# Can someone calculate time neede to accelerate to light speed for me? **URL:** \ **Category:** Factual Questions\ **Created:** [July 5, 2003, 3:00am UTC](https://boards.straightdope.com/t/can-someone-calculate-time-neede-to-accelerate-to-light-speed-for-me/186334 "2003-07-05T03:00:27Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Whack-a-Mole](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/whack-a-mole/32/141_2.png) [@Whack-a-Mole](https://boards.straightdope.com/u/Whack-a-Mole)\ **Post date:** [July 5, 2003, 3:00am UTC](https://boards.straightdope.com/t/can-someone-calculate-time-neede-to-accelerate-to-light-speed-for-me/186334/1 "2003-07-05T03:00:27Z")
Ok…not light speed since that’s impossible but let’s say 99.9% light speed. For the sake of simplicity assume a constant 1g acceleration throughout the process with instant on/off acceleration. If you’re up to it I’d like an answer for how long it’d take to reach 99.9% light speed under a 3g acceleration (I’m curious if it is a straight three times faster than 1g or if relativistic effects complicate the issue)? On a related note I know that mass increases as you get close to light speed so the assumption is it gets harder to push your spaceship the faster it goes. However, doesn’t your reaction mass increase in mass as well thus providing you with more thrust? Assume we have an antimatter propulsion system (for 100% coversion of mass to energy) does gaining mass have any effect on acceleration at all (since the antimatter is gaining mass too thus providing more energy)? ---
**Author:** ![Q.E.D](https://avatars.discourse-cdn.com/v4/letter/q/51bf81/32.png) [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)\ **Post date:** [July 5, 2003, 3:27am UTC](https://boards.straightdope.com/t/can-someone-calculate-time-neede-to-accelerate-to-light-speed-for-me/186334/2 "2003-07-05T03:27:28Z")
The formula to calculate acceleration is a = (v[sub]2[/sub] - v[sub]1[/sub]) [sup].[/sup] t, where a is acceleration, v[sub]2[/sub] and v[sub]1[/sub] are the final and starting velocities, respectively, and t is time. Thus, given a and needing to calculate t, we use t = (v[sub]2[/sub] - v[sub]1[/sub]) / a. Using your values, I get 118.02 days to reach c at 3 g of acceleration. ---
**Author:** ![sailor](https://avatars.discourse-cdn.com/v4/letter/s/a587f6/32.png) [@sailor](https://boards.straightdope.com/u/sailor)\ **Post date:** [July 5, 2003, 3:31am UTC](https://boards.straightdope.com/t/can-someone-calculate-time-neede-to-accelerate-to-light-speed-for-me/186334/3 "2003-07-05T03:31:02Z")
Q.E.D. I am pretty sure that is not right because that formula only works for small speeds. You can’t just add speed like that or you could exceed C after 118 days. ---
**Author:** ![bdgr](https://avatars.discourse-cdn.com/v4/letter/b/a87d85/32.png) [@bdgr](https://boards.straightdope.com/u/bdgr)\ **Post date:** [July 5, 2003, 3:32am UTC](https://boards.straightdope.com/t/can-someone-calculate-time-neede-to-accelerate-to-light-speed-for-me/186334/4 "2003-07-05T03:32:07Z")
Time from the point of view of someone onboard the spaceship, or from the point of view of a stationary observer? ---
**Author:** ![Whack-a-Mole](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/whack-a-mole/32/141_2.png) [@Whack-a-Mole](https://boards.straightdope.com/u/Whack-a-Mole)\ **Post date:** [July 5, 2003, 3:37am UTC](https://boards.straightdope.com/t/can-someone-calculate-time-neede-to-accelerate-to-light-speed-for-me/186334/5 "2003-07-05T03:37:27Z")
> [@](#): > > \*Originally posted by bdgr \* > \*\*Time from the point of view of someone onboard the spaceship, or from the point of view of a stationary observer? \*\* Good point…stationary observer I think as that would be the longer time. As perceived aboard the spaceship it’d be shorter but I don’t think it’d be all that much. IIRC time dilation only really becomes serious above .85 or .9 c. It exists before that but the dilation is so small that I think it can be safely ignored. ---
