# So You Want to Colonize The Universe Part 4: Velocity Changes and Energy

(1, 2, 3, 5)

Part 4a: Speed­ing Up

Ok, so how do you get up to 0.9 c in the first place?

The com­mon an­swer is “an­ti­mat­ter”, but an­ti­mat­ter ac­tu­ally isn’t that good for mis­sions that are ex­tremely rel­a­tivis­tic. This is be­cause of the Tsiolkovsky Rocket Equa­tion, which ap­plies any­time you’re car­ry­ing your en­ergy source and pro­pel­lant on­board. For­tu­nately, it’s very sim­ple. . is your change in ve­loc­ity. is your ex­haust ve­loc­ity. And is the mass of the rocket full of pro­pel­lant, with be­ing the mass of the rocket with­out pro­pel­lant.

Eye­bal­ling this, we see that the ex­haust ve­loc­ity gives you a de­cent ap­prox­i­ma­tion to how much you can change your ve­loc­ity by, if you’ve got about 2 parts pro­pel­lant to 1 part mass. Get­ting more ve­loc­ity change re­quires an ex­po­nen­tial rise in your mass ra­tio, and very rapidly gets to not be worth it, as pretty much no rocket has a mass ra­tio greater than about 20. Also, for stuff go­ing re­ally fast, the en­ergy de­liv­ered is high, but the mo­men­tum isn’t nearly as high, so high-spe­cific-im­pulse rock­ets that whip their ex­haust up to rel­a­tivis­tic speeds emit an awful lot of en­ergy, but have the sort of thrust typ­i­cally as­so­ci­ated with a fleet of asth­matic hum­ming­birds be­cause they’re very fuel-effi­cient and have a low mass-loss rate.

There are rel­a­tivis­tic ad­just­ments, of course, but the same ba­sic be­hav­ior ap­plies. Also an­ti­mat­ter an­nihila­tion has the prob­lem of spend­ing about 40% of its en­ergy as gamma rays which just go in all di­rec­tions and can’t be used for thrust as a re­sult, so you have to ad­just the equa­tion to ac­count for that in­effi­ciency.

So, even for a beam-core an­ti­mat­ter rocket, it’s a bit more dis­ap­point­ing than you’d think. The clas­sic ex­am­ple of this is the Fris­bee An­ti­mat­ter Star­ship, a hilar­i­ously am­bi­tious star­ship de­sign that is about 700 km long, has about 160,000 tons of an­ti­mat­ter aboard, blasts out 100 ter­awatts of power, and achieves a measly 0.25 c. There have been no­table im­prove­ments in beam-core en­g­ine de­sign since then, but it’s still too much for too lit­tle speed. And eye­bal­ling it, the dust shield looks pretty puny, be­cause it’s sized for ero­sion from rel­a­tivis­tic pro­tons and small dust grains, not the cruise-mis­sile-level dust grains I’m wor­ried about.

Cer­tainly in­suffi­cient for an in­ter­galac­tic mis­sion at high-rel­a­tivis­tic ve­loc­i­ties.

Edit: Found an­other beam-core an­ti­mat­ter star­ship de­sign that does a lot bet­ter, the Valkyrie star­ship. Ap­par­ently the titanic size is partly an ar­ti­fact of try­ing to squeeze high thrust out of an an­ti­mat­ter beam core so it doesn’t take mil­le­nia to get up to full speed, and the an­ti­mat­ter beam core in­nately has very lit­tle thrust, so you have to crank up the power to enor­mous ex­tremes. It’s also partly an ar­ti­fact of hav­ing a gamma-ray shield that’s a lot big­ger than strictly nec­es­sary with a differ­ent con­figu­ra­tion, which re­quires mas­sive ra­di­a­tors, which means you have more dry mass to push, which means you have to make ev­ery­thing else big­ger to com­pen­sate, which in­cludes the rocket and the shield and you make the ra­di­a­tors big­ger again… The Valkyrie claims the abil­ity to get up to 0.92 c and back down with a 20:1 an­ti­mat­ter to ship ra­tio by mass, or 2,000 tons of an­ti­mat­ter, which is a bit much, es­pe­cially be­cause solid (anti)hy­dro­gen isn’t very dense, and if it’s pos­si­ble to go a given speed with­out get­ting de­stroyed by dust, the up­com­ing pair of ap­proaches seems to be strictly bet­ter than any given an­ti­mat­ter rocket de­sign be­cause they com­pletely dodge the rocket equa­tion and the pesky ln term in­terfer­ing with high-rel­a­tivis­tic speeds, and also don’t re­quire enor­mous amounts of an­ti­mat­ter.

