# Acceleration to c at 1 g **URL:** \ **Category:** Factual Questions\ **Created:** [May 19, 2011, 4:14am UTC](https://boards.straightdope.com/t/acceleration-to-c-at-1-g/582412 "2011-05-19T04:14:12Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Johnny\_L.A](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/johnny_l.a/32/1084_2.png) [@Johnny\_L.A](https://boards.straightdope.com/u/Johnny_L.A)\ **Post date:** [May 19, 2011, 4:14am UTC](https://boards.straightdope.com/t/acceleration-to-c-at-1-g/582412/1 "2011-05-19T04:14:12Z")
OK, not to _c_, since that would take infinite energy. But how about ‘near as dammit’? First: It would take just under a year to (theoretically) reach the speed of light at one g acceleration, right? Obviously it’s impractical with chemical rockets. But forget that. Is it physically possible to construct a spacecraft that could accelerate at 1 g for a year (it might be nice to have enough fuel to slow down again, as well), while carrying all the chemical fuel it needs? Could an ion propulsion system do it? And if so, how big would it have to be to achieve 1 g? (AIUI, ion propulsion thrust is much. much smaller than traditional rockets.) What about nuclear pulse propulsion or nuclear thermal propulsion? I’m not asking if such a ship would be at all practical; only whether one is physically possible to build. ---
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [May 19, 2011, 4:20am UTC](https://boards.straightdope.com/t/acceleration-to-c-at-1-g/582412/2 "2011-05-19T04:20:29Z")
Are you asking only about a ship that carries its own fuel, or would that include ships that collect fuel from space as they travel? ---
**Author:** ![Johnny\_L.A](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/johnny_l.a/32/1084_2.png) [@Johnny\_L.A](https://boards.straightdope.com/u/Johnny_L.A)\ **Post date:** [May 19, 2011, 4:27am UTC](https://boards.straightdope.com/t/acceleration-to-c-at-1-g/582412/3 "2011-05-19T04:27:35Z")
> [@TriPolar](#): > > Are you asking only about a ship that carries its own fuel, or would that include ships that collect fuel from space as they travel? I was thinking of a ship that carries its own fuel. Basically: If a ship had to carry its own fuel, would it be too massive for its engines to accelerate it at 1 g (or move it at all)? Of course in that case you’d just build bigger engines… that require more fuel… that require larger engines to move… ---
**Author:** ![Airman\_Doors\_USAF](https://avatars.discourse-cdn.com/v4/letter/a/e36b37/32.png) [@Airman\_Doors\_USAF](https://boards.straightdope.com/u/Airman_Doors_USAF)\ **Post date:** [May 19, 2011, 4:41am UTC](https://boards.straightdope.com/t/acceleration-to-c-at-1-g/582412/4 "2011-05-19T04:41:27Z")
It might be possible to build something like that in Earth orbit where much less power is required to accelerate a considerable mass. As you say, more fuel for bigger engines requires yet bigger engines to compensate for the weight, repeat as necessary. Look at the Saturn V and how it produced massive power yet could only get 3 guys to the Moon and back all told. Earth’s gravity is the limiting factor, so why not remove as much of it as possible? Once that limitation is removed, you must determine how much fuel is required, what type it will be, and you must have a bullet-proof propulsion system. Then you have to account for gravity of other masses, potential impacts at exceptional speeds, resistance in space (not empty, strictly speaking, so there must be some theoretical speed limit), etc. Just imagine the development costs alone. So, could it be built? Perhaps. Economically? Not a chance. ---
**Author:** ![Johnny\_L.A](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/johnny_l.a/32/1084_2.png) [@Johnny\_L.A](https://boards.straightdope.com/u/Johnny_L.A)\ **Post date:** [May 19, 2011, 5:00am UTC](https://boards.straightdope.com/t/acceleration-to-c-at-1-g/582412/5 "2011-05-19T05:00:03Z")
Yeah, the assumption was that such a ship would be so large it would have to be built in space. > [@Airman\_Doors\_USAF](#): > > Then you have to account for gravity of other masses, potential impacts at exceptional speeds… That’s one thing I’ve often wondered about (but forgot in this thread): How would they ‘sweep’ the path ahead of them? It would be a little more annoying to hit a particle, than it is to catch a piece of gravel with your windshield. ---
