How far could a starship travel in 900?

October 3, 2009 11:19 PM

What distance could a ship circumnavigate, using theoretically proven technologies, by the end of the century, traveling as far into space as possible and still returning home in 900 years?

Ie., A craft propelled by (you specify) could travel X distance achieving Y velocity before needing to start on its return mission. Assume breakdown of components is not a problem, crew is irrelevant, just a radio-telescope trying to go on the best sight-seeing mission it can in that time. For kicks, let's assume a mass of 10,000 (just under the Hubble).

posted by marcuswebb to technology (13 comments total)

I don't think a radio telescope would have a much better view 1 light year away then it would 1 AU away.

Anyway, I think it's just a mater of how much energy you have, you could theoretically speed up to near c for half the journey, then turn around and then stop at home, at which point you would have gone 450 light years.

I was going to check on the energy requirements, but interestingly Wolfram Alpha helpfully tells me that if a man weighing 180 pounds were to run at half the speed of light for 30 minutes, he would burn 2.203x10¹⁰ calories, losing 6.3 million pounds
posted by delmoi at 11:34 PM on October 3

Mass doesn't mean much, once you're already in space.

Returning, including slowing down after all that acceleration, is a huge bitch that won't be worth the effort.
posted by rokusan at 12:22 AM on October 4

delmoi's right that a radio telescope is going to perform about equally in Pluto-orbit as it would in the interstellar void. They actually perform quite nicely in Earth orbit. They'd work just perfectly in one of the Lagrange points.

I've written four other responses in this space, before starting on this one.

Basically, there are too many variables, and too few constraints, in your question. Using one set of assumptions, the answer is 0 meters. Using another set of assumptions, you've got something like .05 lightyears. Another, on the order of a thousand AU.

The 0 meter solution is based on the fact that we do not have any propulsion systems forecast that would operate continuously for 900 years. So the naive approach of accelerating to the halfway mark, then decelerating, then doing the same thing again to get home wouldn't work out at all. You could certainly choose not to accelerate the whole time, but that becomes another damn variable: do you stop accelerating at 12km/s or 12.1km/s? Of course, your 10,000kg mass limit leaves almost no space for fuel. Even if you devoted it entirely to chemical rocket fuel (our highest thrust technique), I don't think you would even achieve solar escape velocity.

Furthermore, the actual problem is much more complex than the naive approach. Because the Earth and Sol both move (very fast). You'd actually need some sort of a parabolic path, and I don't have the tools to solve that for you.

On the other hand, Voyager 1 is doing 17 km/s right now. And if it were pointed in the right direction, wikipedia says it'd hit Alpha Centauri in 75,000 years. So, crunching the numbers, you get something like .05 lightyears in 900 years. Of course, it got to 17km/s using gravity assist off all four of our gas giants--we could never have achieved that velocity without the gravity assist. You don't have gas giants in interstellar space.

If you really wanted to come back to Earth, your best bet is a highly parabolic solar orbit. The orbital period of Pluto appears to be about 250 years. Its orbit is 40AU in average radius. Thus its orbital path is about 250AU in circumference. So in Pluto-orbit, it could do 1000AU in a century. A parabolic orbit intersecting Earth-orbit could be found. But, again, I don't have the tools to solve that for you. And I just blew up three different online orbital calculators trying to generate even a circular orbit with a period of 2.8 x 10¹⁰ seconds.

For my money, without some universe-changer like warp drive, the answer is 0 meters. Or maybe around 30 AU if you did a mission to Pluto and returned.
posted by Netzapper at 1:08 AM on October 4

900 years only gets you to Pluto? How profoundly depressing.
posted by BitterOldPunk at 1:21 AM on October 4 [1 favorite]

Forgetting all the random stuff, like limiting yourself to today's technology, here's an amusing link about the relativistic rocket. There's lots of fun talk at what appear to be the XKCD forums talking about '1g space travel'. If you believe those folks, you would take approx. 1 year to get to light-speed-as-near-as-dammit, and then you'd be going where you wanted, and decelerating for a year.

So, if you wanted to travel somewhere "interesting" and then come back, you could get approx. 448ly away, stop to take a couple of touristy pictures, then come back again. No idea how the relative passage of time inside/outside the ship would affect things.
posted by lowlife at 6:52 AM on October 4

Oops, I just remembered that Pluto's orbit is pretty eccentric, so my distance estimates are incorrect--I just pi'd the average Pluto-Sol distance. I'm now entirely too damn tired to find a proper figure on that, and I'm definitely too tired to work out the Kepler on it despite having found the terms.

