stay at home. –  user23117 Apr 14 '13 at 4:49
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Accellerating at g and turning your spacecraft around halfway through your journey will get you to the Moon in 3 hours and to Mars in 2 to 3 days. –  Jitter Nov 12 '13 at 19:29

3 Answers 3

up vote 18 down vote accepted

At constant 1 g acceleration half-way through, then constant 1 g deceleration the remaining half, it takes 7 years in rocket time, 38 years in Earth time:

http://www.cthreepo.com/lab/math1.shtml

Scroll down to Long Relativistic Journeys and enter your data.

To the Andromeda Galaxy (2.5 mil ly) it's 29 years in rocket time! :)

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Great link. So would the occupants age in Earth time or rocket time ? Maybe periodic acceleration would be improve trip time ? I noticed that increasing the acceleration shorten's trip time, but does have much impact on Earth Time. Just realising how little I know about physics.. Should not have done accounting in highschool. –  giulio Sep 14 '11 at 23:31
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For the astronauts, it's rocket time, always. You can't shorten the trip time unless you're willing to undergo higher acceleration. Earth time doesn't change much no matter how much you accelerate, because the rocket goes at almost the speed of light most of the time. The rocket time does get shorter, though, if you're willing and able to put up with the crushing force. –  Florin Andrei Sep 15 '11 at 0:23
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@FlorinAndrei: It gets shorter relative to earth but for the rocket and the people inside, everything will be just fine. They have other things to worry about though, for instance, to avoid being turned into cosmic goo by near-light speed protons hitting them on the way. –  Jus12 Sep 27 '11 at 21:02
    
So you only need fuel for seven years? Yay! –  mart Jul 13 '12 at 11:52
    
Sorry the link is dead down. –  ja72 Apr 14 '13 at 6:23

Inspired by David Zaslavsky's words that "this site is not really about what existing technology allows or doesn't allow":-), I'd like to discuss a possibility that is downright outrageous from the point of view of technology, but seems feasible from the point of view of physics. What maximum constant acceleration can a human survive? According to another answer, it's 4g. Maybe so. Maybe somewhat more. Maybe somewhat less. That does not matter much. However, it is my understanding that there is one exception: if acceleration is caused by gravity, the latter acts in the same way on all parts of the human body. Thus, it does not cause relative displacements and does not kill. Moreover, according to the equivalence principle, free fall is felt like inertial movement (as far as I know, an accelerometer in free fall registers zero acceleration). Therefore, theoretically, we could boost a huge celestial body (say, the Sun) and let a human freely fall on it. I guess the free fall acceleration near the surface of the Sun is about 28g, so if we boost the Sun with such acceleration, the human will freely fall on it as long as the Sun is boosted (if he/she is moving in the same direction as the Sun) without being killed by the acceleration (he/she will need protection from Sun's radiation, but will be protected from meteorites by the Sun). Thus, the flight duration can be decreased dramatically. Raising funds for such a journey is no easy task though:-)

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Since you're doing the thought experiment anyway, there are at least two important engineering considerations that limit this more severely than what accelerations humans can stand (which is trivially solvable with robots anyway):

(1) The energy needs would be huge. What percentage of the total mass would have to be fuel in order to supply enough energy to accelerate and decelerate the payload 36 ly at any acceleration worth doing? I haven't done the calculations, but the engineering case is daunting: (fuel+rocket+payload) all need to be accelerated, fuel may be decreasing as you go, and maybe rocket is if you have a staged spacecraft. Is it even possible, given strength limits of any known materials, to have a few-human-and-life-support sized payload, a big enough rocket to house that and the fuel, and make the equations work out? That very well may be the limiting factor to interstellar flight, regardless of the technology.

(2) If you go fast enough, even a dust-sized micrometeorite would cause fatal damage. I think I've read somewhere that 10% light speed makes hitting a dust grain like a nuclear bomb. So there may be a "speed limit" much lower than light, above which would simply be too dangerous to travel.

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Good observations, all the SciFi we are fed makes us blind to the critical practicalities of it all.. –  giulio Sep 20 '11 at 1:33
    
I have attributed a new question to you physics.stackexchange.com/q/26403 –  giulio Sep 20 '11 at 1:51
    
you could ride on the wavefront of a relativistic jet, which would address 1). Not so much for 2), which would probably be even worse at the beginning of the acceleration phase (due to relativistic gamma rays) physics.stackexchange.com/a/31916/955 –  lurscher Jul 12 '12 at 21:25
    
The mention of 'physical stress' presupposes organic cargo, and puts a limit on the acceleration, and perhaps safe upper velocity of the vehicle. The fuel, however, could probably sustain higher acceleration & be transported at much higher velocities - either to a transit location scouted earlier by a similar high velocity scout, or simply to catch-up with the main vehicle along it's route. –  Everyone Oct 7 '12 at 19:48
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@lurscher I would like to point out that the wording "relativistic gamma rays" is fairly problematic ;) –  Alan Rominger Oct 7 '12 at 19:56

protected by Qmechanic Nov 12 '13 at 19:19

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