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How many people can our solar system support?

Imagine a space city - a habitat designed to house 1 million people.  Something that will provide them with space to live, environmental recycling (food and oxygen) and pseudo gravity (from spin).  You might be imagining a some form of rotating disk, spindle or ring, such as an [O'Neill Cylinder].  The precise form does not matter.  It probably weighs several million tons and is a few kilometers in size.  Got that clearly in mind?

Ok, good.  Now imagine that instead of orbiting a planet, it is floating in sunlight.  Surrounding it is, slowly spinning, a very very thin solar sail, a few thousand kilometers in diameter.  The pressure of the light from the sun bouncing off the sail is balancing the force of the sun's gravity.  Can you see it in your mind's eye?  The sail has to be as low mass as possible, for the light pressure to balance the gravity.  It couldn't be rigid.  You'd have to have tethers from the sail leading down to the colony below it, like a parachute.  From a distance all you'd see would be the sail - the colony, kilometers in size though it is, is far far smaller than it.  A shiny dandylion seed.

In fact, by altering the tension in the different tethers and the speed of rotation, you might be able to get quite good control of the curvature of different concentric rings of the sail.  Which means that you could choose to some extent where to focus the reflected light.  Unless the space city is travelling, the average point the light gets reflected to will be back towards the sun, however it could be varied to shine out at an angle all around the sail, forming a ring, a bit like shining a torch at a shiny ball or directly into a shiny cup.

Now people have proposed creating a sort of Dyson Sphere by having lots and lots of these space cities arraged around the sun (NOT orbiting).  They call it a [Dyson Bubble].  There's only one problem.  With the current strength of sunlight, we don't have a material with a low enough mass per area to make the sail from.  The nearest we have is carbon fiber at 3g/m2 which is 5 times too much.

I propose a solution.

If you have enough space cities arranged, then you don't just have the direct sunlight to push against.  You also have the sunlight reflected from the cities on the far side.  And the light they are reflecting not from the sun, but from all the cities on your side.  And so on.  If all the sails were perfect reflector then to get the required x5 multiplier in sunlight strength, the fraction of total coverage, F, would satisfy:
  N + FN + FFN + FFFN + FFFFN + ... = 5 N
given an 83 % coverage required.  This is lucky as the closest circles can be packed (hexagonal) achieves a 90 % coverage.  So there is room to spare for cities to travel about occasionally, 98% perfect reflection in the sail coating, the very small bit hitting the colony plants or photo cells rather than the sail, etc.

So try imagining it now, this Dyson Bubble.  To get earth normal sunlight, we'd want to position the sphere at about 3 times Earth's orbital distance from the Sun (4.5 x 10^11 m).  How many cities is that?
  4 x pi x ( 4.5 x 10^11 )^2 x 0.83 / ( pi x (3x10^6)^2 ) = 
    = ( 2.5 x 10^24 ) x 0.83 / (2.8 x 10^13)
    = 7.5 x 10^10

That would hold 7.5 x 10^16 people and mass 2 x 10^20 kg.

Of course, they wouldn't have to go for maximum population.  Each 'space city' might be a 'space palace' for just one person or family.  If you could find a material lighter than carbon fiber (such as carbon nanotubes), a small percentage (say 1% which is more than a million palaces for every person now alive) could spend their time gracefully sailing around the static majority, dipping inside and outside the light frame to adjust their average boyancy.  Or, with a bit of help from the cities focusing the light from their sails, no other boyancy adjustment would be needed.

What about the dangers of asteroids hitting the sails?  Two solutions here.  An indivudual city could haul in its sail for a short period, bob down towards the sun, then make it up later - the pressure/gravity ratio works however near or far you are from the sun (both are inverse square laws).  Or a few thousand cities on the far side could focus the reflections from their sails, instantly vaporising any object at the confluence of their beams.  If the focus is a sufficient way beyond the surface of the bubble, the intervening cities would not even have to get out of the way.  One million cities focusing 1 % of their light, and then having that cut down by a factor of 10 by the intervening bubble would still result in a beam 5000 times as strong as sunlight at the focus.

And what would this bubble look like from the outside?  It would have the same luminosity as the sun does now, since the vast majority of the sun light, after bouncing a few times, will still get out of the holes, minus only the tiny amount hitting the living space hung beneath each sail.  Given movement, refraction and other light effects, you might get some frequency splitting, leaving it looking like a glittering sparkling coloured ball.