But if you think about it, why does the en­ergy source for get­ting the ship to go fast have to be on­board?

A far su­pe­rior solu­tion is a light­sail, a gi­gan­tic and very thin and very re­flec­tive sheet that you can fire a laser at to get your pay­load up to speed. Now, I didn’t re­ally de­sign this part to a high de­gree of de­tail, and I think there might be is­sues with hav­ing a suffi­ciently large sheet not crum­ple like tis­sue pa­per un­der the stress of its launch. A spot for fu­ture work on mak­ing a re­al­is­tic de­sign if some­one wants to take it up. You also need a gi­gan­tic float­ing laser lens to shoot the thing up to a dis­tance of about 40 lightyears.

How­ever, as­sum­ing you’ve got a dyson swarm available, you have more than enough en­ergy on tap to bring what­ever you’d want up to high-rel­a­tivis­tic speeds. I was get­ting num­bers that were some­thing like an ex­awatt per ship (and again, we’d need 30 of them). So you’d need as­tro­nom­i­cal lev­els of en­ergy-har­vest­ing and lasers, and es­pe­cially heat ra­di­a­tors, and this wouldn’t be an im­me­di­ate pulse, but you’d be crank­ing out mul­ti­ple ex­awatts for decades at a time. For­tu­nately, as­sum­ing the abil­ity to de­vote enough re­sources to­wards firin an as­tro­nom­i­cally large la­zor, this is peanuts com­pared to the en­ergy that’s available from a star, and it lets you skip the rocket equa­tion com­pletely! No rea­son to be pow­ered by an­ti­mat­ter when you’ve got the fury of a star-pow­ered laser at your back, launch­ing you unto the cos­mic void.

Of course, tran­shu­man tech­nol­ogy might find some­thing bet­ter, or a great re­fine­ment on the ba­sic idea, but I’m still pretty con­fi­dent that they’ll skip de­signs sub­ject to the rocket equa­tion, that is a pretty pun­ish­ing as­pect.

But how do you slow down? That will take just as much en­ergy as speed­ing up....

Part 4b: Slow­ing Down

Once upon a time, Robert Bus­sard had an idea for a star­ship. In­ter­stel­lar space isn’t empty, it has a very thin mist­ing of pro­tons in it. If you could do pro­ton-pro­ton fu­sion, you could have a gi­ant mag­netic scoop that fun­neled the in­ter­stel­lar medium into the rocket, where it’d fuse it for en­ergy, then shoot it out the back, so it’d be gath­er­ing its own pro­pel­lant and en­ergy source as it went, and could get up to very rel­a­tivis­tic speeds.

It cap­tured the pop­u­lar imag­i­na­tion, and then more calcu­la­tions were done. It turned out to be bad. Really bad. So hilar­i­ously bad that it man­aged to achieve the elu­sive feat stated in Re­v­ersed Stu­pidity is not In­tel­li­gence about how a bro­ken car couldn’t go 200 mph in re­verse, even if it was re­ally bro­ken.

The mag­netic field pro­duced a lot of drag. A hell of a lot of drag. In fact, the ba­sic in­sight of “set up a large mag­netic field in the in­ter­stel­lar medium” is the cur­rently known best way to come to an ab­solutely screech­ing halt from rel­a­tivis­tic speeds and is plau­si­bly go­ing to be an in­dis­pens­able part of any se­ri­ous in­ter­stel­lar mis­sion. It pro­duces so much drag that it is used to drop my star­ship de­sign from 90% of light­speed to 2% of light­speed in 1.5 lightyears, pul­ling 1.5 g’s of de­cel­er­a­tion at the peak. This is a lot.

