So You Want To Colonize The Universe Part 3: Dust

(1, 2, 4, 5)

Part 3a: Dust and Explosions

To a first ap­prox­i­ma­tion, there’s ex­actly one thing that sets the speed limit on go­ing fast in space.

Dust.


In the fu­ture, dust will be a Very Big Deal, as it’s the dom­i­nant con­straint on the most-im­por­tant in­stru­men­tal goal of go­ing fast.

An­ders Sand­berg’s pa­per pointed out dust as a con­straint on in­ter­stel­lar probe de­sign, but I didn’t re­al­ize ex­actly how huge of an ob­sta­cle dust was un­til I started play­ing around with a spread­sheet.

To start with, in­ter­stel­lar (and in­ter­galac­tic) dust has a size dis­tri­bu­tion, which tells you, for a given di­ame­ter range, how many dust grains there are of that di­ame­ter in a given vol­ume.

At least for the range of 35-120 nanome­ters, (which shows up es­pe­cially strongly in as­tro­nom­i­cal ob­ser­va­tions) it fol­lows a power-law dis­tri­bu­tion, with an ex­po­nent of −3.5.

How­ever, this dust isn’t what we’re wor­ried about. There’s ero­sion from pro­tons and small dust hit­ting your dust shield at rel­a­tivis­tic speeds, but dou­bling the dust di­ame­ter means it’s 8x as mas­sive and hits with 8x the en­ergy.

At 0.9 c, 180 nm dust hits with 1 joule of en­ergy. So all the nor­mal dust isn’t that much of an is­sue.

Go­ing up to dust that’s 1 microm­e­ter wide, it hits with about 100 joules of en­ergy, the en­ergy of a fire­cracker. For all the fol­low­ing ex­plo­sion com­par­i­sions, note that it’s go­ing to take the form of a su­per-nar­row pin­prick of ki­netic en­ergy di­rected on a sin­gle point, which is more de­struc­tive than a sim­ple ex­plo­sion, which ra­di­ates in all di­rec­tions and has much of its en­ergy dis­si­pated as heat.

Destruc­tive power keeps scal­ing rapidly, with about a fac­tor-of-ten in­crease for ev­ery dou­bling in dust di­ame­ter, un­til we reach 20 microm­e­ter dust, which hits with the en­ergy of a grenade.

40 microm­e­ter dust hits with the en­ergy of 1.5 kg of dy­na­mite. 86 microm­e­ter dust hits with the en­ergy of 30 bricks of C4. 0.18 mm dust hits with the en­ergy of half a cruise mis­sile. 0.4 mm dust hits with the en­ergy of the Ok­la­homa city bomb­ing. 0.86 mm dust hits with the en­ergy of the largest non-nu­clear weapon, the Rus­sian FOAB. 8.6 mm dust hits with the en­ergy of the Fat Man nu­clear weapon, and 1.8 cm dust (a ball bear­ing) hits with the en­ergy of a W87 fis­sion war­head.

So, from about 1 to 20 microm­e­ters, we get a pretty de­cent amount of boom that’s shield­able. Whip­ple shields are the cur­rent stan­dard for microm­e­teor im­pact. They have a pro­tec­tive thin layer that gets hit, turn­ing the blast into a cone of shield-va­por, and then the force of the blast is dis­si­pated over the area of a cross-sec­tion of the cone on the main bulk of the ship, which is much more man­age­able. How­ever, I’m pretty sure that at rel­a­tivis­tic speeds, the cone gets a lot more nar­row, so they get less effec­tive.

20 microm­e­ters to about .1 mm is han­dle­able if your ship is re­ally damn sturdy.

.1 mm to 1 mm re­quires in­creas­ingly large dust shields that will start look­ing more as­ter­oid-like, get­ting big­ger than the mass of the rest of the ship, as they have to be that big to tank a hit from the largest non-nu­clear weapon fo­cused in a sin­gle tiny pin­prick and nar­row cone. Re­mem­ber, by rel­a­tivity, there’s no differ­ence be­tween cruis­ing through the in­ter­stel­lar medium at 0.9 c and be­ing in the beam dump of a par­ti­cle ac­cel­er­a­tor that’s whip­ping stuff up to 0.9 c. Any­thing larger than 1 mm re­quires that most of the mass of the mis­sion is com­posed of an as­ter­oid, with the size of the as­ter­oid rapidly scal­ing with dust size.