But I ran some other numbers for you: a 93.2AU orbit around Sol gives you a period of 900 years. This need not be circular, of course. Here's a pretty neat little orbit plotter--put in 93.2 as the semimajor axis, and whatever you like in the range (0, 1] for eccentricity, leave the rest alone.

With a sufficiently eccentric Solar orbit, in the proper plane, it would intersect Earth-orbit. Launch it right, and you could pick it up on the flip side. Of course, the above numbers aren't quite right, since they're just orbital periods and don't include the portion of the standard orbit that would be cut off by launching and recovering in Earth orbit. And catching it on the other end would be like catching a small comet.

It's also unlikely that we have the technology to put the object in the appropriate orbit. Given that it would need to have a velocity of 42km/s at 1AU (Earth-orbit intersection), and given that the actual relative velocity to Earth may be higher than that given the angle needed, it's a little far fetched. Earth escape velocity is 11 km/s. The space shuttle does about 7 km/s. You'd need some fucking enormous rockets to get it up to our projected orbital velocity. It's certainly not doable inside your 10,000 kg mass limit, which with a 100kg final mass only achieves a Δv of 18km/s. If we hew to your requirements, and put a 10,000kg final mass in for the radio telescope, you need a stunningly gargantuan 400 million kilograms of fuel to achieve a Δv of roughly 42 km/s for your telescope.

And that's pretending that the Earth contributes no velocity. Which is wrong, it does contribute velocity, and in the wrong direction, requiring even more Δv.

Rockets, by the way, are the only technology we have capable of speeding something up in a sufficiently short period of time to actually achieve such an orbit. All of our more interesting propulsion systems have much, much lower thrust but can maintain it for a much longer time. And the above fuel numbers assume that you can contain 400,000,000kg of fuel in 10,000kg of structure--which you can't. For comparison, the launch mass of the space shuttle with boosters appears to be about 4,000,000kg--which is not all fuel.

Heliopause (what we consider the edge of our solar system) is at around 100AU out. 93.2AU is pretty damn close. An orbit with an axis of 101AU orbits in 1016 years, and that would put your craft in technically interstellar space. And, as I mentioned, it doesn't matter if you're a mile or a light year into interstellar space--it's all the same for your radio telescope.

I feel like I'm missing something... but, I can't think of what it is. And I can see the focus of our ellipse lightening the sky here. Which means it's time for bed.

And I think I was a bit unclear before: if you don't want to come back to Earth, you can go pretty damn far in 900 years given an ion drive or one of the proposed plasma drives. You could probably do a flyby of Alpha Centauri, if you wanted. It's just that decelerating is a bitch, whether you're trying to turn around or whether you're trying to enter orbit at your destination.
posted by Netzapper at 6:58 AM on October 4 [1 favorite]

@rokusan: Mass is still very important once you're in space. You have to accelerate the mass out there, slow out, accelerate it back then slow it again. An extra mass will result in many times the original mass in extra fuel.
posted by jefftang at 6:58 AM on October 4 [2 favorites]

lowlife, that's a pretty cool link. Excellent math.

Unfortunately, it doesn't deal with the fuel requirements of a relativistic rocket. No chemical rocket we can envision even kind of suffices. And none of the ion drives we've designed do more than a few grams (force) of thrust. You basically need a Bussard ramjet if you're going to maintain 1G for longer than a few minutes.

So, while that page does avoid the use of causality-breaking technology (warp drive, wormholes, hyperspace, etc.), it really isn't based on current technology.
posted by Netzapper at 7:08 AM on October 4

we do not have any propulsion systems forecast that would operate continuously for 900 years.

Lightsail?
posted by ROU_Xenophobe at 8:11 AM on October 4

Atomic Rockets is the website where you want to read up for questions like these.

I'll start by assuming that the question itself is relevant, which isn't too unlikely. No, the view probably doesn't change much once you're past the heliopause, but maybe you want to do interferometry with a fantastically long baseline, maybe you want to view distant stellar systems from flyby distances, whatever. And for whatever reason (bandwidth?) you want to bring your results back in person.