It turns out the way to de­cel­er­ate from rel­a­tivis­tic speeds doesn’t take a rocket, it just takes a big loop of su­per­con­duct­ing coil towed be­hind you and which slows down by dump­ing ki­netic en­ergy into vi­o­lently shov­ing in­ter­stel­lar hy­dro­gen away.

Now, there’s a caveat. My de­sign ac­tu­ally doesn’t shed most of the ki­netic en­ergy. The anal­ogy is that if you’ve got a crash­ing plane and a pas­sen­ger on it, you’re much bet­ter off at­tach­ing the parachute to the pas­sen­ger than the crash­ing plane. Yes, you’re go­ing very fast, but you’re only go­ing through a lightyear and a half, so much less dust shield­ing is needed be­cause you’re much less likely to get hit in that space in­ter­val, so you can just sep­a­rate from most of the dust-shield­ing block, let it streak through the galaxy at 0.9 c, (and get spec­tac­u­larly wrecked in a vi­o­lent ka­boom by a piece of gravel at some point), and keep dump­ing shield­ing-mass as you slow, which makes it even eas­ier to slow you down, and it feeds on it­self un­til most of the re­main­ing mass is ac­tu­ally in the su­per­con­duct­ing coil.

There’s some fur­ther de­tails, one is about how to slow down from 2% of light speed (mag­sails don’t slow you much at non­rel­a­tivis­tic ve­loc­i­ties, but this is still far be­yond the ca­pa­bil­ities of al­most all rock­ets that aren’t an­ti­mat­ter, but there’s an­other way to cheat this with­out pro­pel­lant), and the other is about how you prob­a­bly can’t hit a spe­cific star from 200 mil­lion lightyears away so you’ll need some ex­tremely beefy en­g­ine to get about 0.1% of light­speed of on ap­proach so you can boost side­ways to aim at a spe­cific star that looks promis­ing, but those are im­ple­men­ta­tion de­tails that I’ll go over later.

Part 5c: Power Sources and the Proper Use of Antimatter

Wait, didn’t that pre­vi­ous stuff about need­ing an en­ergy source for the fi­nal de­cel­er­a­tion and the mag­netic parachute, im­ply the use of power?

To a first ap­prox­i­ma­tion, there’s ex­actly three en­ergy sources that are com­pact enough for space mis­sions (that we know about given pre­sent tech­nol­ogy). There’s an­ti­mat­ter, which re­leases about 100% of it­self as en­ergy. There’s fu­sion, which re­leases about 1% of it­self as en­ergy. And fis­sion of ra­dioac­tive el­e­ments, which re­leases about 0.1% of it­self as en­ergy.

Ob­vi­ously you’d want to use an­ti­mat­ter, right?

Well, it de­pends on how much you’re us­ing. You see, an­ti­mat­ter an­nihila­tion has ex­tremely pen­e­trat­ing de­cay prod­ucts. There’s a bunch of very high-en­ergy gamma rays (low hun­dreds of mega­elec­tron­volts, MeV). There’s a bunch of charged pi­ons with a similar en­ergy range, which go about 60 m or 60 ft (I for­got) be­fore de­cay­ing into muons and neu­trinos. Both muons and charged pi­ons are re­ally pen­e­trat­ing. We reg­u­larly find no­table lev­els of muon ra­di­a­tion from cos­mic rays 100 me­ters down in the earth, which is why many sen­si­tive par­ti­cle physics oc­cur in deep mines, and pi­ons are about equally pen­e­trat­ing due to a similar mass. Now, these pi­ons and muons are much lower-en­ergy than cos­mic ray muons, so the situ­a­tion isn’t quite that bad, but they still have a ten­dency to re­quire an awful lot of shield­ing. And a cou­ple per­cent of the en­ergy is ra­di­ated as kaons, which have similar is­sues, and can be charged or un­charged, the lat­ter of which is un­af­fected by mag­netic fields.