Ok, that's the first step.  A shell, 3 AU in radius.  Now let's take it a bit further.

Suppose we don't support a city underneath every sail.  Suppose 4 out of every 5 sails are just there to reflect light and only have to support their own weight.  That would let us get away with a much lower sunlight multiplier that x 5.  And as long as they can control their reflections a bit, we can still achieve a x5 multiplier for those sails that do have cities under them.

How could they control their reflections that well?  If they don't need to support a city, there is no particular reason for them to be thousands of kilometers in radius.  A much smaller sail would present fewer structural problems, and might not need to spin or could be part of linked triplets, allowing off axis reflection without unbalancing the position (because the other two sails in the triplet could counterbalance).

Indeed, such smaller sails, or collections of them, could be used to pack the gaps left in the hex tesselation of city sails.  Using a fractal like arrangement of increasingly small sails an arbitrary amout of coverage could be reached.  Not just 90% but 99% or 99.9%.  In fact the limiting factor would become the efficiency of the reflective material (99.7 for [Spectralight], over 99 % for polished gold at [most wavelengths], unknown for [Kapton] and [PET]) and the the ratio of actual city area to sail area (100 - 100 * PI * (3 * 10^4)^2 / 5 * PI * (3 * 10^7)^2 > 99.9999 %)

So we could really rack up the sunlight multiplier inside a shell if we wanted to.  Let's be really conservative and assume 98 % reflection from the inside of the shell.  That gives approximately a x50 multiplier on sunlight strength.  What could we do with that?

Option 1 : Forget carbon fiber membranes, go for something more solid.  Or just hang heavier weights off the sail - such as 10 cities per sail rather than just one. (Or just hang cities from sails that have 1 tenth the surface area originally required.)

Option 2 : To build a shell that receives the same intensity of sunlight as we get on Earth, at x50 you would build it at 7 AU, giving another x 5 population boost because of ratio of the surface areas of a sphere with radius 7 to one with radius 3.

Option 3 : Here's the option I like.  Coat the sail with reflective material on both sides.  Even if the coating is most of the weight, that can't more than double the mass per area.

Why do I like option 3?  Well, supposing you put one shell inside another.  What would happen?  Let's consider two shell:
Shell 1 on the inside at radius R1, with a sunlight multiplier of x M1
Shell 2 on the outside at radius R2, with a sunlight multiplier of x M2

You might think, if M1 = M2 then the same force is hitting the outside of S1 as the inside, and that it would collapse due to gravitation.  But you need to bear in mind that the sunlight that S2 is multiplying is the natural sunlight intensity at R2 away from the sun.  It is a factor of (R2/R1)^2 weaker than the natural intensity at R1.  If the net multiplier pushing away from the sun at R1 is to remain x5 then the equation that needs to be satisfied is:
M1 = 5 + M2 (R1/R2)^2

And of course this recurses.  You can have a 3rd shell outside shell 2, obeying the same relationship, and so on.  Think of a Russian [Matrioshka Doll].  Or an onion.  But instead of solid shells, each one is made up of trillions of space cities floating independently.  The inner shell floats on direct sunlight.  The other shells each float on the combination of the light leaking out from holes in the coverage of the inner shell and their own light reflected back at them from both the far side of their own shell and the reflective outer surface of the next shell in.

How close could the shells be?  Well, we don't need to worry about shade anymore, as most of the light will be reflections from the backs of sails rather than the leaks.  If we started at a multiplier of x50 and had 9 shells, each one with a multiplier 5 less, then the shells could be very close indeed (say 10 times the size of the largest city, to allow nagivation and give the reflections time to spread out), perhaps on the order of 10^9 m, less than a 1% change in radius.

On the other hand, if we kept the multiplier constant at x50 for each shell, each radius would need to be just over 5% larger that the previous one.  That means, starting from just outside the radius of Mercury (0.4 AU) and heading out to just inside the radius of Neptune (30 AU) we could fit in 82 shells.  Let's say 64 to give room for avoiding inconvenient gravitational obstacles and the asteroid belt, not to mention that 50 times the intensity of sunlight at Mercury's radius will cause significant temperature challenges.  Perhaps for the next shell out we could use selective reflection to avoid making it quite so intense in the city itself.

