…with the speed very close to the speed of light, to some place 1 light year away would it still take you 1 year (from your point of view) to get there?
No. It would take some fraction of 1 year from your POV depending on how close to c you were travelling. At the limit, as your speed tends to c your journey would tend to 0 seconds.
When you travel at relativistic speeds there is a length contraction such that to someone at rest relative to you, your ship would appear squashed along its direction of motion. However, from your POV your ship has its normal dimensions and it is everything else that has been squashed. So, to you, your destination is less than 1 light year away, hence there is no contradiction in your reference frame from travelling that distance in less than 1 year.
However, you’ll still need to accelerate and decelerate to and from 0.99999c – and that would take a while – so you’re not going to be able to make the trip in anything like overnight 
More to the point, if you pull 1 G (10m/s^2), it will take you something like a year just to reach your terminal velocity; you will have traveled roughly 0.005LY in that time.
Repeat for deceleration.
So – at least 2 years just for getting up to and down from speed, this assuming you don’t run into a limit of how close you can get to c during your acceleration.
Math:
1 G = 10m/s^2
Number of seconds required to reach 3x10^8 m/s (yes, that’s more than c; bear with me…) = 3x10^7 s = 347 days (so, call it one year)
Realized I mangled this sentence a bit and “someone at rest relative to you” is rather misleading.
What I mean is e.g. you get in your ship, put your foot down and the speedo reckons with your current amount of thrust you should be doing .9c. You look out your window and see an asteroid whizz by at .9c exactly opposite your direction of motion. That’s “something at rest relative to you”.
I always see this (for good reasons). But why constant acceleration? Like 0-60 in 7.5 vs 0-60 in 3.5? Ditto deceleration to 0: say you have super crash protection as well? Don’t come in for a soft landing, but smash into your landing place.
I have a sense that the total energy involved may wind up as a wash. But my senses in these things have been known to be wrong…
- Because the human body cannot pull too many G’s for a significant length of time (depending on the direction of the acceleration relative to your body, well trained fighter pilots with the best gear known to humanity will black out after 10 seconds of no more than about 10 G.
- Crash-land at 0.99999c? Your landing place will likely be… no more :dubious:
That’s only if you neglect relativity, such that v = at; including relativistic effects (which will obviously be very significant in this case), you will reach 0.99999c in about 5.92 years, having traveled roughly 216.7 light-years by then.
5.92 of whose years? The pilot, an observer on the planet from which they took off, some other frame of reference…?
Seems to me like it should take less time to reach “cruising” velocity (of 0.99999c) in the frame of reference of the space-ship, and I was acceleration (and distance) were held constant / measured in the FoR of the origin – and I got ~1 year to reach 0.99999c, not ~6
Of course, holding a constant acceleration if the FoR of the origin will require exponentially more energy as the velocity (in the FoR of the origin) increases… But I was ignoring that and assuming we had the energy somehow.
I remember hearing, it might have been here, that if you start with how fast the ship can accelerate and for how long, and use that to construct an imaginary flight plan ignoring any relativistic effects, the total duration of that flight plan will accurately predict your elapsed time from the pilot’s POV. You can’t actually travel faster than light, but as you reach relativistic speeds time will dilate, or distances foreshorten, to get you to your destination in the same subjective time as if you did.
The pilot’s.
The problem with the naive v = at approach is that you would eventually exceed c without any problem, which is a big relativity no-no. For an outside observer (on the planet from which they took off), it would take the ship about 216.7 years to reach 0.99999c.
You use constant acceleration because it makes the equations so much easier to solve.
I mean that literally. When you use a constant 1 g acceleration the equations simplify to a series of hyperbolic functions that an amateur can put into a spreadsheet and pump out answers. I know because I did this for a story I wrote many years ago.
T = (0.9687) sinh^ 1 (t/0.9687)
t = (0.9687) sinh (T/0.9687)
V = tanh (T/0.9687)
X = (0.9687) [cosh (1.032313T) 1]
X T t v
4.115 2.2685 4.9986
8.23 2.85 9.16 .9944492
15 3.39 15.94 .9981762
17.26 3.51 18.21
39 4.27 39.96 .997033
126.715 5.40 127.679 .9999712
126.847 5.401 127.81 .9999713
126.979 5.402 127.943 .9999713
127.111 5.403 128.075 .9999714
128.04 5.41 129.00 .9999718
299.04 6.2275 300 .9999948
7.316796 923.58585 .9999994
7.316797 923.5868 .9999995
7.3168 .9999995
7.317 .9999995
7.32 .9999995
7.329 935.295 .9999995
938 7.33 938.96 .9999995
7.3328 939
19230 10.258 19231.4 .9999999987
20938.39 10.340 20939 .9999999989
200980 12.531 200,939
2,000,986.9 14.757 2,000,939
That gets slightly out of alignment in the middle but just mentally line up the .999 column.
Anyway X is distance in light years; T is elapsed time as felt inside into spaceship; t is elapsed time as experienced on earth; V is percent of light speed.
You all should play with the equations inside a spreadsheet. The effects are mind-boggling.
*A reminder. Those numbers are are pure acceleration. To do a trip to a star with arrival speed of 0, treat the trip as two half-trips - one accelerating and one decelerating - and add the times together.
This is a plotline in Haldeman’s The Forever War and Card’s Ender’s Game.
In Ender’s Game,
Several characters age more slowly with respect to people on Earth because of their fast but sublight space travel.
This happens to
Mazer Rackham
Ender and his sis
It was the plotline is Robert Heinlein’s Time for the Stars, too, which influenced several generations of writers. And probably a thousand other stories. Mindboggling = good science fiction. We’ve even done a thread on it.
But the one I stole it from was Poul Anderson’s Tau Zero, which was nominated for a Hugo Award. That came shortly after using an interesting variation of the effect in the short story “Kyrie,” which was nominated for the Nebula Award.
I don’t think there’s much point in worrying about G forces. By the time we’re rocking .99c say we’ll probably be able to freeze humans into some kind of protective stasis or be cyborgs or whatever.
Not that acceleration will be unlimited, but I doubt somehow it will be limited to 9.8ms-2.
But the hypothetical is about how much time the pilot (for want of a better term) would experience… They’ve got to be awake for that.
I disagree. I think it’s more like the OP meant simply your reference frame.
But anyway, I wasn’t having a go at anyone just trying to make sure we weren’t all discussing a variable that isn’t very significant.
Oh SURE, if you want to do it SAFELY.
The mind-boggling parts are…? I notice immediately the tiny increases (the fantastic difficulty) of nudging V. Is that the main thing?
I meant that you should play with it yourself and put in your own numbers. This isn’t the spreadsheet; it’s a tiny slice that was in my story notes and easier to copy. Creating a trip and seeing what happens along the way is fascinating.
However, just these limited numbers show a lot.
This is answered here, for example. Look at the t column compared to the X column. After a short trip, around 39ly, the time elapsed on Earth becomes about 1 year more than light speed would take and stays that way for pretty much any trip inside our galaxy. So you can off the top of your head predict the duration of any 1 g voyage just by knowing the distance.
The shortening of time onboard is also amazing. At a constant 1 g you can “circumnavigate” the universe in a human lifespan. (That’s more or less the plot of Anderson’s Tau Zero.) There are other relativistic issues that come into play that aren’t apparent here, like the redshifting of the view. That’s what allows you to write so many stories on the theme.
And yes, the asymptotic rise of the 9s gets hypnotic until your spreadsheet refuses to display any more.