Amus­ingly enough, kaons con­tain a strange quark, which marks the only time the strange quark is ac­tu­ally rele­vant to a prac­ti­cal en­g­ineer­ing de­sign.

I’ll get into more de­tails later, but you’ll re­quire a pretty healthy weight of shield­ing mass un­less you want to lose a bunch of your an­ti­mat­ter en­ergy to space and hose ev­ery star­ship part in the vicinity with enough gamma ra­di­a­tion to give a per­son an in­stant-coma ra­di­a­tion dose in a few sec­onds. Yes, there are no peo­ple, just sili­con chips, but ra­di­a­tion hard­en­ing isn’t that ad­vanced. (Yet)

So, in the limit of large amounts of en­ergy, an­ti­mat­ter is definitely the best. But for smaller amounts, an­ti­mat­ter power’s to­tal mass is dom­i­nated by shield­ing mass, fu­sion’s mass is dom­i­nated by the mass of what­ever the most-com­pact fu­sion de­vice of a given wat­tage the fu­ture can come up with (and neu­tron shield­ing, if they go for that type of fu­sion power), and fis­sion… has a bunch of weight by it­self, but you also need your nu­clear re­ac­tor and the as­so­ci­ated shield­ing.

My de­sign has about 160 g of an­ti­mat­ter on board, which is both quite man­age­able to pro­duce rel­a­tive to the ab­surd 150,000 tons an an­ti­mat­ter star­ship needs (Edit: see above, maybe not), and in the realm where it’s kind of un­clear which power source does best. I picked an­ti­mat­ter over “ul­tra-com­pact fu­sion re­ac­tor” mainly be­cause it’s sexy and more fun to spec­u­late about. I used about 3 tons of shield­ing, so maybe fu­sion would be bet­ter if the fu­ture can make a fu­sion re­ac­tor that pro­duces 10 megawatts and weighs un­der 3 tons. Or maybe a fis­sion re­ac­tor could make it work, al­though the fuel alone (with a very effi­cient 20% bur­nup) would weigh a ton, and this ne­glects the rest of the re­ac­tor and neu­tron shield­ing.

Part 5d: You’ve Gotta Have Radiators

Vacuum is a great in­su­la­tor! This is why vac­uum-layer win­dows are awe­some for in­su­la­tion, be­cause the only way heat can leave is by ra­di­at­ing away. This is a big prob­lem in space travel, though. If you’re crank­ing out a gi­gawatt of heat en­ergy, your space­craft will heat up un­til it’s ra­di­at­ing a gi­gawatt in ther­mal ra­di­a­tion and glow­ing bright or­ange, toast­ing any­thing on­board that re­quires tem­per­a­tures lower than molten iron to func­tion.

So most of a prac­ti­cal space­ship’s vi­sual space is com­posed of ra­di­a­tors. Or­di­nary chem­i­cal rock­ets drop much of their en­ergy in the form of hot es­cap­ing pro­pel­lant, but fu­sion, fis­sion, and an­ti­mat­ter rock­ets are very effi­cient with their pro­pel­lant, so this av­enue isn’t available.

You’ll need some way to deal with this if you want to do any space mis­sion with a fis­sion, fu­sion, or an­ti­mat­ter power source of any ap­pre­cia­ble mag­ni­tude. Re­mem­ber the Fris­bee An­ti­mat­ter Star­ship I men­tioned ear­lier? 500 of the 700 km of length is just a gi­gan­tic ra­di­a­tor to dis­si­pate the heat be­ing ab­sorbed by the gamma-ra­di­a­tion shield of the an­ti­mat­ter en­g­ine. I got my ra­di­a­tor for the an­ti­mat­ter re­ac­tor down to a paltry 14 of a kilo­me­ter, and I feel pretty proud about that.