Or we could just have the inner shells use a lower multiplier than x50 (which would entail a sacrifice of increasing the shell seperation ratio between those shells).  Maybe they could use the innermost shells for energy intensive industry and the closest one for anti asteroid activities.  Unlike the single shell model, though, to do effective anti asteroid blasts you'd need to make pre-arranged gaps, you couldn't just depend on leakage.  On the other hand, with more precise aiming allowed by smaller non-city mirrors, there is no reason why you couldn't effectively play pin-ball, shooting each beam through a gap and having it bounce along a pre arranged path of angled mirrors before combining at the outer shell (or for that matter, a rogue space city in one of the shells - something which might happen whether you imagine dictatorship, rational anarchy or just really picky art critics).

You could also use such pinpoint beams to speed navigation - a constant 1 g acceleration gets you around solar distances quite nicely.  With enough precision (maybe some fresnel lenses) you could even boost an interstellar journey, though that's more likely to require laser. (Then again, you need to do something with all that energy you have available, and the solar sails will reflect laser light just as well as sun light.)

But there is a more important use for being able to channel sunlight.  The limiting factor on outward expansion is the intensity of sunlight on the city part.  Now, if you can channel additional beams to provide pin point illumination in the gloomy outer levels then why stop at Neptune?  The [Kuiper Belt] goes out to 50 AU and the [Oort Cloud] goes out to 100,000 AU.  With intense beams to melt raw materials and less intense but longer lasting beams to change their orbit, getting raw materials out there is not a problem.

Construction is also an interesting question.  How do you make one of these in the first place, when it requires already existing to have the solar intensity to support itself?  Once you have the first shell, you can use aimed beams from that to support the next shell out during construction.  Looking at radii we can see that if a shell can aim 1 % of the light it leaks, that could support the construction of the cities destined to make a complete shell at 1.05 times the radius, if the construction is done at 10 times the radius.

Constructing the original first shell is harder.  You'd need either to use artificial energy sources during the positioning phase of construction or you'd need to start the cities off in orbits of different radii, gradually reducing the orbital speed as coverage increases and sunlight pressure takes over fighting gravity.

If we could go all the way out to 100,000 AU (And that's about a light year, so planning ahead would be vital), that would be more than 200 shells.  That's more than 10^8 times the mass required for our original shell, which is about 10^28 kg or 5 masses the size of Jupiter.  Not available.  Let's work backwards.  I think the planets are pretty and the conservation lobby would probably have something to say about vaporising Mars.  Let's stick to [the asteroid belt] which weighs 1% of Earth, or 6 x 10^22 kg.  Assume for the moment that our x50 multiplier will let us get away with making our sails from pretty much anything polishable and that we could use of all that.  How many shells would that be?  Most of the mass is in the outer few shells, which let's us work out that we can't afford a complete shell much beyond Saturn at 9 AU.  Say 40 shells.

So.  Back to our original question. "How many people can our solar system support?".

Starting at Saturn and working back in, decreasing the radius by 1.05 % each shell, we realise that just over half the population would be living in the outer 7 shells.  However at 9 AU those shells contain 9 times as many space cities as our original shell at 3 AU. 
7.5 x 10^16 x 2 x 7 x 9 / 5 = 1.9 x 10^18 people.

At an annual growth rate of 1.5 % to get there from our current global population of 6 x 10^9 people would only take just over 1300 years.  Better start planning now.

I like this, it's nice.  But I don't see how you can bootstrap it.  The first few people to attempt it would fall into the sun - you'd have to build it all at once to benefit from the increased reflected pressure.  --Vitenka
To construct an initial 'bootstrap' shell, at as small a radius as your materials can stand the temperature of, say 0.3 AU, you'd need to stash somewhere in your solar system 8 x 10^8 satellites ("space cities") until you are ready to move them into position 'all at once'.  Luckily a solar system has a lot of space, and the cities don't need their sails to be actually open until you are ready to position them.  In a Dyson Ring, radius R, you could store R satellites where
R = 2 * PI * R / 10^5
So to store all we need, either we use one ring of radius 1.3 * 10^13 m (100 AU), 10 rings of 10 AU or 100 rings of approximately 1 AU.  Since during the construction and storage phase we don't actually care about sunlight or power, there's nothing to stop us storing them in concentric rings in the plane of the solar system, which will have the handy effect of reducing orbit perturbation.  Between Earth (1 AU) and Mars (1.5 AU) we could store 100 rings of cold stored satellites, and have over 0.75 million km between each ring.  Plenty of space.

