“The odds are approximately 3,720 to 1”

It’s been our trendsetting exoplanet week at the RBC. After the heavy stuff from Mike on tenured stargropers with too much immunity and from me on Renaissance cranks with not enough, here is something lighter for a rainy Sunday.

Fan image of Niven's puppeteer
Fan image of Niven’s puppeteer

We love Bruno-style speculations about intelligent aliens from other stars. Thrint, tnuctipun, puppeteere, kzin, kdatlyno, grogs, pak, moties, and outsiders – and that’s just from Larry Niven’s imagination. But they all come up against Enrico Fermi’s famous question, made in a Chicago cafeteria in 1950:

Where are they?

I had a nice explanation for the non-appearance of intelligent aliens. No, not the one that intelligent life does not exist on earth either. Human history indicates that contact between societies at different levels of culture and technology is normally disastrous for the weaker. Any ethical civilization would minimize it, except to prevent disaster. Now any civilization capable of building interstellar ships must be ethical, or it would have destroyed itself by ecocide or the genocidal warfare enabled by the weapons available well before that technological level. Ergo, any alien civilization surviving long enough to launch interstellar ships would refrain from doing so on ethical grounds. QED.

Cute, isn’t it. The weakness is the disaster cop-out. Iain Bank’s SF novels about the very ethical and advanced Culture depend on this loophole, in the adventures of agents of the embarrassing spook agency Special Circumstances. This is set up to carry out deniable interventions in murderous lesser civilizations, for their own good of course. Closer to home, when European colonialists reached Easter Island in 1722, weren’t they justified in intervening to halt the self-destruction of the Easter Islanders described by Jared Diamond? Their population had crashed 80% to at most 3,000. It might have been – only in fact the colonialists made the situation much worse by disease and slave-raiding, reducing the native population to 111 by 1877.  Non-interference looks the better course.

I now have a much more prosaic explanation. Space is full of junk.

Oort cloudAstronomers believe (based on robust inference) that the solar system is surrounded by a vast spherical cloud of small to midsize rocks called the Oort cloud. A very few of them get knocked loose and become comets.


The Oort cloud … is a theoretical spherical cloud of predominantly icy planetesimals believed to surround the Sun at a distance of up to around 100,000 AU (2 light years). This places it at almost half of the distance to Proxima Centauri, the nearest star to the Sun…The outer Oort cloud may have trillions of objects larger than 1 km.

Since Sol is an unremarkable, middle-of-the road, Mom-Dad-John-Jane-and-Rover sort of star, it is reasonable to assume that Proxima Centauri and other stars have similar clouds. Here’s an estimate of the mean separation between stars in the galactic arm of 5 light-years. Chances are the whole neighbourhood is loosely packed with Oort clouds, like untended suburban gardens.

Unfortunately the next-door neighbours do not have any potentially habitable planets. The nearest known exoplanet in the habitable zone of its star is Kapteyn-b at 13 light-years, though it’s far too massive to be livable for us. We can take this as the minimum distance for a worthwhile interstellar voyage. The nearest exoplanet habitable for humans is likely to be much further away.

Remember the scene in Star Wars where Han Solo, pursued by Empire fighters, escapes through a belt of whirling asteroids, missing them by inches? Interstellar travel is like that only worse.


(C3PO’s probability estimate is 2:05 minutes in)

[Update: the fallowing section has been extensively revised in response to comments pointing out mistakes. Blog archaeologists can find the uncorrected original at the end.]

Suppose our Millennium Falcon is only travelling at a footling 1% of the speed of light, or 3,000 km per second. Hitting a 20-kg basketball-sized lump of ice at that relative velocity is equivalent to blowing up 23 tonnes of TNT. You can only survive with massive shielding, needing huge amounts of extra fuel. A 125-kg exercise ball is 407,000 tonnes of TNT, quite unsurvivable. We therefore need radar capable of detecting small rocks infallibly at 10,000 km –  the distance from Barcelona to Los Angeles. Also very powerful, responsive and infallible software and manoeuvering rockets to miss them with 3 seconds warning. Just conceivable – but at that speed we will still take 1,300 years to Kapteyn’s Star.

