Space 19a: Solar Power Satellites, Take 3 Redux


… we can have a station at L2 behind Mercury and still have a wide variety of orbits available. Which is good because I don't know how else we can do a fixed collection point.

I really should know better.

If we're really going to depend on power satellite orbits following the Kepler rules, then we need to keep them far away from any actual planet. Mercury can't be there; end of story. If Mercury is there, then there's no way around having to solve a 3 body problem, and while it might be possible (like I've been assuming) to perturb the Kepler orbit into an actual orbit that works and stays in synch with Mercury, my gut feeling at the moment is that'll be a huge mess to get right.

Also Mercury's orbit is really eccentric which severely screws up the only 3-body solutions I know about.

And if Mercury is not there, then there's no way to hang a station at aphelion. By default, anything stationary at aphelion falls into the sun, unless we do weird space elevator shit and tether it to something (no idea); but, as with the Earth space elevator, that probably entails unobtanium cables with insane tensile strength and we're in Not Gonna Happen Land.

And I'm realizing now there's a much, much simpler solution available:

Put rockets on all of the antimatter cells.

That's it. Once a cell finishes charging, the satellite releases it and it flies off to wherever it needs to go.

(Yes, Rockets are Still Stupid, but if we put a mass driver on the satellite, then the satellite will nearly always have to do an orbit correction every time it launches a cell and we won't actually have saved anything. So rockets it is…)

Chances are, for the sake of administrative sanity if nothing else, we'll still want to have a collection point somewhere. And we'll probably want it to be a Lagrange point so as to have access to all of the best IPTS orbits. But this can be any of the ones available in the inner solar system.

Hell, we could even use Earth-Moon L2. That might even make sense if it's still fairly early in the agenda and lunar orbit is where we need to have antimatter arriving.

In case you were wondering, the energy cost of moving a kg from, say, Mercury's orbit to Earth's is about 2.5 billionths of a kg, which somebody has to be paying anyway. Unless we want to be really stingy and do some stupid funky Mercury/Venus flyby to bleed off momentum, which I suppose we could do, but bleah.

What to do with the empties is potentially more complicated. Maybe our software will be good enough that calculating ballistic trajectories to get them all back to some power satellite somewhere will be workable.

Or we can just make a point to never discharge a cell below the 2.5 billionth mark (or just keep an extra cell around with power in it to do infinitesimal recharges as needed), so that it'll always have enough energy to go find itself a power satellite. KISS.

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Space 20: Dyson Spheres

(you'll want to read about solar power satellites first, where we cover all of the sensible stuff)

On Dyson Spheres and the other ridiculous things truly advanced civilizations will be doing with all of their free time

I should note that the scenario that I fleshed out in the previous post, i.e., having a cloud of independently orbiting power satellites that would start blocking out the sun if we really were able to populate huge numbers of orbits, is a lot more what Freeman Dyson was talking about in his original paper. The fixed sphere that people tend to imagine when they hear about this stuff really makes no sense at all if you think about it (and Dyson knew this at the time and said so). I mean sure, let's waste a whole lot of effort and materiel fighting solar gravity directly; that should be oodles of fun.

Making only slightly less sense is the flotilla of stationary habitats supported by solar sails. We're doing this why? Because we have this pathological hatred of orbital mechanics and don't want to make use of it? So much better to be depending on a sail that can get a hole in it and then we go plummeting straight into the sun. That sounds so much like a place I would want to live; really. Sign me up, please.

At best, I could see it as a kind of Bite Me, Universe gesture by a civilization that really has Done Everything, is now completely bored, and just wants to build some kind of insane, completely pointless artifact, just for the hell of it, because they can. Sure. Why not?

But I can't see it as something we're going to do while we're still on our way to the stars.

And I still wonder:

Can we really build all that?

Forget the full Dyson sphere, let's consider just one of the solar power satellite orbits. The chart in my previous post is calling for anywhere between 600,000 and 10 million square kilometers of satellite area.

Now, at this point, I don't even know what we're going to be making them from or what the preferred tech is going to be for solar power generation. Photovoltaic? Big-ass mirror driving some kind of heat engine? Or maybe we'll be supplying light to a mini-farm that's going to grow megatons of gerbil food, and then, in the next module over, we have billions of gerbils running their little wheels at top speed (at which point our movie instantly loses its "No Animals Were Harmed..." designation)?

Yeah. No idea.

But we can always make some kind of half-assed estimate. Let's just build aluminum sheeting; whatever the solar collector is, we'll need someplace to mount it. How much sheeting can we make out of the asteroid belt? We can vaguely do this:

  • total mass of the asteroid belt (kg) is 2.3910×10²¹ kg.

  • people estimating relative abundances in the universe say aluminum is 58 ppm of everything. Fine, so asteroid belt might have 1.38678×10¹⁷ kg of aluminum.

  • let's be pessimistic and imagine that only 1% of it is mineable, or we lose 99% in the smelting process for whatever reason. Now we're at 1.38678×10¹⁵ kg.

  • the thinnest sheeting you can buy online is 1/32"=0.79375mm thick. Meaning we need 793.75 m³ of aluminum to make a 1 km² sheet.

  • Density of aluminum is 2.7g/cm³=2700kg/m³, so that's 2.143 kg to make a 1 m² sheet or 2.143 million kg to make a km² sheet.

  • So we get 650 million 1 km² aluminum sheets if we harvest the entire asteroid belt. Which is somewhere between 60 and 1000 times the number of km² we need to populate one of our orbits, i.e., if it were the case that collecting solar energy only needs the km² aluminum mirror and everything else on the satellite is really cheap and easily available.

  • So by this completely stupid measure, depending on which orbit we choose, anywhere between 60 and 1000 orbits are doable using the h= 36.635km⁻¹ separation and the Mercury L2 point.

  • Note that these orbits were designed to suck off 86400 kg/day which is 1/4.26×10⁹ of the sun's output. Meaning blotting out the sun will entail filling 4.26 billion orbits, assuming we get the geometry exactly right.

Which seems to suggest that we'll get our 86400 kg/day power production and maybe even be able to go up to 1000 times that, but as far as blocking out the sun goes, just forget about it.

But then we have this interesting fact that I only learned about recently:

The Asteroid Belt is way smaller than you think

On the off-chance that anybody's still trying to convince you that the asteroid belt is the remains of a planet that got destroyed, here's something that really makes that not work:

The total mass of the asteroid belt is about 3% of the mass of the moon.