**Author:** ![gazpacho](https://avatars.discourse-cdn.com/v4/letter/g/6f9a4e/32.png) [@gazpacho](https://boards.straightdope.com/u/gazpacho)\ **Post date:** [May 19, 2011, 5:14am UTC](https://boards.straightdope.com/t/acceleration-to-c-at-1-g/582412/6 "2011-05-19T05:14:34Z")
> [@Johnny\_L.A](#): > > That’s one thing I’ve often wondered about (but forgot in this thread): How would they ‘sweep’ the path ahead of them? It would be a little more annoying to hit a particle, than it is to catch a piece of gravel with your windshield. Traditionally you would sweep the area ahead of you with a magnetic field. You would use this magnetic field to compress the hydrogen you swept and fuse it into helium for propulsion energy. Wiki seems to think that there is not enough stuff in space to gather enough hydrogen. So perhaps once you have left the area of a star bugs on the windshield are not much of a problem. > **[Bussard ramjet](https://en.wikipedia.org/wiki/Bussard_ramjet)** > > The Bussard ramjet is a theoretical method of spacecraft propulsion for interstellar travel. A fast moving spacecraft scoops up hydrogen from the interstellar medium using an enormous funnel-shaped magnetic field (ranging from kilometers to many thousands of kilometers in diameter); the hydrogen is compressed until thermonuclear fusion occurs, which provides thrust to counter the drag created by the funnel and energy to power the magnetic field. The Bussard ramjet can thus be seen as a ramjet v... ---
**Author:** ![Simplicio](https://avatars.discourse-cdn.com/v4/letter/s/c37758/32.png) [@Simplicio](https://boards.straightdope.com/u/Simplicio)\ **Post date:** [May 19, 2011, 5:20am UTC](https://boards.straightdope.com/t/acceleration-to-c-at-1-g/582412/7 "2011-05-19T05:20:48Z")
You need an exponentially increasing amount of mass depending on how close to c you want to get, as acceleration gets more difficult the closer you are to the limit. So you should probably decide how close “near as dammit” is. IIRC from old hwk problems, .9c its not so bad (something like a fuel mass of 10x the payload mass), but .99 c is much much harder. ---
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [May 19, 2011, 5:48am UTC](https://boards.straightdope.com/t/acceleration-to-c-at-1-g/582412/8 "2011-05-19T05:48:01Z")
**Simplicio** - are you saying a ship with about 90% of it’s initial weight in fuel could reach .9c? That doesn’t sound too tough. Is this with a feasible engine that could be built now? ETA: Assuming the craft is at least in earth orbit initially. ---
**Author:** ![matt](https://avatars.discourse-cdn.com/v4/letter/m/a6a055/32.png) [@matt](https://boards.straightdope.com/u/matt)\ **Post date:** [May 19, 2011, 7:48am UTC](https://boards.straightdope.com/t/acceleration-to-c-at-1-g/582412/9 "2011-05-19T07:48:49Z")
> [@TriPolar](#): > > **Simplicio** - are you saying a ship with about 90% of it’s initial weight in fuel could reach .9c? That doesn’t sound too tough. Is this with a feasible engine that could be built now? > > ETA: Assuming the craft is at least in earth orbit initially. I’m pretty sure that’s using antimatter -matter as a fuel, so no. ---
**Author:** ![Smapti](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/smapti/32/17938_2.png) [@Smapti](https://boards.straightdope.com/u/Smapti)\ **Post date:** [May 19, 2011, 8:04am UTC](https://boards.straightdope.com/t/acceleration-to-c-at-1-g/582412/10 "2011-05-19T08:04:33Z")
The answer is “14 k of g in a f d p”. ---
**Author:** ![Novelty\_Bobble](https://avatars.discourse-cdn.com/v4/letter/n/a3d4f5/32.png) [@Novelty\_Bobble](https://boards.straightdope.com/u/Novelty_Bobble)\ **Post date:** [May 19, 2011, 11:26am UTC](https://boards.straightdope.com/t/acceleration-to-c-at-1-g/582412/11 "2011-05-19T11:26:54Z")
I read this as “acceleration of cat at 1g” and immediately assumed that Mr. Schrodinger was up to his old tricks again. ---
**Author:** ![DrFidelius](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/drfidelius/32/3447_2.png) [@DrFidelius](https://boards.straightdope.com/u/DrFidelius)\ **Post date:** [May 19, 2011, 12:18pm UTC](https://boards.straightdope.com/t/acceleration-to-c-at-1-g/582412/12 "2011-05-19T12:18:13Z")
> [@Novelty\_Bobble](#): > > I read this as “acceleration of cat at 1g” and immediately assumed that Mr. Schrodinger was up to his old tricks again. Maybe, and maybe not. ---
**Author:** ![jjimm](https://avatars.discourse-cdn.com/v4/letter/j/ba8739/32.png) [@jjimm](https://boards.straightdope.com/u/jjimm)\ **Post date:** [May 19, 2011, 12:25pm UTC](https://boards.straightdope.com/t/acceleration-to-c-at-1-g/582412/13 "2011-05-19T12:25:02Z")
I once posted this idea on the SDMB: accelerate a manned Mars mission at 1g. At the halfway point flip the thing and start to decelerate at 1g. That way you have artificial gravity for the astronauts, and you get there really quickly. Everyone told me I was an idiot. ---
**Author:** ![Gray\_Ghost](https://avatars.discourse-cdn.com/v4/letter/g/c0e974/32.png) [@Gray\_Ghost](https://boards.straightdope.com/u/Gray_Ghost)\ **Post date:** [May 19, 2011, 12:34pm UTC](https://boards.straightdope.com/t/acceleration-to-c-at-1-g/582412/14 "2011-05-19T12:34:47Z")
> [@jjimm](#): > > I once posted this idea on the SDMB: accelerate a manned Mars mission at 1g. At the halfway point flip the thing and start to decelerate at 1g. That way you have artificial gravity for the astronauts, and you get there really quickly. > > Everyone told me I was an idiot. Nope, you’re not an idiot. If we lived in a decent hard science fiction universe like Larry Niven’s Known Space, that’d be just how you’d do it. (this assumes no artificial gravity or inertia-less drives) It’s just that we don’t have fusion drives or any other space drive that can manage anything within a bunch of orders of magnitude of that delta V. ---