Let’s try to shorten this by speeding up to half the speed of light, 150,000 km/sec. The trip will only take 26 years plus a year or so for acceleration and deceleration, just doable. The radar signal is only travelling twice as fast as the ship, so by the time the pulse hits the rock, the ship has closed half the gap in Newtonian space (somebody else can do Einstein’s). On the return trip, the pulse does 2 km to the ship’s one. So they meet at 1/3 of the original gap. Sticking to the 3-second warning, we need to receive the return pulse at 450,000 km, which means we have to send it at 1.35m km. We also have to detect much smaller rocks: the basketball is equivalent to 1.14 megatonnes of TNT. Together, this does not look feasible. We have therefore to go slower, much slower. Let’s drop to 25% of the speed of light. The trip now takes 52 years plus. Sticking to the 3-second warning, and using a similar calculation, our ship needs to detect the basketball (0.57 megatonnes of TNT) at 225,000 km, and send the radar pulse at 400,000 km, more than the distance from the Earth to the Moon. The Star Wars missile defence problem is trivial in comparison. I can’t believe it can be done reliably.

Quadrillions of rocks and pebbles are not the only hazard. There are plenty of full-sized rogue planets out there, floating free of any star, and undetectable from a distance in the dark. We aren’t likely to hit one, as the captain of the Titanic said, and size makes no difference to the catastrophe.

We can’t however avoid interstellar dust.  The density is estimated at 10-6 dust grains/m3. Assume our spaceship has a cross-section of 100 m2. We will hit one grain every kilometre. En route to Kapteyn-b, we will hit 1.23 x 1014 grains. That’s only 10 grammes in total, similar to our killer pea. But at high velocities, they will together destroy the ship, and radar will not help. [Update correction: the kinetic energy of impacting 10 gm of matter is 37 kg of TNT at 3,000 km/sec, 815 kg at 75,000 km/sec, and 1.6 tonnes at 150,000 km/sec. So it looks as if dust imposes a large extra shielding cost rather than ruling out the trip. Remember that this is unavoidable damage, additional to the rocks.]

Interstellar travel therefore looks suicidally dangerous or impractically slow. To get round these problems you have to posit unknown and completely new technology like force fields: magic it used to be called. This is not the way to bet. If an alien civilisation were prudent enough to have survived – we don’t need virtue here – it would not go in for aliened interstellar spaceflight. This solves the Fermi paradox. QED again.

There is a wrinkle though. The strictures don’t apply to robot spacecraft, since losing one is only money, provided it isn’t sentient. You can either send them fast, accepting a high attrition rate, or safely slow. “Slow” means tens of thousands of years. It could look prudent to keep an eye on possible threats in the neighbourhood, or just satisfy curiosity about life elsewhere. So where are the alien robot spycraft?

Puppeteer robot spycraft will naturally be extremely well protected: stealthy to the point of invisibility, with gnat-sized microdrones. As backup, they will have psywar capabilities including memory manipulation. You don’t see them and if you do you will forget. But once in a millennium, both systems fail. That’s why there are persistent reports that one has been captured and concealed in a secret government base in … [uutyfd ffgvg vxu n88c pn c c uun c90nn cn likjf 3e984 318n99  nv4n9vn]  [The RBC apologises for the temporary loss of service, due to a small glitch in a scheduled software upgrade. Normal service will be resumed shortly.]

The argument above (not the robots or Roswell) is adapted freely from The Straight Dope.


Remember manned space exploration? Your children don’t. The last men on the moon were the American astronauts Eugene Cernan and Harrison Schmitt, who left it on December 14 1972. Most of the people alive today have not witnessed a moon flight. The Mars mission keeps being put off. The exploration that actually takes place is done by robots. Robots get more capable and cheaper all the time, humans stay expensively the same.

The last man on the Moon: Eugene Cernan
The last man on the Moon: Eugene Cernan

Footnote: Original of corrected section above, for the hall of shame

Suppose our Millennium Falcon is only travelling at a footling 1% of the speed of light, or 3,000 km per second. Hitting a pea-sized rock at that relative velocity will be instant annihilation. To survive, we need radar capable of detecting the peas infallibly at 10,000 km – the distance from Barcelona to Los Angeles. We also need very powerful and responsive software and manoeuvering rockets to miss them with 3 seconds warning. Just conceivable – but at that speed we will still take 1,300 years to Kapteyn’s Star.