To be sure, I always knew the asteroid scenes you see in The Empire Strikes Back were bogus (space is big), but I'm still surprised that there's not even remotely enough there for any kind of respectable planet. (Sorry, James Hogan and whoever else wrote SF stories that had a planet breaking up a million years ago)

Which calls into question some of the premises of asteroid mining.

I will grant that there's stuff that won't be available on the moon. But for what is available, which probably includes all sorts of building materials, why not just mine the moon?

We can obtain 3% of the moon by strip-mining the top 12 km of its surface, and we might even vaguely be able to do that with present-day tech. And it's right here; no needing to travel hundreds of millions of km to get to Ceres or wherever else. Probably get huge economies of scale, too.

Granted, this won't really help with the Dyson Sphere. Even consuming the entire moon is only giving us a factor of 30, which is a long way from the 4.26 billion we need. Even eating all of Jupiter only gets us a factor of 800,000.

I think I can safely say that there is not enough aluminum in the solar system to cover the sun. Switching to a more abundant metal like iron gains us another order of magnitude or two, but I suspect we're still hosed.

Though, again, I'm obliged to point out how dubious this particular estimate is. It's not an impossibility proof by any means, and if the materials science folks do manage to come up with some carbon-nanotube/ceramic bullshit unobtainium that's insanely lightweight and can be built out of anything — much like I'm expecting them to do for the laser ships and light-sails we need for the transit tube — then all bets are off.

But I still think I'm pretty safe in putting the Dyson Sphere on the Not Gonna Happen list. If not because it's impossible, then because I'm not convinced we're going to need it.

Granted it is a bit weird finding myself in the position of wanting to say that 86,400 kg of matter+antimatter per day really ought to be enough for anyone — sounds a little too like that apocryphal Bill Gates quote — and having to stop myself.

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Space 19: Solar Power Satellites, Take 3

After my previous forays into the question of How to do Solar Power Satellites Right, here and here, there seem to yet more ways to simplify the math and get a better sense of the design space. Very annoying.

In particular, that WTF/4A energy flux formula is not, in fact, the final word on simplifying and, it seems, we can have a station at L2 behind Mercury and still have a wide variety of orbits available. Which is good because I don't know how else we can do a fixed collection point.(No no no no no)

So, rewind. Let's try this again:

Doing Solar Power Right

The plan: Have a ring of satellites in a single, not-necessarily-circular orbit around the sun, all soaking up sunlight and using it to charge antimatter cells. How do we get this to produce some number of kg per day? What are our actual choices?

One would think the number and sizes of the individual satellites shouldn't matter a whole lot. To first order, we'll just have some total acreage of solar panels being crammed into the orbit. Multiply by solar power flux and we're done, right?

However, if we make the satellites too small, then we're making more of them to cover the same area, and if they're all vaguely square/circular — the sensible way to build them — and thus correspondingly less wide, they'll use up more linear space in the orbit and eventually start bumping into each other. Which we very much don't want.

Life will also be easier if our satellites are evenly spaced, whatever the hell "evenly spaced" means in a non-circular orbit where, at any given time, individual bodies in orbit will necessarily have all different velocities and constantly changing mutual distances.

The key observation is that if they're all in the same orbit, then they're all moving in lock step. Assuming that none of the satellites are big enough to be gravitationally messing with any of the others, we're back at the two-body problem that Newton solved 300+ years ago. They're gonna do what they're gonna do and Ellipses are Forever. If it takes one of them, say, 5 days to go from point A to point B, the same will be true of the next satellite following along. So if we make measurements of the km²/day passing point A, we must get the same numbers at point B 5 days later.

Which means that when we're first injecting satellites into this orbit, we want to be sure to inject them at a constant rate — call this our solar panel current, i.e., make it so that the number of km²/day passing the insertion point remains constant.

Once we do this, the current will then be constant and also be the same constant everywhere else along the orbit. Individual velocities can still vary, but anywhere that we have satellites moving faster, they'll have to be more spread out to keep the current the same.

Thus, the place where we have to worry most about stuff colliding will be at aphelion, that point farthest from the sun where everything is moving slowest and hence most bunched together. A panel density can be obtained from dividing the panel current (km²/day) by the aphelion velocity (km/day). This number (km²/km) is how many km² of panel you'll see in any snapshot of 1 km's worth of orbit — or, rather, in every km of an imaginary circular orbit in which everyone is going at (constant) aphelion velocity and spaced out exactly as how they arrived at aphelion.

… which will necessarily be a lower bound on the actual spacings you see in the real orbit. Since I prefer to think in terms of spacings rather than densities, I'll be working in terms of this inverse number instead. That is, we'll define the spacing to be:

h = (panel current) / (aphelion velocity) = 1/ (panel density)

which gives us a number (km/km²), i.e., the number of km of (imaginary circular) orbit you need to snapshot/grab in order to see/accumlate 1 km² of solar panel.

If each individual satellite has area A, then hA is how far apart the satellites will be at aphelion. And if we're comfortable with that being the distance of closest approach, we'll be good to go.

Getting into the ball park

We can now give the formula for this orbit's total power production:

power = W / (2 R h)

where R (km) is aphelion distance, h (km⁻¹) is the spacing, and W is total output of the sun as before (use whatever energy-per-time units you want).

And, yeah, that's it. Just like the WTF formula, this is an exact solution (*) and somehow has none of the other factors you'd expect to see. Inverse-square-law fields have all of these wacky hidden tricks and stuff that cancels unexpectedly. Gauss is probably laughing at me.

(*) or, at least, as exact as we get in what is actually an n-body problem (Yes! This!) and, given that we're in close to the sun, maybe also some General Relativity bullshit lurking (what causes Mercury's orbit to precess) as well. It's also possible I'll lose because I'm ignoring Mercury's gravity (Yes! This!). we'll probably want (small) engines on the satellites to correct perturbations.

So,… if, say,

  1. we want aphelion to be at the L2 point behind Mercury (58,130,000 km) (We don't, but this is just as good an example number as any), that convenient place I keep wanting to put a station — which is annoyingly just outside the total solar eclipse zone by about 18,000 km, but maybe having a mere 84% of the sun blocked might be good enough, and also maybe that distance is short enough that we can do some space-elevator bullshit so that the inhabited part of the station(No no no no no) — assuming there even needs to be one — can be hanging down inside the total eclipse zone anyway — and

  2. we want the spacing factor to be, e.g., 36.635 km⁻¹ (to pick a completely random number),

we can just turn the crank:

3.68×10¹⁴ (kg/day, total solar power)= 86,401 (kg/day)
2 × 5.813×10⁷ (km, aphelion) × 36.635 (km⁻¹, spacing)

… which is roughly the number we were getting before, except we're not counting satellites, computing periods, or velocities or anything.