**Author:** ![kanicbird](https://avatars.discourse-cdn.com/v4/letter/k/5f8ce5/32.png) [@kanicbird](https://boards.straightdope.com/u/kanicbird)\ **Post date:** [May 19, 2011, 12:40pm UTC](https://boards.straightdope.com/t/acceleration-to-c-at-1-g/582412/15 "2011-05-19T12:40:00Z")
I did the calculation years ago. Came up with a theoretical trip to Alpha Centuri system, accelerating at 1 g for the first half of the trip then decelerating at 1g for the second half. From what I remember the ship was something like 95%+ (perhaps 99%+) fuel weight, engines were 100% efficient and I’m pretty sure the the fuel/reaction was antimater/matter. Another possible way around the limitations is to make a laser sail ship, powered but the sun powering a orbital laser, this way you don’t have to carry the fuel, and in space a laser should stay together for quite a distance. At your target destination using the laser sail as a solar sail (or steller sail). ---
**Author:** ![MikeS](https://avatars.discourse-cdn.com/v4/letter/m/919ad9/32.png) [@MikeS](https://boards.straightdope.com/u/MikeS)\ **Post date:** [May 19, 2011, 12:41pm UTC](https://boards.straightdope.com/t/acceleration-to-c-at-1-g/582412/16 "2011-05-19T12:41:38Z")
If you want to calculate some numbers yourself, the Wiki article on [relativistic rockets](http://en.wikipedia.org/wiki/Relativistic_rocket) is pretty handy; just plug some of the numbers for the specific impulse into the equations for ∆v midway through the article. The specific impulse for most chemical rockets is about I[sub]sp[/sub] ≈ 10[sup]-5[/sup], and ion thrusters are about ten times greater; if you run the numbers you’ll see that you’re going to have some trouble getting up to near lightspeed with these methods. ---
**Author:** ![Novelty\_Bobble](https://avatars.discourse-cdn.com/v4/letter/n/a3d4f5/32.png) [@Novelty\_Bobble](https://boards.straightdope.com/u/Novelty_Bobble)\ **Post date:** [May 19, 2011, 12:51pm UTC](https://boards.straightdope.com/t/acceleration-to-c-at-1-g/582412/17 "2011-05-19T12:51:53Z")
> [@DrFidelius](#): > > Maybe, and maybe not. Nice, well played sir. ---
**Author:** ![Johnny\_L.A](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/johnny_l.a/32/1084_2.png) [@Johnny\_L.A](https://boards.straightdope.com/u/Johnny_L.A)\ **Post date:** [May 19, 2011, 1:51pm UTC](https://boards.straightdope.com/t/acceleration-to-c-at-1-g/582412/18 "2011-05-19T13:51:07Z")
> [@Smapti](#): > > The answer is “14 k of g in a f d p”. > [@Novelty\_Bobble](#): > > I read this as “acceleration of cat at 1g” and immediately assumed that Mr. Schrodinger was up to his old tricks again. Both expected replies. 😛 ---
**Author:** ![Earl\_Snake-Hips\_Tucker](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/earl_snake-hips_tucker/32/3269_2.png) [@Earl\_Snake-Hips\_Tucker](https://boards.straightdope.com/u/Earl_Snake-Hips_Tucker)\ **Post date:** [May 19, 2011, 2:22pm UTC](https://boards.straightdope.com/t/acceleration-to-c-at-1-g/582412/19 "2011-05-19T14:22:20Z")
> [@Novelty\_Bobble](#): > > I read this as “acceleration of cat at 1g”. . . So did I, at first. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [May 19, 2011, 4:42pm UTC](https://boards.straightdope.com/t/acceleration-to-c-at-1-g/582412/20 "2011-05-19T16:42:21Z")
For any given target speed, any given propulsion technology, and any given desired acceleration, there is some initial value of fuel mass to payload mass that’ll do the trick. The catch is that the mass ratio grows exponentially even before you account for the relativistic effects. To clarify: Suppose that it takes a mass ratio of R (total mass to payload mass) to get to a speed V. What fuel ratio is needed to get to a speed 2V? Well, first you need to get from rest to V, and then you need to get from V to 2V. For the second leg of this, you’ll need a mass ratio of R, so if your payload has mass m, you’ll need to have a total mass of R_m at the start of the second leg. But as far as the first leg of the trip is concerned, all of the fuel you’re saving for the second leg can be considered payload. So at the start of the first leg of the trip, you’ll need to have a total mass of R_R_m. Similarly, to get to 3V, you’ll need to start with R^3_m, and so on. Better rocket technology might make this a slower-growing exponential, but it will always be exponential. [Next page](https://boards.straightdope.com/t/acceleration-to-c-at-1-g/582412.md?page=2)