Let’s try to shorten this by speeding up to half the speed of light, 150,000 km/sec. The trip will only take 26 years plus a year or so for acceleration and deceleration, just doable. The radar signal is only travelling twice as fast as the ship, so whatever the range of the radar, the pulse gets back to the ship at the same moment as it hits the rock. Not good. We have therefore to go slower, much slower. At 25% of the speed of light, the trip takes 52 years plus. Sticking to the 3-second warning, our radar needs to detect the pea at 450,000 km, more than the distance from the Earth to the Moon. The Star Wars missile defence problem is trivial in comparison. I can’t believe it can be done reliably.

Author: James Wimberley

James Wimberley (b. 1946, an Englishman raised in the Channel Islands. three adult children) is a former career international bureaucrat with the Council of Europe in Strasbourg. His main achievements there were the Lisbon Convention on recognition of qualifications and the Kosovo law on school education. He retired in 2006 to a little white house in Andalucia, His first wife Patricia Morris died in 2009 after a long illness. He remarried in 2011. to the former Brazilian TV actress Lu Mendonça. The cat overlords are now three. I suppose I've been invited to join real scholars on the list because my skills, acquired in a decade of technical assistance work in eastern Europe, include being able to ask faux-naïf questions like the exotic Persians and Chinese of eighteenth-century philosophical fiction. So I'm quite comfortable in the role of country-cousin blogger with a European perspective. The other specialised skill I learnt was making toasts with a moral in the course of drunken Caucasian banquets. I'm open to expenses-paid offers to retell Noah the great Armenian and Columbus, the orange, and university reform in Georgia. James Wimberley's occasional publications on the web

31 thoughts on ““The odds are approximately 3,720 to 1””

  1. If you decided to Go Big on the starship, what you'd do is put a giant piece of ice in front of it to absorb the impact. It would gradually get ablated away, but in the mean-time you'd have some usual shelter.

    Agreed that robot starships will be small, if they exist. It's so expensive in energy terms to accelerate and decelerate a spacecraft at high velocity that you'll be using hundreds of thousands of tons of fuel to send single tons (or kilograms) of payload to another solar system. "Fuel" possibly meaning "nuclear bombs", because Orion is the only paper starship among all the paper starships where the power source actually exists versus being mere speculation (laser-propelled starship might get there eventually, if someone ever manages to build a large space laser that doesn't melt itself or become a Weapon of Mass Intimidation).

    Remember manned space exploration? Your children don’t.
    . . . .

    Robots get more capable and cheaper all the time, humans stay expensively the same.

    The poor International Space Station doesn't get no respect, no respect at all. Sure, it's an incredibly over-expensive way to do orbital laboratory experiments even if you concede that you need people up there to do them, but at least we get to hear them play David Bowie songs!

    . . . One beauty of the robots getting better is that they could eventually make it easier for humans to go into space. Tell your robots to build you a space colony, let them do all the work, then send your people out to it.

    In the mean-time, though, it frustrates me enormously that we can't redirect the $8 billion/year NASA spends on crewed spaceflight to robotic missions. That's a lot of very good robotic missions that would tell us vastly more about space and the solar system in a mere ten years versus the twenty-year timeline NASA is looking at just to send humans to orbit Mars (assuming they ever do that, which I don't think they will).

    1. The ice looks good, though it pushes up the propulsion cost a lot. Would it work? Against space dust, probably. Not so sure about Oort rocks.

      We can estimate the kinetic energy of hitting a rock. Wikipedia: "the energy of TNT is 4.6 MJ/kg, and the energy of a kinetic kill vehicle with a closing speed of 10 km/s is of 50 MJ/kg."
      So at 3,000 km/s the energy released by impacting a 10gm pebble is 32 kg TNT-eq, a 1 kg rock 3,200 kg TNT-eq, a 100 kg rock 320,000 kg TNT-eq, etc.
      At 75,000 km/sec, this rises to: 10 gm, 815 kg TNT-eq; 1kg, 81,500 kg TNT-eq; 100 kg, 8,152,000 kg TNT-eq.