So, up to about 10 microm­e­ters, we need a de­cent dust shield, 10 microm­e­ters to 0.2 mm re­quires the sort of dust shield that can tank a hit from a cruise mis­sile fo­cused in a sin­gle point, and be­yond that we ba­si­cally have to whip an as­ter­oid up to 0.9 c and at­tach a small ship to it with very rapidly scal­ing as­ter­oid size. This re­quires quan­tities of en­ergy that could blow the crust off a planet.

We know a lot about low-di­ame­ter dust that can be con­ven­tion­ally shielded with lit­tle is­sue, but we know very lit­tle about the dis­tri­bu­tion of higher-di­ame­ter dust, and that’s the dom­i­nant con­straint on mis­sion speed and coloniz­ing the uni­verse. Of course, if we get a re­ally bad dis­tri­bu­tion of higher-di­ame­ter dust, we can always go slower. For non-rel­a­tivis­tic speeds, halv­ing the ve­loc­ity cuts the im­pact en­ergy by a fac­tor of 4, and for rel­a­tivis­tic speeds, you get a lot more than that be­cause of de­creases in the rel­a­tivis­tic-mass of the dust grain.

Maybe we’ll get lucky and find that there’s a sharp dust-grain cut­off be­yond a cer­tain size. Maybe we’ll get un­lucky.

Part 3b: Dust Distri­bu­tion Facts and Implications

There are three rele­vant con­sid­er­a­tions I found, try­ing to work it out from first prin­ci­ples and as­tron­omy facts. The first is that a dust size dis­tri­bu­tion im­plies a cer­tain amount mass in a vol­ume of space by do­ing the ap­pro­pri­ate in­te­gral over di­ame­ter. The −3.5 ex­po­nent means that the amount of mass di­verges. In or­der for the in­te­gral to con­verge and have finite dust mass in the uni­verse, you need an ex­po­nent a hair be­low −4. But we don’t know the di­ame­ter where the ex­po­nent shifts down to −4 or lower.

The sec­ond is that the as­ter­oid belt has a size dis­tri­bu­tion of −3.5, and this is ap­par­ently char­ac­ter­is­tic of frag­men­ta­tion pro­cesses. The rea­son there isn’t in­finite mass in the as­ter­oid belt is be­cause there’s a size cut­off at the mass of Ceres. And we get the in­tu­itive re­sult that the mass of the as­ter­oid belt is mostly in large as­ter­oids.

The third con­sid­er­a­tion is that dust comes from many pro­cesses. Su­per­novae and dy­ing stars floof out a bunch of dust into the en­vi­ron­ment. We found a su­per­nova grain as large as 25 microm­e­ters once, which is wor­ry­ing. But most su­per­nova dust is a lot smaller than that. For the mil­lime­ter-size dust grains, I imag­ine it’d come from plane­tary for­ma­tion discs that got dis­rupted, which is a differ­ent pro­cess with a differ­ent dust pro­duc­tion rate. So I’d ex­pect differ­ent re­gions of space to have differ­ent dust size dis­tri­bu­tions, some of which might come with a nat­u­ral mass cut­off. Maybe molec­u­lar clouds with form­ing stars are es­pe­cially dan­ger­ous. Maybe the void be­tween galax­ies is mostly de­void of fatal dust (rel­a­tive to the hy­dro­gen den­sity). Maybe dust gets more and more abun­dant as a galaxy ages so it’s much more dan­ger­ous to travel in dis­tant galax­ies that have aged by the time we get there. We don’t know, but it’s prob­a­bly mod­e­lable.

Now, there’s two more things to note.

The first is that re­quired-as­ter­oid-mass to shield against the largest dust grain likely to be en­coun­tered is ridicu­lously sen­si­tive to the scal­ing ex­po­nent, and pretty sen­si­tive to how fast you’re go­ing. Pretty much, if you make your as­ter­oid have twice the ra­dius, you get 8x the mass, so you can tank 8x larger ex­plo­sions, right? Well, maybe tank­able ex­plo­sion power doesn’t scale lin­early with mass, I’m un­sure. But more im­por­tantly, your as­ter­oid now sweeps out 4x the area be­cause it has 4x the area, so you’re 4x more likely to hit dust of a given size. Now, over­all, you’re still bet­ter off, but an in­crease in mass doesn’t buy you nearly as much dust pro­tec­tion power as you’d naively as­sume, so dust still sets a pretty hard speed limit with quite rapidly scal­ing as­ter­oid mass for trav­el­ing longer dis­tances and higher ve­loc­i­ties.

