# Anyone remember their calculus? Time to get to Alpha Centauri? **URL:** \ **Category:** Factual Questions\ **Created:** [December 31, 2011, 7:16pm UTC](https://boards.straightdope.com/t/anyone-remember-their-calculus-time-to-get-to-alpha-centauri/607967 "2011-12-31T19:16:08Z")\ **Posts on this page:** 9\ **Page:** 2
**Author:** ![md2000](https://avatars.discourse-cdn.com/v4/letter/m/73ab20/32.png) [@md2000](https://boards.straightdope.com/u/md2000)\ **Post date:** [December 31, 2011, 9:52pm UTC](https://boards.straightdope.com/t/anyone-remember-their-calculus-time-to-get-to-alpha-centauri/607967/21 "2011-12-31T21:52:58Z")
Just eyeballing the chart in the link - I guessed about 2.75 years to halfway earth time; maybe about 1.5 years ship time. It’s somewhere between 1 year and 2 years ( 0.56 lightyears and 2.90 ly) ship time. So double that for the trip out. Repeat for return. The next fun trick is to pick a fuel (deuterium fusion, hydrogen fusion, pure matter conversion?) and guess what proportion of the vessel has to be fuel to make the trip. ---
**Author:** ![Terr](https://avatars.discourse-cdn.com/v4/letter/t/839c29/32.png) [@Terr](https://boards.straightdope.com/u/Terr)\ **Post date:** [December 31, 2011, 9:55pm UTC](https://boards.straightdope.com/t/anyone-remember-their-calculus-time-to-get-to-alpha-centauri/607967/22 "2011-12-31T21:55:33Z")
> [@md2000](#): > > Just eyeballing the chart in the link - > I guessed about 2.75 years to halfway earth time; maybe about 1.5 years ship time. > It’s somewhere between 1 year and 2 years ( 0.56 lightyears and 2.90 ly) ship time. > So double that for the trip out. Repeat for return. > > The next fun trick is to pick a fuel (deuterium fusion, hydrogen fusion, pure matter conversion?) and guess what proportion of the vessel has to be fuel to make the trip. The link I gave does all that for pure matter conversion. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [December 31, 2011, 9:58pm UTC](https://boards.straightdope.com/t/anyone-remember-their-calculus-time-to-get-to-alpha-centauri/607967/23 "2011-12-31T21:58:28Z")
> [@These are my own pants](#): > > 1. For someone on Earth’s point of view it would take the spacehip 290 million years to reach Alpha Centauri. Back of the envelope calculation: If it takes you 300 million years to travel 4.5 light years, your average speed is about 10 miles per hour. I don’t know much physics, but I’m pretty sure you don’t have to accelerate at 1 g for very long to get going that fast. ---
**Author:** ![Jamicat](https://avatars.discourse-cdn.com/v4/letter/j/c67d28/32.png) [@Jamicat](https://boards.straightdope.com/u/Jamicat)\ **Post date:** [December 31, 2011, 10:14pm UTC](https://boards.straightdope.com/t/anyone-remember-their-calculus-time-to-get-to-alpha-centauri/607967/24 "2011-12-31T22:14:09Z")
1g acceleration up to C for half the distance, then 1g deceleration for the rest of the distance. e.g., 1g for a distance to 2+1g,then 3+1g, 4+1g, ect… I don’t know the speed ratio of 1g in a vacuum. :dubious: ( I read someplace, more or less 100k years a while back, at that rate, but I don’t do calculus) ---
**Author:** ![CanTak3](https://avatars.discourse-cdn.com/v4/letter/c/f14d63/32.png) [@CanTak3](https://boards.straightdope.com/u/CanTak3)\ **Post date:** [January 1, 2012, 2:12am UTC](https://boards.straightdope.com/t/anyone-remember-their-calculus-time-to-get-to-alpha-centauri/607967/25 "2012-01-01T02:12:48Z")
> [@Terr](#): > > [http://www.phys.ncku.edu.tw/mirrors/physicsfaq/Relativity/SR/rocket.html](http://www.phys.ncku.edu.tw/mirrors/physicsfaq/Relativity/SR/rocket.html) > > According to it, at 1g accel/decel it will take 3.6 years for you to get to the star 4.3 light years away. On Earth, about 5.2 years will pass, if I calculated it correctly. > > Double the numbers for getting back, obviously. Terr, thanks for that link. It explains what I was wanting to know. ---