**Author:** ![Q.E.D](https://avatars.discourse-cdn.com/v4/letter/q/51bf81/32.png) [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)\ **Post date:** [July 5, 2003, 3:38am UTC](https://boards.straightdope.com/t/can-someone-calculate-time-neede-to-accelerate-to-light-speed-for-me/186334/6 "2003-07-05T03:38:15Z")
> [@](#): > > \*Originally posted by sailor \* > \*\*Q.E.D. I am pretty sure that is not right because that formula only works for small speeds. You can’t just add speed like that or you could exceed C after 118 days. \*\* This is assuming constant acceleration, per the OP. In reality as you approach C. the energy needed to accelerate also increases, approaching infinity as V approaches c. ---
**Author:** ![Whack-a-Mole](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/whack-a-mole/32/141_2.png) [@Whack-a-Mole](https://boards.straightdope.com/u/Whack-a-Mole)\ **Post date:** [July 5, 2003, 3:41am UTC](https://boards.straightdope.com/t/can-someone-calculate-time-neede-to-accelerate-to-light-speed-for-me/186334/7 "2003-07-05T03:41:16Z")
> [@](#): > > \*Originally posted by sailor \* > \*\*Q.E.D. I am pretty sure that is not right because that formula only works for small speeds. You can’t just add speed like that or you could exceed C after 118 days. \*\* Clearly we can never exceed light speed no matter how hard we try but your point stands and is the reason for my question. I am assuming the acceleration to relativistic velocities isn’t as simple as doing the same thing at more sedate speeds. I know you can’t simply add two relativistic velocities together (such that two ships going in opposite directions at .9c does not equate to a closure rate of 1.8c). I figure you have to adjust something for acceleration as well (but I’m just guessing). ---
**Author:** ![Terminus\_Est](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/terminus_est/32/3087_2.png) [@Terminus\_Est](https://boards.straightdope.com/u/Terminus_Est)\ **Post date:** [July 5, 2003, 3:54am UTC](https://boards.straightdope.com/t/can-someone-calculate-time-neede-to-accelerate-to-light-speed-for-me/186334/8 "2003-07-05T03:54:19Z")
The formula for relativistic acceleration can be found on [Scienceworld](http://scienceworld.wolfram.com/physics/Acceleration.html). I’m too lazy to do the actual calculation. I’ll just point out that there is indeed an adjustment for “[relativistic gamma](http://scienceworld.wolfram.com/physics/RelativisticGamma.html)”. This doesn’t really come into play, however, until you reach velocities exceeding 0.8_c_. ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [July 5, 2003, 3:58am UTC](https://boards.straightdope.com/t/can-someone-calculate-time-neede-to-accelerate-to-light-speed-for-me/186334/9 "2003-07-05T03:58:39Z")
For my sins, I once had to calculate this. For 1 g acceleration: 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] Capital T is shipboard time elapsed. small t is Earth time elapsed X is distance in light years V is velocity as a percentage of C For V = 0.9999, I get T = 4.797, and t = 68.5 years. 99.99% C is a fantastically huge velocity. But I don’t know the transformation to 3 g. ---
**Author:** ![Q.E.D](https://avatars.discourse-cdn.com/v4/letter/q/51bf81/32.png) [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)\ **Post date:** [July 5, 2003, 4:01am UTC](https://boards.straightdope.com/t/can-someone-calculate-time-neede-to-accelerate-to-light-speed-for-me/186334/10 "2003-07-05T04:01:39Z")
> [@](#): > > \*Originally posted by Exapno Mapcase \* > \*\*But I don’t know the transformation to 3 g. \*\* On inspection of your formulae, it is a linear relationship, and you can therefore multiply by 3. ---
**Author:** ![Whack-a-Mole](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/whack-a-mole/32/141_2.png) [@Whack-a-Mole](https://boards.straightdope.com/u/Whack-a-Mole)\ **Post date:** [July 5, 2003, 4:09am UTC](https://boards.straightdope.com/t/can-someone-calculate-time-neede-to-accelerate-to-light-speed-for-me/186334/11 "2003-07-05T04:09:42Z")
> [@](#): > > \*Originally posted by Exapno Mapcase \* > **For V = 0.9999, I get T = 4.797, and t = 68.5 years. 99.99% C is a fantastically huge velocity.** Yipes! Not being an expert (essentially no clue) I hate to a call into question your answer but 68 years? I have a super dim recollection from somewhere that the acceleration was on the order of weeks/months…not decades. Are you sure we’re talking about the same thing (1g constant acceleration througout the process)? Also, any comments on the issue of your reaction mass gaining mass along with the mass of your ship to counteract how hard it is to push the thing? ---