An es­pe­cially cool tech­nol­ogy for this is the liquid drop ra­di­a­tor, which uses some sort of molten metal, and sprays it out as a sheet of fine droplets which has mas­sive area, which is then col­lected and re­cir­cu­lated. It’s un­suit­able for re­ally long mis­sions be­cause of very slow metal evap­o­ra­tion into space, but pretty nifty.

Due to the un­suit­abil­ity of these for re­ally long mis­sions, the part in my de­sign where there’s a 10,000-year burn of a dusty-plasma-fis­sion rocket, (The an­ti­mat­ter beam core is also ac­cept­able, and prob­a­bly has more man­age­able ra­di­a­tion shield­ing is­sues, but I wanted to high­light an ob­scure de­sign that shows that fis­sion can be sur­pris­ingly effec­tive) for steer­ing to a good-look­ing star, crank­ing out 3.5 gi­gawatts of heat the whole way, re­quired some­thing a bit more… solid. Di­a­mond is the best heat con­duc­tor, and I’m as­sum­ing it’s available by nan­otech, so the gi­ant cylin­dri­cal plug of graphite is also go­ing to have ex­ten­si­ble di­a­mond ra­di­a­tor fins that will glow bright or­ange on ap­proach.

Part 5e: More Notes On An­ti­mat­ter Shielding

I think mag­netic fields can con­fine the pi­ons and muons and charged kaons to a finite re­gion un­til they in­ter­act with some­thing, dis­si­pat­ing their en­ergy, and then you just need gamma ray shield­ing. Also, beams of charged par­ti­cles can have en­ergy ex­tracted from them in a much more effi­cient way than dis­si­pat­ing heat. This would prob­a­bly be used in a prac­ti­cal de­sign, but I was be­ing stub­born and wanted to cap­ture the neu­tral kaons too, and figured “hey, if we’re shield­ing gamma rays, is it prac­ti­cal to shield ev­ery­thing and drop the mass of the mag­net and en­ergy-ex­trac­tion sub­sys­tem and have a vanilla tur­bine op­er­at­ing off the heat from the shield?” Ba­si­cally, it’d just be a solid ball of shield­ing, and you shoot the an­ti­mat­ter into the cen­ter, where ~all of the ra­di­a­tion is ab­sorbed, and the ball can be cooled down by a coat of liquid metal be­ing pumped over it.

Now, the muons only show up later, and if you can stop the pi­ons, the ki­netic en­ergy of the de­cay muons is low enough that they ac­tu­ally aren’t that pen­e­trat­ing. So the task is to stop a flux of high en­ergy gamma rays and pi­ons and kaons. The dom­i­nant en­ergy loss mechanism at these en­er­gies is in­elas­tic col­li­sions, where the pion or kaon smacks an atomic nu­cleus di­rectly, blast­ing it to bits, which smack into other nu­clei, and the en­ergy level and pen­e­trat­ing­ness of the ra­di­a­tion dras­ti­cally falls as en­ergy drops, un­til the en­tire cas­cade is con­tained. For gamma rays, they smack an atomic nu­cleus di­rectly, and turn into an elec­tron-anti­elec­tron pair, which does a smaller cas­cade and is less pen­e­trat­ing. Still, even a more sen­si­ble de­sign with charged par­ti­cle en­ergy ex­trac­tion is go­ing to need the gamma ray shield­ing (or just in­cred­ible ra­di­a­tion re­sis­tance) and weigh a de­cent amount.

Crunch­ing the num­bers, I dis­cov­ered some­thing hilar­i­ous. There’s a num­ber that is ba­si­cally “what thick­ness of ma­te­rial gets half of your beam to in­ter­act”, and for very dense el­e­ments, this gets thin enough to coun­ter­act the in­creased den­sity of your ball. Lead is used in con­ven­tional gamma-shield­ing be­cause it’s cheap and pretty dense. But, as star­ship de­sign is a very im­por­tant pri­or­ity for a civ­i­liza­tion, they’d prob­a­bly splurge on what­ever ma­te­rial is op­ti­mal.