**Author:** ![JWT\_Kottekoe](https://avatars.discourse-cdn.com/v4/letter/j/3ec8ea/32.png) [@JWT\_Kottekoe](https://boards.straightdope.com/u/JWT_Kottekoe)\ **Post date:** [January 1, 2012, 6:11am UTC](https://boards.straightdope.com/t/anyone-remember-their-calculus-time-to-get-to-alpha-centauri/607967/26 "2012-01-01T06:11:46Z")
I’ve always enjoyed the coincidence that one g times one year is very close to the speed of light (accurate to about 3 percent as shown above), thus without doing any math, it is obvious that the time to go to Alpha Centauri is only a bit larger than 4.4 years as viewed from Earth. ---
**Author:** ![standingwave](https://avatars.discourse-cdn.com/v4/letter/s/9de0a6/32.png) [@standingwave](https://boards.straightdope.com/u/standingwave)\ **Post date:** [January 1, 2012, 7:18am UTC](https://boards.straightdope.com/t/anyone-remember-their-calculus-time-to-get-to-alpha-centauri/607967/27 "2012-01-01T07:18:19Z")
> [@JWT\_Kottekoe](#): > > I’ve always enjoyed the coincidence that one g times one year is very close to the speed of light (accurate to about 3 percent as shown above), thus without doing any math, it is obvious that the time to go to Alpha Centauri is only a bit larger than 4.4 years as viewed from Earth. I’ve always felt that meant that humans (or at least Earthlings) were destined to travel to the stars. 😃 But it should be noted that while 1g = 1.03 lyr/yr^2, accelerating at 1g for one year only gets you to 0.77c because of SR effects. But it is handy for calculations I’ve also used the rather tortureous 1g = 22mph/s for estimating air time (weightlessness) on roller coasters and other thrill rides based upon their velocities. For example, a ride like Superman at SFMM shoots you straight up at 100 mph where you coast to a stop and fall backwards. In theory that could get you eight seconds of air time, four seconds falling up and four seconds falling down. In practice it’s about seven seconds. ---
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [January 1, 2012, 9:09am UTC](https://boards.straightdope.com/t/anyone-remember-their-calculus-time-to-get-to-alpha-centauri/607967/28 "2012-01-01T09:09:22Z")
Here’s a cite I picked up from another thread on star-travel several weeks ago. [The Twin Paradox](http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html) As I recall from reading it (several weeks ago), this is not particularly technical or heavy on the math, and it doesn’t work through the detailed arithmetic, but it does give a fairly clear but non-technical discussion of how relativistic interstellar travel works. It focuses on the question: If Stella travels to a distant star and back at near-light speeds, and she and earthbound Terence keep an eye on each other during the trip, which of them will see the other’s clock slowed down relative to his/her own, and why? ---
**Author:** ![Jinx](https://avatars.discourse-cdn.com/v4/letter/j/c6cbf5/32.png) [@Jinx](https://boards.straightdope.com/u/Jinx)\ **Post date:** [January 1, 2012, 11:10am UTC](https://boards.straightdope.com/t/anyone-remember-their-calculus-time-to-get-to-alpha-centauri/607967/29 "2012-01-01T11:10:34Z")
Didn’t you ask if anyone remembered their calculus? Calc \<\> The integral of Physics, dt. [Previous page](https://boards.straightdope.com/t/anyone-remember-their-calculus-time-to-get-to-alpha-centauri/607967.md?page=1)