The sec­ond is that, due to the fact that dust is the dom­i­nant ob­sta­cle to go­ing re­ally fast, there will be an awful lot of op­ti­miza­tion power di­rected at this prob­lem, so the stan­dard caveats ap­ply about con­clud­ing that even a tran­shu­man civ­i­liza­tion can’t do high-speed mis­sions due to dust. Two ob­vi­ous im­prove­ments I can see are mak­ing ma­te­ri­als that are re­ally good at dis­si­pat­ing mas­sive pin­point ki­netic en­ergy strikes, and find­ing some way to deflect dust. I think there’s ways of charg­ing the dust ahead of you and us­ing a mag­netic field to move it out of your way, but it’s hard be­cause we’re mostly in­ter­ested in large dust which is a lot less sus­cep­ti­ble to these shenani­gans, though I’d have to check. Also, any dust deflec­tion sys­tem (and the power drain im­posed by it) must be run­ning full-time over the in­ter­galac­tic voy­age, which brings in the stan­dard prob­lems about mak­ing ma­chin­ery that long-last­ing.

Edit: In the three hours since typ­ing this, I found that some­one in­vented a com­pletely novel deflec­tion strat­egy I missed, and I also in­vented an­other one on the spot, prov­ing my “don’t un­der­es­ti­mate the fu­ture” point very well. The one I didn’t come up with is throw­ing a bunch of liquid metal droplets ahead of your ship, enough to en­sure that a dust grain hits at least one of them and ex­plodes, like an ex­tremely long-dis­tance whip­ple shield and very slightly ac­cel­er­at­ing the whole way so you can re­cap­ture the droplets and launch them back ahead of you. This has the is­sue of re­quiring con­tin­u­ous ac­cel­er­a­tion, and los­ing mass the whole way due to cos­mic ray spal­la­tion of the droplets, and droplet va­por­iza­tion when they get hit by smaller dust grains. Off the top of my head, it’d be pretty de­cent for an in-galaxy mis­sion, but I worry that for in­ter­galac­tic mis­sions, the cu­mu­la­tive mass loss from droplets get­ting de­stroyed, and the pro­pel­lant/​con­tin­u­ous en­g­ine op­er­a­tion re­quired to con­tin­u­ously ac­cel­er­ate the whole way, would be a bit much, plus it doesn’t work on de­cel­er­a­tion, just coast­ing. No, I’m not go­ing to redo my de­sign from scratch to take this into ac­count, it’s eaten enough time already. As for my in­sight, it’s that if you have many space­craft in a line, each can pro­tect the next one, so the vol­ume of space swept out by the fleet is much lower. Or, heck, you can just have the first dozen in the train be­ing in­ert blocks of rock and only build im­por­tant at­tach­ments for the stuff in the back.

So, for my mis­sion, I as­sumed we’re just di­rectly tank­ing the im­pacts on a gi­ant block of graphite, and there’s a dust scal­ing ex­po­nent of −5 in in­ter­galac­tic space (there are less pro­to­plane­tary discs which is where I think a lot of the scary dust comes from, and there aren’t a lot there), a scal­ing ex­po­nent of −4 in in­ter­stel­lar space, and −3.5 closer to a star. As an ex­am­ple, shift­ing the dust scal­ing ex­po­nent of in­ter­galac­tic space to −4.5 in­creases the mass of the as­ter­oid we have to send by about 3.4 mil­lion times. This is what I meant by mass be­ing ridicu­lously sen­si­tive to scal­ing ex­po­nent size. The re­sult­ing dust shield mass per su­per­cluster-ship (mostly dust shield though) is about 120,000 tons for a squat cylin­der of graphite 42 m or about 140 feet long , or about 1/​5th the mass of the titanic. Also we’ll need about 30 of these for a 99.9% chance that at least one sur­vives (higher sur­vival prob­a­bil­ities are at­tain­able by just send­ing more) It’s far more effi­cient on a mass ba­sis to send a fair few ships with a mod­er­ate chance of sur­vival than to send one big ship with a 99.9% sur­vival chance.

So in sum­mary, dust size is the dom­i­nant con­straint by far on how fast you can go, with un­ac­cept­ably rapid-scal­ing mass in­creases as the ex­po­nent on the power law goes up.

Edit: Un­less tran­shu­man or mere-hu­man in­ge­nu­ity comes up with a way to cheat some part of the dust prob­lem, in which case we’re back in busi­ness.