The actual bootstrap manoeuvre, going from orbiting in rings to deployed stationary in a sphere would be a spectacular 'once in the evolution of a species' type event, and very costly to get wrong.  Timing would be crucial.  To start with, I'd think you'd want alternating cold store rings to be orbiting in opposite directions, to help avoid angular momentum problems.  The simplest way would be to use physical propellent and engines for the once of manoeuvre.  Other alternatives include electromagnetic breaking, exchanges of big lumps of iron, thrown and caught by electric catapults (the 'catcher' would get back the energy used by the 'pitcher' when it decelerates the lump of iron before throwing it back again).  Imagine two boys heading towards each other on skate boards.  They throw a basket ball back and forth between them as they get closer and closer until they have exchanged sufficient momentum that they are stationary.  The most elegant method would be to just unfurl sails and break orbit to all head far far out, beyond Pluto, on a 100 year voyage.  Over that 100 years use vectored solar thrust to cancel the orbit, so that they then all drift back down into the system, sails open, the multiplier building up as they get closer in and the coverage nears 100%.  You'd have to time things carefully so your momentum just reaches 0 at the same point as you are all in position. --DouglasReay

Additional thought - by furling the correct sails for a few minutes, once a year, they could let the Earth continue in its current orbit still getting its original direct sunlight.  Harder would be to make sure it did not get additional sunlight.  Using two of our 40 shells we could create an 'Earth Environment Preservation Zone' with a low multiplier and strictly controlled navigation and reflections to leave the planet as untroubled as possible.  Easier still than making the entire space be Earth normal intensity, have a localised area ten times the orbit of the moon be low reflection while the Earth-Moon system passes by.  This would require the shell (or the bits of it in the plane of the solar system) outside the Earth's orbit to be able not just to furl up, but to cease reflecting (or at least make sure the reflections do not disturb the sleep of those on the night side of Earth).  --DR

Building it all in one go (8x10^8 is 'all in one go' enough) is a solution, but unless human nature changes radically, or you've got a lot more than one solar systems production capacity that's not a boot-strap. --Vitenka
Compared to 40 nested shells it is.  Just 0.1 % of the final number of statites needed. --DR
Keeping the cities stored also needs some way to give them enough light energy to keep them at least on standby if not running - which you can't do unless they are close to their final depth.  --Vitenka
1AU would be close enough for good solar power.  But, actually, you wouldn't need the big rotating human habitation bits for the initial manoeuver, just a command and control module.  Better just to make the sails, and leave them on auto at near absolute zero until you are ready to go.  Once in place, you could then start constructing cities in-situ.  Or dropping in new sail+city from the production area, to swap with a placeholder sail (which would then sail off to get its city fitted). --DR
You need some small number (say, 10?) to prove the concept before you get the whole human race to sign onto it and disassemble Mars.--Vitenka
For a small bootstrap inner shell they wouldn't need Mars, just one sizable asteroid (ie Ceres).  And if you are producing just the sails with enough automation to do position holding and sail pre-programmed orbit changes, you need much less than that.  Suppose you could land an automated sail making factory on an asteroid, which it would mine to produce one sail a month.  And your civilisation could produce and site one such factory per day.  The project would take a little over 100 years to complete.  --DR
(And a 'once in the lifetime' really REALLY isn't the sort of thing you want to do without having had a trial run)--Vitenka
You can test individuals parts of the system.  There is nothing to stop you using conventional propulsion to support 5 mirrors for a few years, which could be used to provide the necessary light conditions for a 6th mirror to test just hanging there in the intense sunlight. --DR
Or 20 concave mirrors in orbit, constantly changing their angle, so that the beams of the 10 best positioned at any one time point at the floating test sail, if you want to save on fuel. --DR
Testing the navigational abilities of the automated sails is not only possible, it could be immense fun; races to get from the asteroid belt to the storage ring.  ballet.  Paired trials where two sails in opposing orbits use each other to come to a dead stop, start dropping, then use the same method of exchanging objects carrying momentum to speed back up against each other so they regain orbit. --DR
The actual positioning maneuver itself, you could have an abort route, where by the statites falling towards the sun angle their sails and brush past in an elipse rather than fall right into it.  Given how tight a really thin membrane might be able to pack, your command and control module could have a heat sheild ready to protect the furled up sail, allowing it to survive for a short period closer to the sun than the designed operating radius. --DR

Solid Spheres

There have been numerous designs for a solid Dyson sphere, including really ingenious ones with mini planetoids rolling around the inside of the sphere at faster than orbital speed to push against it and keep it up.  They all suffer from the same problem - materials.  Nothing strong enough.