And, also, you can now easily see that if you want 10 times this much power, one way to get there is to reduce the spacing by a factor of 10, to a mere 3.6 km/km². Which will work reasonably well if the individual satellites are 1 km² (and thus 3.6 km apart), but not so well if they're 1/5 that size (200m square ⇒ area is 0.04 km² ⇒ spacing is 3.6km⁻¹×0.04km² = 144m, which is going to lose badly),
… and even with 1km² satellites we're arguably close to the size limit for this orbit.

… which in general will be a diameter of 4/𝛑h for circular satellites, with square ones being able to get away with being 1/h on a side provided you can keep them from turning.

Getting the Actual Orbit

Note that this does not yet nail down the orbit. If we want to find out, say, how much stuff we have to actually build or how close it'll all be getting to the sun, that's more work. There's one more parameter to specify, which we choose depending on what we most care about:

  • if we want to keep our satellites out of the solar corona, we probably care a lot about the perihelion (closest sun approach) distance, for which the formula that matters is

    ε = (aphelion − perihelion) / (aphelion + perihelion)

    where ε is

  • eccentricity, which we could just specify directly, if we have a number we like.

    This is the measure of how much the orbit is squunched, ε = 0 being zero squunch (circular orbit), and values approach 1 as the orbit gets narrower with satellites diving in closer and closer to the sun, the limit being ε = 1 which would normally be a parabolic escape-velocity orbit except those have infinite aphelion, so if we also specify a finite aphelion, that means we're in this degenerate case where the satellites are just being dropped from aphelion directly into the center of the sun and never heard from again.

    Suffice it to say, we really want ε < 1.

  • semi-major axis, usually denoted a, this being the distance from the geometric center of the orbit (not where the sun is) to either perihelion or aphelion, since ellipses are symmetric that way.

    In case you were wondering:  aphelion = a(1+ε) and perihelion = a(1−ε).

    As it happens, there are lots of other numbers you can use as proxies for the semi-major axis (i.e., they're all conveying the same information), including
    • orbital period, T = 2𝛑aa/GM, but only if you know the magic constant GM/4𝛑² = 2.509462183311675×10¹⁹ km³/day² (M being mass of the sun and G being the gravitation constant, but for this you don't need those numbers separately)

    • orbital energy, E = −GM/2a

    and so on.

  • total satellite area = panel area A × number of satellites N.

    If h is how far you have to travel (along that imaginary circular orbit) to see 1 km² worth of panel, and hA is how much linear space one satellite is taking up at aphelion, then hAN is all of the space, the circumference of that imaginary circular orbit, how far you go to see all of the satellites. You can also get this number from the aphelion velocity and the orbital period.

    So calculating AN given ε is somewhat straightforward:

    hAN = vT = 2𝛑a(1-ε)/(1+ε) = 2𝛑(aphelion)√(1-ε)/(1+ε)³

    Calculating ε given AN is unavoidably mysterious. If I were sane, I'd just use Newton's Method, but since there actually is a formula for solving cubic polynomials (like the quadratic formula, but people tend not to know this one because it's hideous) we can do this:
    ε = s/3 − k/s − 1 where s = 3k(9 + √3(27+k))
    and k = (2𝛑(aphelion)/hAN)²
    As for where that comes from, well,… you can ask. Maybe one of these days I'll do a page on Galois theory.

    and AN has its own proxies, notably
    • the aphelion velocity v = hAN/T = √GM(1−ε)/(aphelion)

    • the aforementioned panel current = AN/T = v/h

    and so on.

And then we do the wall of numbers to show the range of possibilities you get where production is 86,400 kg/day, satellite spacing is 36.635 km⁻¹, and aphelion is at the Mercury L2 point our chosen distance:

perihelion (km)AN(km²)εcurrent (km²/day)
 1,000,000  665,0550.966176 20,724
 2,173,7631,000,0000.927906 30,256
 3,000,0031,190,8710.901848 35,303
13,764,3133,000,0000.617095 69,729
58,129,9909,969,649   3.2×10⁻⁸ (~circular)112,685

Radius of the sun is around 700,000 km so it's not really advisable to try for closer approach than a million km. And while I'd like to think the corona doesn't go past 3 million km, it probably will whenever the sun gets in a bad mood.

That last column is the area (km²) of solar panel that will have to get serviced per day at the L2 station, which you'll notice is Rather A Lot (if the satellites are 1 km² each, then you've got one arriving every few seconds). Yes, this whole operation, like everything else in space, will have to be highly, highly, automated. Surprise.

Not that it should be that difficult. I imagine 99.99999% of the time a satellite will just pass on through, toss its charged antimater cells into a receiving net, and then the station will have a mass driver firing the empties at just the right speed so that the outgoing satellites can pick them up easily. Since the relative velocities will range from 8 to 40-some-odd km/sec, that's probably going to be the only way to do this.

Somewhat more interesting is the repair scenario, where you're either having to send a ship out to catch up with a broken powersat, and either fix it in situ or haul it away somewhere, which will be really expensive because you're totally changing its orbit. However, being at Power Collection Central you'll have as much energy as you need. Somewhat cheaper would be catching it with a tether and using that to swing it out of the stream sufficiently fast so that the next powersat coming along a few seconds later won't crash into it. And wow, will that have to work right the first time.

I still get amused at shows like "The Expanse" where it's imagined that people are going to be out there in space suits doing these jobs with their bare hands. Not that there can't be a role for humans. Person-In-Charge sitting in the Gods-Eye-View office in the total eclipse zone, running some Really High Level Software to monitor things. Maybe.

Personally, I think I'd feel better if actual people were kept well away from these sorts of operations.

All of the above is, of course, for just one orbit. At some point, the power needs will get beyond what one orbit can provide, and then …

… we, of course, start a second one.

which shouldn't be that big a deal at that point. Give it a slightly different orbital plane and the only places the new satellites will have any chance of running into any of the old ones in the first orbit will be at aphelion or perihelion. If we shift both of those numbers by a kilometer or two, that will suffice. We can even have them managed from the same L2 station, (unless we want multiple stations for redundancy, which we will at some point,… probably a lot sooner than we'll need that second orbit).

And then we build a third. You can probably see where this is going.

(Next: Dyson Spheres)

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Space 18: A Holiday Card for the Kelvans

(continued from here)

So, now what?

Intergalactic Travel

This is where we get full-on, batshit crazy. (You knew this was coming, right?)