The op­ti­mal ma­te­rial turned out to be os­mium (al­though iridium and plat­inum would be about as good). Yes, in star­ship de­sign, where ev­ery gram counts, I found a perfectly le­gi­t­i­mate en­g­ineer­ing rea­son to stick a 3-ton ball of os­mium in the mid­dle, as the an­ti­mat­ter re­ac­tor core. As a bonus, an­ti­mat­ter re­ac­tions tend to split heavy nu­clei, so there’s an en­ergy boost from in­duced fis­sion in the os­mium, and os­mium is re­ally hard to melt so it can definitely ac­com­mo­date the re­ac­tion.

• In­ter­est­ing idea about mag­netic brak­ing, I didn’t know about it.

Not sure you need a very pow­er­ful laser to ac­cel­er­ate. Stu­art re­cently pointed out here that you can add an­other mir­ror at the source, so the light keeps bounc­ing be­tween the ship and the source, im­prov­ing effi­ciency by a huge fac­tor.

• Seems like that’s go­ing to be less effec­tive than it might sound be­cause of (1) beam di­ver­gence and (2) the fact that if there’s even the tiniest mis­al­ign­ment be­tween the mir­rors then af­ter a cou­ple of bounces the light will be miss­ing its tar­get.

• Some op­tions you didn’t men­tion (maybe on pur­pose be­cause they are less effi­cient?):

• Cheat­ing the rocket equa­tion us­ing pulse propulsion

• Break­ing a laser sail space­ship by hav­ing a mir­ror that de­taches and re­flects the laser back to the space­ship but from the op­po­site di­rec­tion (don’t re­mem­ber whose idea that is)

Also, your rocket equa­tion is non-rel­a­tivis­tic, al­though IIRC the rel­a­tivis­tic equa­tion is the same just with change in ra­pidity in­stead of change in ve­loc­ity.

• Yeah, I think the origi­nal pro­posal for a so­lar sail in­volved de­cel­er­a­tion by hav­ing the cen­tral part of the sail de­tach and re­ceive the re­flected beam from the outer “ring” of the sail. I didn’t do this be­cause IIRC the beam only main­tains co­her­ence over 40 lightyears or so, so that trick would be for nearby mis­sions.

• I’m con­fused. Wouldn’t it mean that even with­out this trick laser sail is only for nearby mis­sions?

• I’m talk­ing about us­ing a laser sail to get up to near c (0.1 g ac­cel­er­a­tion for 40 lightyears is pretty strong) in the first place, and slow­ing down by other means.

This trick is about us­ing a laser sail for both ac­cel­er­a­tion and de­cel­er­a­tion.

• Makes perfect sense, for­get I asked.

• Minor nit­pick: di­a­mond is only metastable, es­pe­cially at high tem­per­a­tures. It will slowly turn to graphite. After suffi­cient space travel, all di­a­mond parts will be graphite parts.

• Ac­tu­ally, no! The ac­ti­va­tion en­ergy for the con­ver­sion of di­a­mond to graphite is about 540 kJ/​mol, and us­ing the Ar­rhe­nius equa­tion to get the rate con­stant for di­a­mond-graphite con­ver­sion, with a ra­di­a­tor tem­per­a­ture of 1900 K, we get that af­ter 10,000 years of con­tin­u­ous op­er­a­tion, 99.95% of the di­a­mond will still be di­a­mond. At room tem­per­a­ture, the di­a­mond-to-car­bon con­ver­sion rate is slow enough that pro­tons will de­cay be­fore any ap­pre­cia­ble amount of graphite is made.

Even for a 100,000 year burn, 99.5% of the di­a­mond will still be in­tact at 1900 K.

There isn’t much room to ramp up the tem­per­a­ture, though. We can stick to around 99%+ of the di­a­mond be­ing in­tact up to around 2100 K, but 2200 K has 5% of the di­a­mond con­vert­ing, 2300 K has 15% con­vert­ing, 2400K has 45%, and it’s 80 and 99% con­ver­sion of di­a­mond into graphite over 10,000 years for 2500 K and 2600 K re­spec­tively.