Let's assume we could get a working nested statite shell structure - a Matrioshka Dyson Bubble.  Is there any way we could use it to bootstrap to a full solid dyson sphere?

First I want to look at the weight requirements.  How much mass would we really need to hold up?  An atmosphere covering the entire sphere would [be nice] - you could float in dirigibles across the surface.  Earth has about 7000 kg of atmosphere for every square meter.  We could get rid of 4/5 of that by changing the mix of gasses, and another factor of 2 by reducing the pressure, and still end up with something breathable.  But 700 kg per meter square is way too much.  2 x 10^5 more than our staties could support if it covered the entire surface.  Even if we stopped being conservative about the possible albedo of our inner surface, and achieved a multiplier of x300 instead of x50, that wouldn't help.  So forget having an atmosphere.

What about foot traffic?  If we could find a way to support 1 kg per square meter, we could have a surface to walk over, possibly drive over if roads spread their pressure carefully.

I can think of three mechanisms that might help get us towards that target.

First, most obviously, we'd make the inner surface reflective, with as high a multiplier as possible.

Secondly, there is a variation on the rolling planetoids idea.  Think of CERN.  Charged particles going around and around a loop at near the speed of light.  They are kept in by superconducting magnets.  The magnets are pushing the particles into a circle.  By Newton, the magnets are thus being pushed outwards, due to the equal and opposite reaction.  There's no real limitation on the size of beam, other than the magnets.  And space is good on vacuum and low temperatures.

Thirdly, we talked about transfer of momentum between statites by exchanging lumps of iron.  This is a very efficient process in space.  There is no friction.  And if you use a linear accelerator to throw the lump, and a second one to catch it, then there is no net energy loss because the catcher actually gains energy as well as momentum.  So we could have our nested shells of floating statites and, on the final outer layer, a solid Dyson shell.  Each of the inner layers, instead of supporting cities, would support linear accelerators which would throw lumps upto the solid shell where they'd be caught and thrown back down again.  Because the structure does not move, you don't need to alter the aim once you have the trajectory correct, and you can use gaps in the shells above.

Unfortunately that doesn't work.  To support one meter square of solid shell at 1000 g per meter squared, using statites with a spare 'boyancy' of 5 g per meter squared, you need 200 times the number of statite sails to support an equivalent area of solid shell.  Or, put it another way, since we know that the area increases as we go outwards, we'd need more than 200 shells.  Which we earlier showed could not be done.  Sure, you could support pieces of shell that way.  Great floating platforms millions of kilometers across.  Vast plains of land, greater than the surface of the Earth, and with an atmosphere (given high enough walls to keep it in).  But you couldn't do it for an entire shell.  Not with the solid shell outermost.

But what if you put the solid shell on the inside of the statite shells?  You'd need a few holes in it to let the projectiles through, and they'd need curved orbits to avoid the sun and be caught on the opposite side on the inner solid shell.  Now the size factor works in our favour.  Let's look at the numbers for our 40 layer shell starting out at Saturn, and imagine we are trying to support a solid shell at 0.2 AU out from the sun.  The solid sphere wouldn't even need to be polished on top, as long as the next shell of statites out was far enough away that it could survive on reflections from its own opposite side.  We've already said it would need a few holes to let projectiles through, so they could double in purpose and also leak sunlight up and out to the surrounding statite shells.

Given the assumptions above, 5 g per square meter spare boyancy, perfectly efficient momenum transfer, and the full 40 layer statite shell entirely dedicated to supporting the solid shell, it looks on first glance that with 280 support sails for each equivalent area on the solid shell, it could support 1.4 kg per square meter. (Ignoring the question of [where we'd get that amount of mass])

But that misses a factor - acceleration due to gravity.  Now we're shooting downhill rather than uphill, we are not limited by spare boyancy.  In fact, if we shoot enough lumps in a constant stream, we wouldn't need the sails at all.  We could use our nested shells to support each section of solid sphere until the entire structure was in place, and then the solid sphere could start shooting to itself and become entirely self supporting.