      The full equation includes the risk of impact, taking account of the impact cross-section (which the ice shield pushes up); the impact's kinetic energy; and the weight of fuel needed to accelerate and decelerate the starship plus iceberg. The calculation is beyond me. Going by uninformed intuition – not a good guide – , it looks as if it might be possible to shield against 10-kg impacts at the slow speed and 1kg ones at the higher. Anything bigger and you are small pieces of frozen toast. Can you see a space iceberg standing up to a 100 kilotonne impact? Then a second?

      1. Probably not. For the really big stuff, you'll just have to hope for the best – and maybe use telescopes and earlier probes to find out if there are any areas out in the Oort Cloud that are relatively empty. It's a good thing it will be small. In fact, it will need to be small, because otherwise slowing it down will be a nightmare.

        . . . . You know what, I'm in agreement. I think most civilizations just don't bother – or they do it in a super-gradual way wherein they have outposts in their Oort Clouds before sending anything out into interstellar space.

        If you're an interplanetary civilization, you can build some truly enormous space telescope arrays, and put them far enough out that they might be able to use the sun to create a gravity lens with the Sun. The astronomer Francis Drake actually proposed putting a telescope with a 10 meter lens out at 150 billion kilometers. The gravity lens would magnify what it could see so effectively that you'd be able to resolve rivers and hills on a planet orbiting Alpha Centauri A.

  2. As far as robots, any sufficiently advanced technology for robots to navigate interstellar distances and make contact (or avoid contact) might require a level of intelligence in the robots that would mean they were sentient. The civilization is ethical so they can't just treat these robots as disposable slaves and you are back to square one. More likely, you have clone copies that make the trip (either robotic or biological or cyborg).

      1. I was thinking some future cloning technology that allowed for the splitting and merger of consciousness (if the clone survived the trip and returned – of course the differential aging would mean earthbound twin/clone would likely be dead of old age if biological) or maybe like the reboots in Doctorow's Down and Out in the Magic Kingdom.

    1. What you would do is send the uploaded AI aboard the probe, have it do its mission – and then transmit itself electronically back to home before shutting down. In fact, that's why I don't think we see robotic probes all over the place in the galaxy. Why have intelligent AI hanging around pointlessly by themselves in studied solar systems after you're done with your mission? Just have them send themselves back after they're done, and periodically send out new ones.

  3. The radar signal is only travelling twice as fast as the ship, so whatever the range of the radar, the pulse gets back to the ship at the same moment as it hits the rock.

    This paragraph, in which you attempt to show that at speeds greater than 0.5c it's impossible to see oncoming objects, needs some polish. I can't construct a reasonable set of assumptions, with or without special relativity, that leads to that conclusion.

    1. I didn't write see, but detect. The rocks emit no light or other radiation – at those distances we can ignore reflected starlight. The argument depends on the need for a round trip by the electromagnetic signal. Where do I go wrong?

      1. It would seem that the ship would have traveled two-thirds of the way to the object when it encounters the returning radar signal.

      2. Sure. Detect. But that changes nothing–either way you've got an object headed toward us at 0.5c, and EM radiation carrying information about the object headed toward us at 1.0c. Whatever the distance to that object was when our signal bounced off it, the thing has closed only half the distance when the return signal reaches us.

        Recall that the speed of light is the same to all observers, regardless of the motion of the source. Even though you're moving at 0.5c with respect to that onrushing object, you can reason about the situation as though it's moving toward you and you're at rest and the signals you're bouncing off it are moving at c.

      3. The ship is moving while the signal is in transit. Suppose the ship is some distance d from our hypothetical pea-sized rock. The ship sends out a radar signal that travels the distance d and reaches the rock. During that time, the ship will have moved d/2 of the distance (travelling half as fast as the signal). So now the reflected signal is headed back (at speed c) toward the ship which is still closing the distance at half of c. I don't feel like working out the math to figure the exact point the ship and reflected signal intersect, but the time-to-impact is greater than 0.