If we're talking about any great distance, then the acceleration is negligible; as the man said, 1G is roughly one "light-year per year squared". All you need to worry about is your total deltaV - your top speed is going to be roughly one fourth of this, because you'll need to change velocities to accelerate, then to stop at your destination, then to turn around, then to stop again at your return. (We'll neglect the extra work fighting the Sun's gravity well, and we'll neglect the opportunities for gravitationally assisted swingarounds, and we'll hope those errors balance out and are small compared to our total results).

The last chunk of assumptions we'll need is your definition for "currently proven technologies, by the end of the century". The "nomogram" here is an interesting reference. If what you really mean is "scientifically possible technologies", then notice that we've created antimatter before, antimatter-based drives have a ludicrously high effective exhaust velocity, and if our spaceship is 75% fuel (lower than any current launch vehicle) then we're looking at max speeds over 10% speed of light; you can actually get out to a wide selection of other stars and back before the millenium is out.

If what you mean is "technologies that could be developed and made economically reasonable before the end of the century", it gets uglier. Making nanograms of antimatter isn't cheap, and we've never made megagrams... And note that our best existing technologies for liftoff from Earth are below the "Chemical MAX" label, way way down at the *bottom* of that exhaust velocities list. Also note that some of the stuff which is technologically possible and might be economical would be difficult politically. The Nuclear Salt Water Rocket, for example, would still need a mass ratio of 90% to get up to about 0.9% light speed for your round trip - but it would have to be assembled and started in orbit, to avoid irradiating everything within miles of its launch site. And at 0.9% of light speed, you're not moving quite fast enough to get to Alpha Centauri and back within 900 years.
posted by roystgnr at 8:37 AM on October 4

You could use a solar sail to go out, but good luck getting home again.
posted by blue_beetle at 8:47 AM on October 4

blue_beetle: There are schemes for deceleration/return missions with lightsails; for example, take a look at this paper by Robert Forward (scroll down to the diagram of the ε-Eridani mission at the bottom of the page).

If you can find a sufficiently dense object at your destination (say an unusually dense Kuiper-belt object) you could use a flyby to reverse course, which might lop your needed delta-v almost in half.

That's a handy nomograph, roystgnr. Project Rho is a great resource for this kind of question.
posted by hattifattener at 2:32 PM on October 4

Yeah, I agree you have a weird mix of constraints and vagueness.

For starters, what technology will be available by end of century is unknowable. But I think it's reasonable to conclude that we may be able to launch something to relativistic speeds by then.

I don't think the 900 year timeframe is realistic, though. Some sf authors have really looked at this as a social organization question. For instance, what civilization could be depended on to maintain a lightsail station year in and year out for hundreds of years? We just don't know. Imagine a war, a crisis, a religious revival.

So maybe you ditch the lightsail and depend on yourself. Either way you have the problem of technology that must self-sustain without access to any kind of civilization. Most of our technology is hard to keep going past ten years. The more advanced it is, the shorter its obsolescence. After just 15 years in space, Mir was a jumble of power and data cables and various types of plumbing that even old hands had difficulty deciphering.

Then you have the aspect of sending something into space and basically gambling that whatever advances have brought you to the point of launching it will not progress such that you can later beat it to its own destination.

A good metric has been proposed, I forget by whom originally, as a flight that could be completed within the lifetime career of a scientist or engineer. So, about fifty years. Longer than that, and it's almost not worth signing onto as a project.

That applies, obviously, to any particular destination. Obviously we can reach Pluto sooner than 900 years from now, but I'm not sure how much faster we could get people there than the current mission's ~9y. We probably can't really even back-of-the-envelope out such a mission until we have some experience with crewed flight to Mars and back. But again, I think it might be reasonable to assume that a mission would be possible by some means this century. (The main issue is that Pluto passed perihelion in 1989 and thus won't be that close to the Sun again until the 23rd century. But it may not actually mean that much if you have the means to get to Pluto perihelion in a reasonable human mission timeframe.)

I have no idea -- nobody really does -- when a 50-year mission to Alpha Centauri might be realistically possible. But then what I find fascinating right now is how many new destinations have opened up as the Kuiper Belt and TNOs reveal themselves. Dark worlds they all would be, but not that different from Pluto, either (and then again, not that different from Pluto, a pro and con). There are a couple almost-as-near stars, too, although the interest in A Centauri is primarily about the higher possibility of an Earthlike world somewhere in the system, if the binary would permit it.

So anyway, I think those are more interesting and relevant frames for a query. I hope you see my reasoning.
posted by dhartung at 10:11 PM on October 4 [1 favorite]