Quick reminder in case you forgot or didn't know: M31, i.e., item #31 on comet enthusiast Charles Messier's list of things that annoyed the shit out of him because they weren't actual comets, otherwise known as the Andromeda galaxy, is one of our nearer galactic neighbors, perhaps not the nearest, but it's the one everyone thinks of, so let's just go there.

It is 2.54 million light-years (2.62 million aLY) away. No problem, right? Let's have a look at the numbers:

accel / decel total
shiptime (aY)
mass Cost
shiptime (aY) distance (aLY)

Yes, these mass costs do look a teentsy bit prohibitive.

And yes, you're reading that right:  Even in the cheap case where we're opting to have the journey take 43 years — presumably, by the time we're contemplating this, we'll have figured out how to make an interstellar cruise ship tolerable for a few decades of travel rather than merely a few years (unless we're doing the Australia Thing, it's all prisoners, and we don't care) — we're still burning an entire Enterprise-class aircraft carrier (100,000 metric tons) for every five people we send.

On the other hand, it's a fair bet we won't even be considering this until we've developed, say, a substantial fraction of the Milky Way, say, 100 billion systems. Note that for this particular purpose "developed" means having gotten as far as building energy collection infrastructure and transit tubes; we don't need for them all to be inhabited. If they've all got the same 43,200 kg/day transit budget and we just declare a one day Transit Holiday for everybody, that's … rather a lot of aircraft carriers filled with antimatter, enough to send 200,000 people.

Do that a few days a year for a century and we're basically sending a Europe or 1/3 of an India. Which is not entirely bad for starting off a new galaxy.

But it's possible I'm being too conservative here. Because of something I haven't mentioned yet (it really only occurred to me today).

The Absolute Best Power Plant Ever

By the time our exploration sphere has expanded 25,000 light-years to include the center of our galaxy, we will then be encountering the Sagittarius black hole

… which I originally thought we'd be wanting to stay the hell away from, but…

It spins, see, which means if you throw shit into it at just the right angle and arrange for it to break apart inside the ergosphere (weird-ass 2nd-event-horizon thing that spinning black holes have that you can actually get out of) at just the right time, then half of it will be spit out way, way, way, faster than anyone should reasonably expect, and then you collect all of that extra energy at some safe distance (hahahaha) and use it to charge up antimatter cells.

And then we're building the Really Big version of the solar energy conveyor thing to get all of that antimatter shipped out of there.

These guys say the rotational parameter for the SBH is around 0.44, which means that about 2.6% of its million-some-odd solar masses is rotational energy that can be completely extracted in this way, meaning there's about 5×10³⁴ kg theoretically available to be harvested.

That's half a billion billion billion aircraft carriers. Possibly more as long as there's crap continuing to fall in to speed up the hole. If we don't get greedy and, say, only take a trillion aircraft carriers per year, that's 3 trillion star systems worth of power generation right there.

Without having to explore and settle 3 trillion star systems.

… modulo certain engineering issues that I will not be attempting to address at this time. I suspect we will need to be using both sides of the paper for this one.

I'll grant that my original timeline has the explorers taking a few million years to reach the center of the galaxy and the SBH. It may be that once we have sufficient infrastructure in our immediate neighborhood, we may want to splurge and launch a few Really Fast explorers in the general direction of Sagittarius so that they're getting there a lot sooner, say 30,000 years.

This will be expensive: We're talking 5/6 lightspeed, which means mass cost ratio of around 11 and recall the explorer ships are big, ten aircraft carriers each, so that's 110 aircraft carriers to launch each one or 7000 times our annual single-system transit budget. Then again, recall that Earth is going to have thousands of years of downtime waiting for those first terraformed exoplanets to come on line. Or we could wait the 2500 years to have energy infrastructure set up in 100 systems so that launching the SBH-explorers won't be as big of a bite.

There's also be risk in launching explorers that far that fast in that we currently have no idea what the solar systems are like in closer to the center of the galaxy, whether the mining/reproduction stuff is even going to work out there; the advantage of the slower plan would be in knowing what's there long before we arrive.

But it may well be worth it if we can have this fucking huge energy pipeline up and running in a mere 60,000 years.

If we have the FHEP, we're definitely getting to Andromeda.

Or, if we want to be more ambitious some year and can extract just 0.00000000000002% of the SBH energy available, that's enough to send a billion people each to every single galaxy in the Local Group using the completely wasteful Andromeda-in-29.56-years schedule (first line of the chart above).

Doing the Long Range Exploring

The economics get a little weird, because there's no getting around spending a few million years on exploration and tube construction, and if we're willing to wait another million years, then the entire galaxy will be already terraformed and harvesting energy by the time we get there.

Also, Andromeda almost certainly has it's own big-ass black hole, and unlike with the Milky Way, our explorers can be heading straight there first thing to get that pipeline started. Which then gets us started on the next galaxy quite a bit sooner than you might think.

Never mind that we're now operating on a timescale where there'll be time to build some real Earths, not just the fake ones you can throw together in a few thousand years. Assuming we even care about that anymore (we might!).

We're clearly going to need to run the explorers differently, since proceeding at 1/100 lightspeed and waiting 250 million years for the explorers to get to Andromeda is really not optimal anymore, nor is the randomly expanding-in-all-directions thing going to work for us. We need to be a lot more goal-oriented now.

Also, intergalactic space is really, really thin. The most we're going to be able to expect is maybe 1 star every 1000 light-years and the mineralogical pickings may be slim once we're away from places where Type III supernovas have happened (though maybe building everything out of aluminum will work just fine). But there are indeed going to be stars. Assuming we can find 2500 systems vaguely lined up 1000 light years apart, we can then have the explorer taking, say, 500 years to build up some energy infrastructure in a system — again, all we need is a stupid little red dwarf — to accumulate enough energy to do the next 1000 light-year hop at 2/3 lightspeed and then begin construction of that portion of the transit tube backwards towards the Milky Way, so as to generally progress at 50% lightspeed and get there in 5 million years (starting up the Replication Thing and going back to the old explorer schedule once we get close to the end) with the transit tube mostly completed.

And we'll probably want to wait an additional 2.5 million years, because, among other things it might be nice to hear back and find out that our explorers actually made it there and were able to do stuff, and also confirm that the tube's been completed, before sending the first actual payload ships with Actual People, (though I suppose it'll be possible to have the transit tube start turning payloads around if the laser ships entirely lose contact with the far end, or receive an "oops", or attain some other reason to believe there isn't actually a far end).