        Not very much greater than 0, mind you, unless our radar is able to detect pea-sized objects and work out their trajectories *very* far out, which is, as you point out, a decidedly non-trivial problem.

      4. At point A you emit a radar signal towards an object 6 light seconds away. It arrives 6 light seconds later, at which point you are only 3 light seconds from it.

        Two seconds later, the returning signal has traveled two light seconds in your direction, and you have traveled the other 1 light second, and caught up with it. You still have another second before you reach the object.

        Traveling close to the speed of light dramatically reduces the warning time, but it doesn't go to zero until you actually reach the speed of light.

        Hitting large objects is along the way is an extreme example of bad luck. We know the average density of the interstellar media in this area, (About 1 atom per cc) and it's low enough that the odds of hitting even a pebble are pretty low. A square meter of ship traveling from here to Proxima Centauri would sweep a volume of 1 E16 cubic meters, and encounter along the way about 1 E22 atoms, most of it hydrogen gas. That's about 17mg of hydrogen gas.

        Because you'd be, in this example, hitting it at half light-speed, that represents a pretty nasty radiation flux, you need a shield. But if you hit anything along the way larger than a dust particle, you'll have guaranteed your place in the history books as the world's unluckiest astronaut.

        Hitting rocks is an issue in stellar systems, not out between the stars.

        1. What is wrong with Wikipedia's density of interstellar dust? I used this to get my much higher estimate of unavoidable impacts of 10 gm to Kapteyn. There is experimental evidence for this dust, since it's the simplest solution to the Bentley-Halley-Olbers paradox: why is the sky dark at night? (Strangely, the Wikipedia article on the paradox ignores the smog theory.)

          "Hitting rocks is an issue in stellar systems, not out between the stars." If typical stellar systems include Oort clouds, which must be odds-on as it's a hypothesis based on a standard model of stellar and planetary formation, then as soon as you leave Sol's cloud you are in Proxima Centauri's. Basically the galactic arms are packed with the things. Intergalactic space may be empty, because there's nothing there to see.

          The existence of the Oort cloud is only a strong conjecture, with only indirect observational evidence from comets. A fortiori the density and distribution of its contents are highly uncertain. Shouldn't the rocks cause tiny perturbations in the light from nearby stars as they pass in front of them? Here's a free suggestion for one of the women astronomers abused by Professor Marcy: investigate the Oort cloud density. It would be a very pretty revenge to show that all his exoplanets are well enough, but we can never go there.

          1. Nothing's wrong with Wikipedia's density of interstellar dust, you just have to note that the dust particles are rather tiny, (Smaller than most bacteria!) so that even at 1/2C they don't pack much energy individually. They're more like high mass cosmic rays than little bombs.

            I think you'd probably levatate a light sail ahead of the ship, that would nicely ionize the gas passing through it, and any dust particles would be turned into charged particle jets. Since your speed would be so much higher than the relative speeds of the dust grains, you could keep that sail a long way out, and guarantee that all you'd face would be the average mass flow distributed over the face of your shield, and ionized to boot.

            Actually much easier to deal with than the original problem, of getting up to 1/2 C in the first place. That's the tough one, IMO, not the shielding issue.

          2. I repeat: what is wrong with my calculation? "The density is estimated at 10exp−6 × dust grain/m3. Assume our spaceship has a cross-section of 100 m2. We will hit one grain every kilometre. [That's 10 grains in 10exp5 m3.] En route to Kapteyn-b, we will hit 1.23 x × 10exp14 grains. That’s only 10 grammes in total," That changes the basis of your power law argument by a factor of 10.

            You also do not address my argument that true interstellar space on your sense will be rare in our galactic neighbourhood. To a first approximation, you will be travelling through Oort clouds all the time. The first precondition for interstellar travel is to find out their density.

          3. At last we agree: Hard numbers are needed. We need to know the actual density and mass distribution of the particles that might be encountered. I believe it's quite low, integrated over the distance. (We can see the stars! That tells us a lot.) But hard numbers are lacking.