**Author:** ![Whack-a-Mole](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/whack-a-mole/32/141_2.png) [@Whack-a-Mole](https://boards.straightdope.com/u/Whack-a-Mole)\ **Post date:** [July 5, 2003, 4:12am UTC](https://boards.straightdope.com/t/can-someone-calculate-time-neede-to-accelerate-to-light-speed-for-me/186334/12 "2003-07-05T04:12:47Z")
> [@](#): > > \*Originally posted by Terminus Est \* > \*\*The formula for relativistic acceleration can be found on [Scienceworld](http://scienceworld.wolfram.com/physics/Acceleration.html). I’m too lazy to do the actual calculation. \*\* I don’t blame you. I figured I might give it a go and checked the website but…whoooosh…not a chance with my math background. ---
**Author:** ![chorpler](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chorpler/32/2888_2.png) [@chorpler](https://boards.straightdope.com/u/chorpler)\ **Post date:** [July 5, 2003, 7:23am UTC](https://boards.straightdope.com/t/can-someone-calculate-time-neede-to-accelerate-to-light-speed-for-me/186334/13 "2003-07-05T07:23:00Z")
68 years is the time elapsed on Earth, which is much longer than the time elapsed on the ship … which is more like 4.8 years. Slight hijack here, but I have a question somewhat related to this: a few years ago, I calculated (using the non-relativistic formula for velocity from acceleration) that you would reach light speed in under a year at a constant 1g of acceleration. Obviously it doesn’t quite work out that way, but it got me thinking. The reason you would accelerate at 1g would be to provide a normal environment for the people on the ship. But obviously, using the standard nonrelativistic _v_=_a_t formula, there’s a fundamental limit on how long you can accelerate at 1g – once you accelerate to within 9.8m/s of c, you can’t keep accelerating at 9.8m/s[sup]2[/sup]. So what I wondered was, once you get beyond (c-9.8m/s), can you still produce a 1g gravitational field by acceleration alone? Or would the gravity the crew of the ship experiences grow smaller and smaller as the ship velocity asymptotically approaches c? ---
**Author:** ![John\_Kentzel-Griffin](https://avatars.discourse-cdn.com/v4/letter/j/ccd318/32.png) [@John\_Kentzel-Griffin](https://boards.straightdope.com/u/John_Kentzel-Griffin)\ **Post date:** [July 5, 2003, 9:52am UTC](https://boards.straightdope.com/t/can-someone-calculate-time-neede-to-accelerate-to-light-speed-for-me/186334/14 "2003-07-05T09:52:54Z")
Yes you can still produce a 1g gravitational field. Remember velocity is relative. If you are going c-9.8m/s relative to me, you are going 0 relative to you. ---
**Author:** ![Varulv](https://avatars.discourse-cdn.com/v4/letter/v/82dd89/32.png) [@Varulv](https://boards.straightdope.com/u/Varulv)\ **Post date:** [July 5, 2003, 10:24am UTC](https://boards.straightdope.com/t/can-someone-calculate-time-neede-to-accelerate-to-light-speed-for-me/186334/15 "2003-07-05T10:24:44Z")
mm, i’m no genius, but i was under the impression that the timedifferences would only be appearing to differ? i mean, it’s not like you are actually doing timetravel, sure the light takes \ from the ship to earth, so you are looking at the past, but it still happened earlier. or did i miss something vital in my understanding of the world? so, how can you at _less_ than lightspeed reach 68 years difference from only 4.8 years of acceleration? ---