And yes, to anticipate Vitenka, this is something you could start small.  Imagine two space stations on opposite sides of the Earth.  They are not orbiting, and infact are far far higher than geostationary orbit.  For convenience sake, I'm going to assume one over the North Pole and one over the South Pole.  Each station has 4 linear accelerators.  2 for catching, two for throwing.  Paired so as not to get knocked out of position.  We could label them NP1 NP2 NC1 NC2 SP1 SP2 SC1 SC2 N=North, P=Pitch, C=Catch, S=South.  So lumps sent by NP1 would be caught by SC1.  These accelerators are not all in a plane.  Instead they are angled down towards the Earth.  Not directly at it, but as close as possible without grazing the atmosphere.  You'd want a fairly constant stream, and you'd need to aim at where the station will be when the lump arrives.  A good damper between the accelerators and any living quarters would also be a good idea. :-)  (See also [Space Fountains])--DR

Large Scale Engineering

So far we have not assumed any particular technology breakthrough (eg FTL, Anti-Gravity, materials with arbitrary properties, AI, etc).  There is one technology breakthrough, though, that I would like to consider in combination with Dyson Bubbles.  Nanotechnology.

We assumed that to create the statites we'd need an existing developed civilisation in the solar system producing great factories that could slowly mine an asteroid belt and churn out statites.  But what if it didn't take a massive factory?  What if, using nanotechnology, the statites could effectively self-replicate?  Orbiting around the sun in the asteroid belt, using a partially spread sail to modify orbit to drift from asteroid to asteroid, they could gather materials using the sail as a solar furnace.  If the belt could sustain that many statites mining at the same time, you'd reach 8x10^8 statites in just 30 generations.  From requiring the unified support and commitment of an entire civilisation, it become practically a one person project.

A bit hard on the solar system, though, if individuals start using up large chunks of it at random.  Let's assume we want to keep it more or less intact.  What could you do with just 10 generations?  A thousand or so statites?  They fit quite happily in a near-sun orbit in satellite mode, not needing any light pressure to keep afloat.  They wouldn't have to block light going to the planets, as they don't need to be in the same planar orbit as the planets.  Simple station-keeping software can use the light pressure to maintain an steady orbit and resit any perturbations from the planets.

What use would that be?  Well, with a sufficient base to generate laser propulsion, [Interstellar Travel] is possible using solar sails.  The first sail you sent to a new solar system would need to sacrifice much of its mass to decelerate, but that's ok because as long as there's enough of it left to navigate to and mine an asteroid, it can start producing full size sails again, in the new system, all ready to be a breaking system, which will allow far larger packages to be sent if needed (such as ones carrying people).

Once we can send significant packages of mass between stars, we are no longer limited to just the easily take able bits from a single solar system.  Which means we can build shells that require 5 times the mass of Jupiter, simply by scavenging parts of the asteroid belts from a thousand systems.  Our [local bubble] is 150 light years in radius and contains more than [1000 stars], so with luck the needed materials could be gathered in under 500 years. (Because light sails don't carry reaction mass or fuel, they can accelerate for the whole of their journey, so can reach significant fractions of the speed of light).

That's sending stuff away from Sol.  Because each new star in turn becomes its own launcher, Sol would only be sending out about 10 missions (if we stick to the 'every generation, each colonised system sends out a new mission' plan).  But what about receiving the mass back again?  Wouldn't the Sol system have to catch all the packets?  That's not impossible, given enough time or enough of the Sun's output dedicated to decelerating lasers.  But it is also unnecessary.

To catch packets aimed at Sol, ideally the decelerating laser would be based at Sol.  While laser beams do not drop off their intensity with distance, in the same way that unfocused light does, there is still some loss from interstellar debris, lack of collimation, etc.  However, if the trajectory of the incoming packet is known in advance, there is nothing in theory to prevent it being decelerated by multiple beams from systems on the far side of Sol, whose vector sum equals a single beam from Sol.  The packet could open or close its sail a bit along the way, to control the trajectory and keep it 'in the beam'.  And, once a significant number of sails have arrived, there's nothing to stop an orbiting receiving station being set up in the Oort cloud that accepts incoming beams and reflects them out again to do the breaking.  In other words, the sending system sends two beams.  One aimed at the packet to accelerate it on its way.  And a second, aimed just to the side, which hits the receiving station and reflects back to do the decelerating on the second half of the packet's journey.