            In any event, I expect we'll first colonize the asteroids, Moon, Mars, move on to the gas giant moons, and then one day somebody will colonize a hyperbolic comet, fire up a fusion rocket, and just keep going. Barring a major physics breakthrough, relativistic star travel is going to be absurdly expensive.

            But, if you've got the power to accelerate a ship large enough for humans to 1/2 C, you won't be worrying much about running into anything. You'll just pour some of the power out the front, and vaporize any obstacles long before you reach them.

  4. Do you know the story in Hitchhikers Guide to the Galaxy in which a mighty invasion fleet travels across space and then is swallowed by a dog? Maybe aliens will be so teeny tiny that they can just slip between the cracks, as it were.

  5. James, you might want to calculate the energy of impact for the average dust grain. 10 grams /10E14, that's 1E-13 grams per dust grain. Even at half light speed, each individual grain would only carry a tiny amount of energy, because they're really, really small, much tinier than the dust you see on Earth. There are cosmic rays with more energy than those dust grains.

    1. Doesn't matter much. The kinetic energy is proportional to the mass, so it is quite legitimate to add up. A lot of little impacts, like a high-pressure jet of sand, does the work of one bigger one. The difference is that the grains would impact at different times all over the shield, the rock at one point and instant, so that would create a shock wave with a non-linear effect. The difference is that between getting hit by 100 bullets from a machine-gun and by one hand grenade.

      1. I continue to think you don't quite appreciate how empty space is, once you get out of the inner solar system.

        You are, fundamentally, right about the inability to detect objects large enough to destroy a ship far enough out to dodge them, if you're traveling at any appreciable fraction of light speed. But you just haven't internalized how rare such objects really are.

        A hydrogen molecule every cubic centimeter or so. Perhaps 20 mg of hydrogen will impact each square meter of ship on a trip of 4 light years. And that's most of the mass between the stars.

        A dust particle smaller than most bacteria, every million cubic meters or so. That's about 0.04 mg of dust per square meter over the same trip. And that's most of the remainder. Five hundred times less dust than gas.

        Suppose grains of sand, macroscopic grains of sand a mm across, represent a similar fraction of the dust. There's 500 times less dust than gas, say 500 times less sand than dust. That's a fairly plausible power law.

        In your 4 light year trip, one square meter of ship would encounter 0.04/500, or 0.00008 mg of sand. Where the sand particles are 1mg, so to put it another way, in a 4 light year trip you'd have one chance in 125 that your 100 square meter ship would hit a single grain of sand.

        Baseball sized rocks? Might as well worry about running into rogue planets.

        Well, I'll grant you this is interstellar space. You wouldn't want to plow through the inner solar system at half light speed. The sand is a lot more common.

  6. Our concept of what "intelligent life" might consist elsewhere in the universe is so intensely speculative that it undercuts all further lines of speculation here. Also, the universe (let alone cosmos) is soon darn big that even if there are semi-quasi-humanoids out there somewhere that we would love to meet, the distance barriers are just plain crippling. Finally, your Easter Island history needs review. Per the book The Statues that Walked: Unraveling the Mystery of Easter Island Hardcover, Hunt and Lipo, 2011: The island was probably first settled about 1200, more recently than previously thought. Those first settlers found a forest of palm trees, which in due course got wiped out, but not for the carelessly self-destructive reasons previously thought. It is likely that the problem was the semi-domesticated rats the settlers brought with them, which proliferated and ate the palm seeds so thoroughly that the trees stopped reproducing. Before European contact, the islanders were actually wringing a fairly stable agricultural sustenance out of a very difficult environment. Is this holds up, the argument that European contact — although inevitable — was much of a blessing is problematical.

  7. I think all of you are forgetting the notions of long-term tracking and bistatic radar. We can already track kilometer-scale items out in the Ort Cloud using a single not-that-big dish.A civilization with the resources to do serious interstellar exploration (and one for whom 0.001C is an issue) is going also be in a position to build a synthetic-aperture radar dish roughly the size of its home solar system. That's enough angular resolution and power to track much of the small-to-middling stuff out to a pretty distant range (and once you have a few observations you can predict paths for quite a while to the future) and also enough power to illuminate items closer in (with coded signals so that the ship could distinguish illumination bursts from interstellar background light, and also as a result so that the "radar" would be essentially undetectable to outside observers.) So the detection-range calculations need to be revised again.