Because once we get into the intergalactic realm, we're now operating on timescales where evolution can happen.

In other words, this is where we're more likely to be running into Opposition.

(next up: Aliens… oh wait, I'm lying; there are a few other things to cover first)

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Space 14 (cont.): Solar power satellites redux

(as I was saying in my tech wish list,)

To put some actual numbers on this, if we have the satellites grazing the sun (1 million km out)

So, this was all based on this theory that I had that there'd be a point to putting solar power satellites in close to the sun, that having them dive through the corona for a few hours is what you want. (I've apparently been watching too much Stargate: Universe.)

Strangely enough, this turns out not to actually matter in the way that I thought it would.

More generally, you would think that the energy flux (energy per m² of solar panel) received by a satellite over the course of a single orbit or portion thereof would be really complicated. What with distance from the sun and velocity of the satellite constantly changing, there'd be this nasty integral to do, there being any number of questions about ellipses, e.g., how to calculate the perimeter, that don't have easy answers in terms of familiar functions.

But this isn't one of them.

Herewith I present the formula for total energy flux received for a satellite traversing some angular fraction F of its full orbit — doesn't matter which F, i.e., it's the same energy for any wedge having a given angle at the center, no matter whether it's pointed towards perihelion (closest approach), aphelion (farthest away) or any other direction — where we let

  • W = total wattage of the sun and
  • T = the orbital period

(so that WT is the total energy emitted by the sun over a full orbit). Get ready for it...


(Yeah, okay, I'm 12 today. But this is kind of how I feel about it.)

In case you were wondering A is area of the orbit for which there are any number of formulae depending on which information we have, e.g., πab if we have semimajor and semiminor axes. Or πa²√(1-ε²) or πb²/√(1-ε²), if they give us eccentricity instead. And so it goes.

Just to sanity check:  For a circular orbit radius r, area A = πr² and doing a full orbit we get (WT)/4πr², as one might expect from projecting the sun onto a sphere of radius r with the satellite always being on that sphere. But the funky thing is how this all works no matter what the shape of the orbit is.

Short Reason Why:  Angular momentum L = r²dθ/dt is conserved, so when we integrate received power over time to get energy, a whole lot of constants move outside: ∫(W/4πr²)dt = (W/4πL)∫dθ. Also L is twice the area swept out per unit time i.e., L = 2A/T. The rest is setting θ = 2πF and shuffling letters around.

To be sure, we want to be cranking the flux up as high as we can, which means making the area A as small as possible. But you can do that just as easily with a circular orbit as with that weird, highly eccentric one I was using, and then the satellites wouldn't have to deal with corona storms and other nastiness.

The only disadvantage is losing the convenient dark place behind Mercury where service station can hide from getting blasted by the sun. But perhaps if this is 10,000 years from now, our tech may be to the point where building something like that at, say, 1/3 of a Mercury orbit radius without there being a planet to shield it won't be that big a deal (after all, the satellites themselves will have to stand up to all kinds of abuse).

Also, it really won't make much difference having one big-ass satellite vs. lots of little satellites — my original reason for lots of little satellites was so that there could always be one in the corona getting charged up at any given time (on the assumption that the corona was the only place worth bothering having things charge up because that's the only place we get the huge energy flux, which is what turns out to be wrong, i.e., we actually do pretty well using the whole orbit), — …

… other than the usual Economies of Scale vs. the Putting All of Our Eggs in One Basket issues that need way more info about what the technology is actually going to be than we have at present.

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Space 17: Running the Numbers

(galactic empire continued from here)

Some Vaguely Actual Costs

Here, have a wall of numbers:

Shipboard Time (aY)Distance*
for acc+dec
System Time (aY)Mass Cost Ratio
acc+decper aLY* of
acc+decper aLY* of
2.55/8 1.78 3.20 7/6 3.20 2.490.71 11
3.08/17 2.70 4.2611/10 4.26 3.480.78 19
3.55/14 3.93 5.5817/16 5.58 4.750.83 32
4.03/11 5.52 7.2528/27 7.25 6.390.86 54
4.53/14 7.59 9.3846/45 9.38 8.490.89 89
5.01/6 10.2612.1075/7412.1011.180.92147
5.51/8 13.7115.58123/12215.5814.640.94244
sinh φ
2(cosh φ − 1)2sinh φ1
tanh φ
2sinh φeφ − 11 − e−φe − 1

*System distances, that is, as measured in the (star) system frame of reference, meaning this is how the planetary/Earth/Tau Ceti/etc folks see them (i.e., and not how the Shipboard/payload folks or any of the laser ships will be measuring).

Assuming we have a place to get to, e.g., Tau Ceti, that's a particular distance away:  11 light-years = 11.34 aLY (see big footnote below about distance and time units). Then we can:

  • Pick a row, but for Tau Ceti, we have to ignore the 5.5 and 6.0 rows, because those require too much distance (e.g., the 5.5 row requires 13.71 aLY for acceleration and deceleration which is more than the 11.34  aLY that we have).
  • The way to read a row: If we use the 5.0 row, that means we're under power for 5 years (subjective/shiptime) during which time we're going 10.26 aLY, so for the remaining 1.08 aLY we do that much coasting in the middle; ×1/6 means 2 more months of shiptime, coasting at 74/75 lightspeed. And for this we're burning 12.1 kg for every kg of payload we want to send.
  • The other rows are cheaper but take longer. The top row takes the longest (8 years, 6 months of shiptime) but for roughly a quarter the price.
  • The times in the star system frame (we can calculate these from the 4th and 5th columns) will all be pretty much the same, as it happens.

If each star system is devoting, say, half of its energy supply to interstellar transit (and not all of it because whatever else we're doing in the system that isn't transit that needs power, we'll need to be keeping that going), then, once we get to the point where Tau Ceti has a new planet ready for settlement, and let's suppose this is the First New Planet, so that both ends of that tube will have their entire transit budget available for shipping people from Earth to Tau Ceti to get that new colony off the ground, meaning we'll have a full 86,400 kg/day to spend.

If we like that third row's travel time (3.5 years shiptime under power, plus another 2 years, 8 months of coasting), then the cost of sending a kg is 5.65 kg (yes, I know the table says 5.58, but see other big footnote below about "unbalanced" tubes), which multiplies out to around 15,300 kg we can send every day, or roughly 69,000 people/year.

Keep that up for a century and you've planted a colony of nearly 7 million people — plus whatever we get from a century's worth of sex.

Later colonies will have somewhat less throughput because Earth will now have existing transit tubes to the other places that it will need to maintain and so will have fewer kg to spend on the new ones. But we'll always get at least half that number out the door because the uninhabited destinations will be able to spend their entire transit budget on shipping people from Earth.