**Author:** ![chorpler](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chorpler/32/2888_2.png) [@chorpler](https://boards.straightdope.com/u/chorpler)\ **Post date:** [July 5, 2003, 10:38am UTC](https://boards.straightdope.com/t/can-someone-calculate-time-neede-to-accelerate-to-light-speed-for-me/186334/16 "2003-07-05T10:38:15Z")
> [@](#): > > \*Originally posted by Varulv \* > **mm, i’m no genius, but i was under the impression that the timedifferences would only be appearing to differ? > i mean, it’s not like you are actually doing timetravel, sure the light takes \ from the ship to earth, so you are looking at the past, but it still happened earlier. > or did i miss something vital in my understanding of the world?** At relativistic speeds, time dilation occurs. The people on the ship would experience 4.79 years, and during the same period 68 years would go by on earth. ---
**Author:** ![Varulv](https://avatars.discourse-cdn.com/v4/letter/v/82dd89/32.png) [@Varulv](https://boards.straightdope.com/u/Varulv)\ **Post date:** [July 5, 2003, 11:35am UTC](https://boards.straightdope.com/t/can-someone-calculate-time-neede-to-accelerate-to-light-speed-for-me/186334/17 "2003-07-05T11:35:34Z")
so if i had a couple of kids and left for some ten year journey out in space my kids could be 120 years old when i came home, but i’d have aged 10 years(or somesuch, based on the speed and whatnot of course)? i’m not being sarcastic, i’m really curious, it seems like theres some accepted truth about it, i just cant see what speed would have to do with time. if i travel at 0.9999 times the speed of light from london to new york i would expect a fraction of a second to pass both on my clock and in new york 🙂 ---
**Author:** ![chorpler](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chorpler/32/2888_2.png) [@chorpler](https://boards.straightdope.com/u/chorpler)\ **Post date:** [July 5, 2003, 11:44am UTC](https://boards.straightdope.com/t/can-someone-calculate-time-neede-to-accelerate-to-light-speed-for-me/186334/18 "2003-07-05T11:44:20Z")
> [@](#): > > \*Originally posted by Varulv \* > **so if i had a couple of kids and left for some ten year journey out in space my kids could be 120 years old when i came home, but i’d have aged 10 years(or somesuch, based on the speed and whatnot of course)?** That’s exactly right. If you want to read more about it, do a google for “twin paradox” and you’ll find a whole lot of information. And there’s plenty of fiction where this time dilation effect comes into play as well. One of my favorites is Larry Niven’s _A World Out of Time_, where the protagonist travels to the galactic core and back, starting as a young man and returning as an old man, but over two million years have passed on earth. ---
**Author:** ![sailor](https://avatars.discourse-cdn.com/v4/letter/s/a587f6/32.png) [@sailor](https://boards.straightdope.com/u/sailor)\ **Post date:** [July 5, 2003, 12:17pm UTC](https://boards.straightdope.com/t/can-someone-calculate-time-neede-to-accelerate-to-light-speed-for-me/186334/19 "2003-07-05T12:17:40Z")
Varulv, I recommend [What is Relativity?](http://www.amazon.com/exec/obidos/ASIN/0486428060/bridgebooks/103-4285326-0235014). It is only about 70 short pages and explains it quite well. ---
**Author:** ![Varulv](https://avatars.discourse-cdn.com/v4/letter/v/82dd89/32.png) [@Varulv](https://boards.straightdope.com/u/Varulv)\ **Post date:** [July 5, 2003, 2:07pm UTC](https://boards.straightdope.com/t/can-someone-calculate-time-neede-to-accelerate-to-light-speed-for-me/186334/20 "2003-07-05T14:07:15Z")
yea i’ve read some books which include time dilation, but they havent given a satisfying exlpanations ☹ looked up some stuff about it, i found alot of, “this is how it is”, but nothing about the whys or hows. if i understood it correctly, it isnt the speed difference, but rather the acceleration that causes the effect? i just cant get my head around the fact that a trip to alpha centauri(4.8 light years or so?) at 99.9% the speed of light would take more than 5 years earth time(conviently accelerating from 0 to max speed in 2 sec of course) hmm, i’m repeating myself! bah, i hate not understanding things, i dont wanna get a degree to get it, but if i have to, i will! 😛 [Next page](https://boards.straightdope.com/t/can-someone-calculate-time-neede-to-accelerate-to-light-speed-for-me/186334.md?page=2)