    1. "We can already track kilometer-scale items out in the Oort Cloud using a single not-that-big dish." Source? All Google can find for me is observations of cometary nuclei from the Oort cloud. They came as far in as the asteroid belt; the report does not say how far out they were when first detected, but there’s no suggestion it was anywhere near the origin. SFIK comets are bigger planetesimals that get knocked inwards by some perturbation, perhaps a passing rogue planet.

      Your supergiant radar tracking quadrillions of currently invisible rocks is fun SF, but show me the math. To get to Proxima Centauri, which we know already does not have a habitable exoplanet, the radar needs a range of 4 light years, since it has to cover two Oort clouds. For Kapteyn C, 12 light years.

      At this point, I think it's for those who believe manned interstellar travel is feasible to come up with credible non-magic roadmaps to solving the huge problems. We stopped writing SF with Martians a few decades ago, once we actually knew what the surface of Mars is like. If there is like on Mars, it's struggling bugs.

      1. You're right; I was working back of the envelope. It turns out that Arecibo hasn't imaged past Saturn (1.2 billion km) because (http://ancientsolarsystem.blogspot.com/2015/03/q-and-with-arecibo-observatory-research.html) it can only point at the same object for about 150 minutes at a time, and round-trip travel for light is longer than that. The simplistic resolution at that distance is about 10km, but detection size tends to be quite a bit smaller than resolution.

        At submillimeter wavelengths, an Oort-cloud-scale aperture would have a resolution (simplistic) 10^-3/10^13 = 10^-16 radian, or about 1 meter at 1 parsec. In the bistatic case, resolution might go down but detection of very nearly on-course objects would go up.

        So for a civilization that has the exawatt-hours of energy to spend on accelerating a ship to 0.1C or above — and the technology to do it at least semi-efficiently — I don't think that this particular problem is the show-stopper. Which doesn't mean I think non-magic "rapid" interstellar travel is plausible, just that it's implausible for other reasons.

        1. For Kapteyn’s star, you need 4 parsecs. Nobody has challenged my calculations of the kinetic energy of the impacts, and I maintain that hitting objects considerably smaller than 1 metre in cross-section would still be fatal. (An exercise ball is about 65 cm in diameter. I also assumed low-density ice rather than rock.) You would expect the distribution of rocks by size to follow a power law – surely gravity can’t be strong enough to clump them, it hasn’t collapsed the denser asteroid belt in 4 billion years. For every object you can just detect, there are probably hundreds of smaller ones that can still kill you.

        2. "So for a civilization that has the exawatt-hours of energy to spend on accelerating a ship to 0.1C or above" you let part of the beam pushing your star ship go by it, and vaporize everything solid in the path of the ship, drilling a hole through the interstellar medium.

          You won't be detecting things, you'll be blowing them way.

          1. Even if you don't vaporize things, you can give them a velocity increment away from your course. And if you're the kind of civilization that does this kind of thing, you can do it pre-emptively for a few decades or centuries.

            Which brings me to what I think might be a primary issue: social and enterprise stability. Unless you invent magic stasis pods or send frozen embryos that you raise to adulthood by robot or some such, even "fast" star travel is going to be a multi-generation affair. (Yes, a lot of the people directing planetary probes now were grad students when planning for the missions started, but they haven't been stuck inside their labs the whole time). So you need a social order like the ones that built the cathedrals or the Great Wall, only an order or three of magnitude more advanced. And (unless you have robots that make the humans unnecessary supercargo) you need at least hundreds of people to maintain the ship and themselves. If you've solved that issue, "fast" travel stops being a necessary part of the deal.

            In addition, once you have the not-quite-magical technology for exawatt-hours and routine short-duration intra-solar-system travel and multi-decade-scale semi-closed habitats, things change quite a lot. Our solar system (not counting the Oort Cloud) becomes capable of supporting populations significantly larger than that of earth, and the question of whether a target star has an earth-style planet becomes moot.

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