Note, by the way, that this is not a way to relieve population pressure on Earth, since we're not going to get here until thousands of years after the point where we've stabilized our population (however we manage to do it), which will most likely stay in the billions.

Eventually, we settle into Commerce Mode, with numerous colonies to talk to. Imagining our various settled systems to be arranged in a vaguely face-centered-cubic lattice so that Earth and everybody else will have around 12 outgoing tubes to the nearest neighbors, then Earth's 43,200 kg/day transit budget allows 3600 kg/day for each tube, which lets us send 645 kg (8 people) per day to Tau Ceti (and now that really is 3600/5.58 because we have balanced traffic).

Granted, economies of scale will probably dictate that these be grouped into monthly shuttles of a few hundred people, or maybe a yearly cruise with a couple thousand. In any event, this will essentially be the First Class cabin on the Concorde and will be priced accordingly.

The rest of this is various big footnotes:

On Tubes vs. Rockets

The last column is there to show just how much we're winning over rockets; … unless someone actually wants to visit a system not yet connected by a tube, in which case, that's what they'll need. And, even then, they'll probably want to do some kind of hybrid approach where they're using a rocket but with this trail of Tube-Building Stuff in their wake so that they'll have an easier time returning home.

Except that since most tube construction will effectively be "financed" by the destination systems, the cost of this tube will be borne entirely by the origin system and thus cut into their resources something fierce. So I still can't see anyone wanting to do this without a really compelling reason (i.e., why they can't just send a cockroach and wait the however many centuries for the tube constuction to be completed from the other end.)

One may, however, reasonably ask, since the costs of acceleration to the midpoint are essentially the same as rocketing there, why we don't dispense with the first half of the tube and only build the decelerator half. Various answers:

  • If there's to be traffic in two directions, you're going to need both halves anyway.
  • If traffic is unidirectional, and we don't have the acceleration part of the tube, then we lose the opportunity for the destination to contribute energy (since laser ships from there are the only reasonable way this happens), which matters for the colonization scenario.
  • We win from having a "road", i.e., a string of ships posted in front of us making sure there's nothing substantive in our way, or, in the unlikely event that Something Big shows up that's hard to move, to route us around it.
  • It could also be — read: I'm doubtful about this but it's worth mentioning — that regular traversal of the tube by near-lightspeed ships will generate a "mini-solar-wind" of sorts (via their wakes in the interstellar medium) that will help keep the vicinity clearer of junk than you might otherwise expect. Or we could have the laser ships, during downtimes when there's nothing passing through, periodically firing low-power unfocused bursts outward to generate such a wind (no, I haven't yet done any math on this one).

About time and distance units: aYs and aLYs

So the table actually uses wacky time and distance units.

  • 1 aY is an "acceleration year" which is roughly 31/32 of a solar year, about 11 days shorter.
  • The unit of distance, the "acceleration light-year" (aLY), is correspondingly about 66 Neptune orbits short of an actual light-year.

Since we've changed both the distance and time units, the speed of light remains at 1 (aLY per aY).

The reason to do this is to have g = 1 (in aLY/aY², aLY⁻¹, aY⁻¹, whatever), which simplifies the math all over the place (last row), the same reason as why navy folks prefer nautical miles to actual miles or kilometers. Or why astronomers prefer parsecs to light-years.

In particular, it's not a coincidence that the system time numbers are exactly the same as the mass cost ratios. Likewise, maximum time dilation (coshφ), in this world, is exactly the half the aLY distance (3rd column) plus 1.

And really, once we get out there, it's hard not to imagine all of the colony worlds using the aY as their common "year", since all of the schedules for everything they care about that's coming from outside their respective systems will be based on it, and their own various orbital years will all be different/useless anyway. Also, it'll be baked into the various tube designs much the way our current railroad gauges derive from decisions the Romans made 2000 years ago (yes, I know, partially myth), because the cockroaches will just be out there continuing to build stuff — changing that software will be very hard — so the star charts of human-explored space will just be scaled in aLY, with parsecs and solar-based (light-)years becoming these weird historical artifacts that'll appear on science contest exams and nowhere else. (Naturally, Earth itself will resist changing over for a very long time, perhaps for even longer than the USA will hold onto miles, feet, and inches.)

Also, if we ever develop transhumans — I might want to slap a Not Happening tag on this, too, but that's a longer discussion — who are happy accelerating at a different rate, say 2g instead of 1g, then we can just halve our distance and time units and keep using the same chart. Or, if we're instead accelerating at 31/32g because we decided to be nicer to the old people, then we can read the chart as actual years and light-years.

More math, if you care:  For any given rate of acceleration (like 1g), the corresponding acceleration year is the amount of proper time it takes to increase (decrease) one's velocity angle by 1 by accelerating (decelerating) at that rate.

(Review: "velocity angles" are to velocities as angles are to slopes; you lose if you try to add or subtract slopes, but adding and subtracting angles works just fine. So, e.g., if you're driving down the road with velocity-angle = 2 (96% lightspeed) and you throw a baseball out in front of you with velocity-angle = 3 (99.5% lightspeed), it'll have velocity-angle = 5 (99.991% lightspeed) with respect to the road, which never causes problems because velocity angles can go up to infinity (∞ = actual lightspeed), unlike the velocities themselves which are capped at lightspeed = 1 (or c if you use stupid distance and time units). The conversion is:  (c ×)tanh(velocity angle) = velocity).

In the formulas on the bottom row of the table above, φ is the maximum velocity angle achieved during the trip (= the velocity we're coasting at once we get to the middle, i.e., if we're doing any of that before turning the ship around and decelerating).

About "unbalanced" tubes

All of the costs in the chart above assume that all propulsion is being done by outbound laser ships, i.e., acceleration is being done by ships coming from the source, and decelerating by ships from the destination, and that all ships are firing forward. We schedule payloads, fuel the lasers, and plan the firings so that all laser ships are depleted by the time they reach the midpoint.

In this case, the "tube velocity" (velocity of the laser ships) has no effect, because any effort you put into accelerating the laser ships reduces the redshift (or increases the blueshift) of the beams being fired, and it's a wash.

This changes if any ships are retaining antimatter/fuel past the midpoint, because anything they do from then on means they're firing backwards and there'll be this extra redshift factor due to the tube velocity that gets applied twice. This can be reduced by reducing the tube velocity, but then laser ships will need higher capacity, need to last longer, scheduling gets more rigid, and life gets more annoying.