But this is still small scale stuff.  Think big.  Mass is no limitation.  Power is no limitation.  So why base your Dyson Bubble around a star?

Our galaxy, the [Milky Way], contains 2x10^11 stars.  Leaving aside for now the possibility of intergalactic construction, what could we do if we used just the nearest 1 % of them ?  Between the [Orion Arm] and the [Perseus Arm] we've got a nice clear area 800 light years in radius, so there is plenty of room for construction.  If a shell 1 ly in radius takes 10^28 kg, then a shell 10 ly in radius will require 10^31 kg.  Which, if we are using 10^9 solar systems, will require 10^22 kg from each - about a fifth of the asteroid belt, which leaves four fifths for a launching system and small Dyson Bubble of its own.

And why limit yourself to a spherical arrangement of statites?  If they are hanging around in interstellar space, then most significant local mass will be the other statites.  That's still too much mass to make it into a single solid Dyson Shell, without a lot of ongoing active measures to balance the weight.  But what about smaller solid structures?  Hollow polished spheres the size of small moons and containing an atmosphere, whose gas pressure helps keep the shape?  Each 'moon' or [bubbleworld] might be 10,000 km across, weigh 10^16 kg, and have a surface area of 10^9 m^2.  And we could build a spherical shell containing 10^15 such moons, held up against the mass of the other shiny moons by the reflected light pressure from the redirected lasers of a billion stars.

Other Possibilities

Are Dyson Bubbles possible without as yet undiscovered materials, and without depending on artifically intensified light intensity?

The mass per area limitation given is specific to Earth's sun.  What about other types of star?  You can get [brown dwarves] exhibiting deuterium fusion as light as 1.3% of Sol, and [main sequence stars] start at 8.5% of Sol.  At the heavier end of the sequence (10 to 20 times Sol's mass) you can get stars with 100 to 1000 times the [luminescence].  Either way, if you can pick your system then a factor of 10 better than Sol's limiting mass per area ratio should be possible, which is easily within the range of known materials.

Also, what about binary systems?  With a solid Dyson Shell, they'd cause insurmountable problems, but do they offer an opportunity to Dyson Bubbles?  A bubble, by using aimed reflection to cause local variations in solar pressure can flex with altering gravitational forces.  Could a bubble be set up around just one of a pair of stars, or would it need to fit around the outside of both?

I think it would be possible to set up around just one, but the bubble would have to be close in, to ensure that the  external pressure on the outside of the bubble could be compensated for in the same way as pressure from nested bubbles.  The pressure from the second star would also have to be low compared to the period of the orbit (the time the two stars take to pass around each other), else the bubble would get knocked to one side and crash into the star it was arranged around.

Let's take two examples.  [Epsilon Indi] is a close neighbour (only 12 light years away).  It consists of a main star (mass 75% that of Sol) being orbited by a pair of brown dwarves (8% the mass of Sol between them) at a distance of 1500 AU.  If a Dyaon Bubble were set up around the brown dwarves, the pressure from the main star would be negligable.  The dwarves have a surface temperature of only 1000 K however, which is not ideal.

[V4641 Sagittarii] is also a binary system, though further away (about 1500 light years).  The two stars weigh about 10 and 6 solar masses, however the luminosity is 14, so the allowed statite mass per area ratio isn't that much worse than Sol.  What is special about V4641 is that it is a microquasar.  The primary is a black hole giving out an immensely powerful magnetic field, providing something additional for the statites to move around with.

Solid Spheres with Atmospheres

Let's look in more detail at the idea of having solid floating islands supported by balls of iron exchanged via [Lieanr Accelerator].

At what radius from the Sun would gravity's pull be of the same strength as at the Earth's surface?  F = G M m / r^2 so (radius of Earth)^2 x (mass of Sun) = (radius of Shell)^2 x (mass of Earth) gives (radius of shell) = (radius of Earth) x root(  (mass of Sun) / (mass of Earth)  ) = 6.4 x 10^6 x root( (2 x 10^30) / (6 10^24) ) = 3.7 x 10^9 m - about 2.5 % of 1 AU.  Far too close to the Sun!

So were's talking effectively zero G habitation.  An atmosphere wouldn't be held against the surface effectively - if you wanted an atmosphere to cover your solid sphere it would be in the form of a pressure dome - a light elasticated skin.  In other words, the skin of a solid dyson sphere would actually be more like a raft of balloons.  How large would each baloon be?  Well, they need to house a linear accelerator, so let's say a minimum of 1 km in diameter (which is a lot of living space, when it is zero G and you can use 3 dimensions fully).  Imagine a cube: it has 8 corners.  There are 4 pairs of opposing corners.  You could run two accelerators between each corner (one to pitch, one to catch).  For simplicity sake we'll assume the balloon surrounding this cube has a radius of 500m and is held at half Earth normal atmospheric pressure.

(mass of balloon) = 1.15 x 4/3 x pi x r^3 = 6 x 10^8 kg

If we hang our raft of baloons just inside Earth's orbit, at 1 x 10^11 m then

(gravitational force on balloon) = G M m / r^2 = 6.67300 10^-11 x 2 x 10^30 x 6 x 10^8 / (10^11)^2 = 8 x 10^6 newtons.

With 8 accelerators, that means each one, every second, must deal with 10^6 kg ms-1 change in momentum.  Which is the equivalent of catching an iron ball weighing 1000 kg and slowing it down from 1000 ms-1 to stand still.  However that's conservative.  [20,000 ms-1 has already been achieved] and an exit velocity of 10^5 ms-1 is not unreasonable, and would require projectiles of only 10 kg (or larger ones less frequently than one per second).

However let's sanity check that.  E = 1/2 m v^2.  While our accelerators make back the energy spent pitching when they catch, there is still going to be a fractional cost from efficiency losses, so perhaps we'd be better off using a slower speed, and more or larger projectiles.  Larger projectiles might be easier to correct and avoid as nagivational hazards, but smaller projectiles would even out the shock to the balloon.  The limiting factor becomes the separation between projectiles compared to their size.  For an exit velocity of 10 ms-1, you can just about fit in 5 projectiles every two seconds, each a 2m cube weighing 40,000 kg and 2m from the next one.

Let's say we can spare 100 Watts per meter squared from solar energy falling on our 1000 x 1000m balloon's lower surface - that's 10^8 watts.  Is that enough to run the accelerators?  E = 2.5 x 1/2 x 40,000 x 10^2 = 5 x 10^6 joules per second for each of the 4 pitching accelerators.  So yes, easily enough, even if they had zero energy capture from the catching accelerators.

Of course if each pair of balloon islands, pitching and catching balls between them around the sun, had to supply enough balls to keep the 2 x 10^11 path between them full of balls, that would be significant mass.  How long would it take a ball to travel that path?  It would go considerably faster than its initial 10 ms-1 near the bottom of the Sun's gravity well.  Let's say it goes in as close as 10^10 m to the sun.  The change in potential energy for a 40,000 mass going from 10^11 to 10^10 is G M m ( 1/(10^10) - 1/(10^11) ) is approximately 6.67300 10^-11 x 2 x 10^30 x 40,000 / (0.9*10^10) = 6 x 10^14 joules leading to a maximum speed of 1.7 x 10^5 ms-1.  So, as an approximation, let's say at any one time, from each of the 4 accelerator pairs, the path would contain over 2 million balls, giving a total mass of 4 x 10^11 kg, far far outweight the 6 x 10^8 kg balloon itself.

Since, as we just worked out above, there is plenty of energy available, we better go for the high exit velocity option, and hope for highly efficient energy reclamation from the catchers.  If we go for the exit velocity of 10^5 (a factor of 10^4 better) we can use 10^4 less mass per second AND the path will contain half as many balls; giving a total path weight of 2 x 10^7 kg - manageable.  If we could get the exit velocity up to 10^6, we'd use 10^5 less mass per second and the path would contain 10 times fewer balls reducing the mass of the path down to 4 x 10^5 kg.

How much would the whole solid balloon raft dyson shell weigh? 

(number of balloons) = 4 pi r^2 / area per balloon = 2 x pi x (10^11)^2 / (10^6) = 6 x 10^16
(mass of the shell) = 6 x 10^16 x ( 6 x 10^8 + 1 x 10^7 ) = 3.8 x 10^25 kg

Whoops, that's more than the asteroid belt.  If we could disassemble Neptune (1 x 10^26) or Uranus (8 x 10^25) for gas we could do it.  Oh well, nobody said that having a solid Dyson shell in your solar system came cheap.  And it could house 10^21 people.  As long as they didn't mind living in zero G.

SeeAlso: InterGalacticTravel
Links: [The Search for Dyson Spheres], [Scholarpedia]


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