This is why the colonization scenario costs a bit more than expected (the 5.65 vs 5.58 question). With the tube being used unidirectionally, and because the energy needed for decelerating is so much less, there will be all of this leftover antimatter from the destination side that you'd want to use, but the only place to use it will be accelerating and decelerating more stuff from Earth, and it's the acceleration part of that getting hit with this extra redshift.

(next: leaving the galaxy)

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Space 16: Building the Tubes / In Your Faces, Romans

(galactic empire, continued from here)

The Colonization Arena

So to recap, we've let loose these self-replicating explorer-cockroaches to visit everything that can possibly be visited, and there will be this sphere expanding at 1/100 lightspeed with us at least vaguely in the middle of it. Everywhere in the interior they're going to be building infrastructure and terraforming whatever they can.

Thus, somewhere within the sphere of Explored Stuff, we'll have the sphere of Terraformed Stuff whose boundary will lag by some distance, be it 20 light-years (i.e., if it's 2000 years before the first terrformings are ready for settlement) or 100 light-years (10,000 years) or more. For the purposes of this discussion it doesn't matter a whole lot which it is.

What matters is that, eventually, we will have new planets coming on line and at a constantly increasing rate. In the 300 years it'll take the radius of the Terraformed sphere to grow from 13 to 16 light years, the number of available planets doubles, and it doubles again in the 400 years after that. (Yes, the doubling rate will be decreasing because this is not exponential growth. It's merely cubic. I don't think anyone will be complaining. Except for the aliens. That is, if they exist, I will be very surprised if they don't have at least some issues with this).

Even if the actual numbers of planets turn out to be depressingly low, say, if, instead of going from 64 to 128 to 256, what I figure is the upper end of plausible, i.e., one planet per system everywhere, we instead go from 2 to 4 to 8, that will still not be a bad outcome. Recall that the main point of this exercise is to get beyond 1. (And, yes, if instead we're going from 0 to 0 to 0, that will indeed suck.)

So let's suppose there will be worlds to settle. Now for the fun part: How do we get there? It being agreed that we need to avoid rockets, what now?

Interlude on Mass Drivers

A mass driver is a method for propelling stuff around, invented by Gerard O'Neill back in the 1970s (i.e., if we're being sufficiently specific about the definition; the basic concept for the railgun, which is really quite similar, goes all the way back to World War I, and catapults go back way further than that, but O'Neill admittedly was most likely the first to consider these things in the context of space colonization).

TL;DR:  What matters most for our purposes is that it's a gun, even if it's using electromagnets to propel the payload. Guns are nice in that they allow the payload to be arbitrarily stupid; it won't need engines, fuel or anything else. You just put it in a shell/bucket and pull the trigger.

In O'Neill's version, there's this really long track for the bucket to accelerate along. Then it reaches the end and lets go of the payload, which sails off into infinity. But also you're doing this in a vacuum using magnets that both handle the propulsion and levitate the bucket above the track so that there's no friction. The end result is that virtually all of the energy you're putting in goes towards moving the payload. This is as about as efficient as it gets.

One annoying disadvantage worth mentioning is that if, for whatever reason, you want to do more acceleration (or deceleration) of the payload later on, you will be out of luck, because the payload will not be there anymore.

I propose to solve that problem by having the track extend all the way to the destination.

Yes, you read that right. Suffice it to say, there will be issues:

  • O'Neill's version is set up on the moon (or an asteroid, or Mars) because he's trying to solve a different problem: How to get crap off of the moon (or said asteroid, or Mars), which one can reasonably expect is slightly easier than gettng crap to another star system light-years away.

  • O'Neill's version is on the order of a few miles long. Well, okay, the length was never really specified. It all depends on how fast you need the payload going, and, in theory, at least, you can make the track as long as you want,… until you run out of moon.

    My version will definitely be running out of moon.

Just to be clear about why the moon matters, I'll mention two useful moon attributes that will not be working for us in the stellar scenario:

  1. Having craploads of mass. When the accelerator pushes on the bucket, conservation of momentum (Newton's 3rd law) requires the accelerator to move in the other direction. An accelerator that has the moon attached to it, is essentially not going to move, so the energy you're applying has no place to go except the bucket.

  2. Being a rigid body. You may not have realized this, but rigid bodies are actually miraculous things:  If, say, I poke something with a 10 foot pole, the pole somehow transmits all of the force I apply without any losses, which really shouldn't be possible, when you think about it (and, to be sure, we lose if we rely on this too much; the pole bends/breaks/whatever).

In case you were wondering, Relativity really hates rigid bodies. (The next time anyone pulls a Relativity problem out of a textbook to try to mystify you and it assumes a rigid body, just remember, "There is no such thing as a rigid body," click your heels together, and you'll have a solution in fairly short order). Meaning even if I were to try to build some 10-light-year long monstrosity out of steel bars bolted together, it will, no matter how tight the bolts are, flap around like the 1940 Tacoma Narrows Bridge. Whack one end of it and the other end won't feel it for another decade. Actual rigidity is quite impossible in this world.

Which is why my accelerator will be lots (billions) of pieces moving independently and we'll just have to cope with that. Any of those pieces that don't have moons attached to them (which will necessarily be nearly all of them) are going to move around, and probably a lot, if we don't do something to keep that from happening, which we can deal with, but it costs us.

Note that I might possibly not care about this. If the act of sending a payload shreds the accelerator and scatters it to the four winds, that won't matter so much if I was only ever intending to use the accelerator just that once. However, (1) this does seem kind of wasteful, and (2) an honest accounting would then have the cost of sending include the cost of (re)building the accelerator, and therefore sending won't be as cheap as you might have originally thought it was.

Once we've gotten away from having it be this rigid thing, you probably won't be all that suprised to find out that I'll be using lasers and light-sails rather than electromagnets. (as the QED folks would say, it's all photons anyway…)

In which we one-up the Roman Army Corps of Engineers

So imagine a conceptual tube, however many light-years long. Let's give it a diameter of, say, 100 km. Mainly, we'll want it to be narrow enough so as to be easy to keep clean, i.e., free of large rocks that will ruin the day of any payload trying to be passing along it at near lightspeed, but wide enough to accommodate at least two lanes of traffic, punting for now on the question of how wide "lanes" actually need to be — which I suspect is not going to have much to do with the actual ship/reflector widths, which will be way smaller than the corridor.

The "walls" of the tube will be streams of laser ships all travelling at some low velocity like the 0.018c we were using for the explorer ships — probably six streams in all, 3 going each direction angularly spaced 120° apart for the sake of having the best control over the payload — individual ships in a stream spaced close enough, let's say 600,000 km, that a payload travelling through the tube will always be in range of one of them. Each ship carries enough energy/antimatter to service its share of tube traffic over the course of its own voyage — 1 to 20 kg dribbled out over the course of 600 years in the case of the Tau Ceti tube.

Among other things, this means any changes to the traffic capacity/configuration of tube will need to be arranged no less than 300 years in advance.

The payload ships are really simple: a corner reflector out in front, pulls a bungee cord attached to the rest of the ship, which will just be the payload surrounded with big-ass sphere of (lightweight!) shielding.

Aaaand…, that's all. No engine. No reaction-mass. No windows. No fuel beyond what's needed to keep the lights on and the occupants alive. Well, okay, I suppose we could put in a small engine for those odd, unexpected emergency maneuvers, but every last bit of non-payload extra mass is going to cost us.

(I suppose the bungee is a bit of a splurge, since we could have just mounted the reflector right on the payload, but it should be possible to make the bungee really light and also the passengers will thank us (1) for converting the probably jerky blasts that hit the reflector into a smooth ride — hmm, I'm guessing there's an interesting Control Theory problem there (i.e., we may need a "smart" bungee) — and (2) for not having the lasers aimed directly at them personally — yes, there'll be shielding but the less we stress it, the better, since there's already a whole lot of other crap in interstellar space they'll need protection from)

(Hmm. Let's hope the bungee doesn't break.)

For that matter the laser ships shouldn't be all that complicated either:  laser + mirrors + antimatter cell + camera/radar + software. Done.

As soon as the payload ship passes a laser ship, the latter begins firing at the reflector and keeps firing until the payload passes the next ship, with the magnitudes of all of the various bursts carefully calculated so that payload does what it's supposed to.

Every time the laser ship fires at a payload, it also sends out an equal burst in the opposite direction so that its own course and speed don't change. So this will be at least double the energy cost of a moon-based accelerator. One might suppose that 2×(best we can do) is still pretty good, but there's still one more issue:

  • O'Neill's version is not attempting to boost anything anywhere near the speed of light…

… the problem being that once the the payload ship gets going fast enough, when various laser blasts catch up, they will have been significantly red-shifted, meaning they will need to have been sent with correspondingly more energy to provide the kick needed. That plus the aforementioned doubling makes the overall cost equivalent to what it would be if the payload ship were self propelled, i.e., we're back to rocket economics. So far, so bad.

But then we get to the midway point, the payload ship flips around. From then on it gets fired at by the laser ships it's approaching rather than the ones behind it.

Which means all of the shots from then on are getting blue-shifted, i.e., amplified by the same ridiculous factor that we were losing in the acceleration phase. Deceleration thus turns out to be incredibly cheap. Which is how we win.

Comparatively cheap, anyway. I suspect there will not be very many people living on AlphaC doing a regular commute to a job on Earth. The vast majority of interstellar commerce will take the form of information flows transmitted relatively cheaply at lightspeed. But now, we at least have a story for what happens when there are actual people and perishable goods that need to get places and not be taking centuries to do it.

(next: counting the beans)

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Space 15: Doing the Boldly Go Thing and Infesting the Universe

(continued from here)

How exploration will work

First: the explorer probes will need to be slow. This is a side-effect of how stupid rockets are. Because in the case where you're arriving at a system for the first time, rockets will be the only alternative for slowing down, you'll need exponential amounts of fuel for that, and since the explorer has to carry all of its deceleration fuel with it, you then have to accelerate all of that fuel at the start of the trip,... so there'll actually be this doubled exponential factor in there.

But if we don't try to get anywhere near lightspeed it won't be too bad. Since all of the terraforming is taking thousands of years anyway, nobody's going to care about the explorers being slow.

Numbers for this:
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Space 14: A Quick Trip to the Technology Gift Shop

(continued from here; yes I did a bit of georgelucasing; original of that last post was way too long, sorry)

Technology Requirements/Assumptions

Given that we won't have Warp Drive/etc, what are we actually going to need/have in order to be able to get places? Or, rather, what's the best we're going to be able to do, sticking to known or at-least-vaguely-likely physics? Are we completely screwed when it comes to getting out to the stars, or is there a way to make it work? I think there is, but it's not going to be pretty, and we have to think big.

Let's start with my wish list, which I'll admit is still a bit ridiculous. To some extent it's really more of a best case scenario and it's also biased towards making the calculations easier (cf. all of the places where I'll be assuming 100% or near-100% efficiency).

To be sure, trying to predict where technology is actually going to be, say, a thousand years from now is at best risky; we have no idea when the next thousand-year dark age is going to set us back (I remain appalled that Archimedes came within a hair's breadth of inventing calculus, that Ptolemy pretty much did invent Fourier series, that the 2nd century Romans really were on the verge of industrialization, that if it weren't for the 3rd century collapse, we might have had all sorts of things 1500 years earlier).

On the other hand, these aren't predictions so much as stuff we're going to need eventually and we'll get it whenever we get it. Unless we truly are screwed.

But, at least, everything on this list is (IMHO) way more plausible than what everybody assumes we're going to have that I was complaining about before: Collapse )

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Space 13: How to Have Places to Boldly Go To

(galactic empire continued from here)

About finding planets that will support life

Here's a radical thought:  We won't. And we won't want to.

This is the #1 thing people are really getting wrong when it comes to looking for exoplanets to colonize.

All indications are that the basic chemical building blocks of life are actually fairly commonplace. Which means any planet that has free oxygen (this in itself is kind of a red flag because life is pretty much the only way we know of getting large quantities of free oxygen), the right distance from the sun so that we can have bodies of liquid water, also actual water so that we can have bodies of liquid water, .. all of the ideal attributes, will most likely also already have its own life of some sort. It may not be much more than algae or protobacteria, but that won't matter.

Because it will have evolved separately from us it'll be subtly different. They may use a slightly different set of amino acids. They may have their own notion of RNA/DNA where the codings are slightly different.

Which means it's going to screw up our biochemistry something fierce. Their neurotransmitters and enzymes and whatever else will interact with ours in really stupid ways. In fact, the whole place will be this Huge Biohazard for us that we'll need to avoid at all costs (thank you, PZ Myers), and hence useless from any kind of colonization point of view.

Which means if we are looking for Earthlike bodies, we are never going to find the right planet, because even if we find another Earth, we still won't be able to live there.

The only way out of this box will be to build the right planet. Which changes the questions we need to be asking.

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