I'm occasionally asked if you can make a planet like Earth, only larger, bigger, and
if so how much bigger?
As we'll see today, the answer is very big indeed.
We often discuss building artificial habitats in space for humans to live on, today we will
discuss building artificial planets.
Not cylinders or rings for providing apparent gravity by rotation and centrifugal force,
but rather the traditional sphere providing gravity by the traditional means of mass and
genuine gravity.
As we have begun finding exoplanets around distant stars, we developed the term Super-Earth,
planets larger than our own, but not so big as a gas giant like Jupiter.
You often hear these compared to Earth but realistically this is not the case.
Even those not too close nor too far from their sun to have liquid water on their surface
are not going to be much like Earth.
The force of gravity strongly controls the makeup of the surface of a planet, its land,
seas, and atmosphere.
Most planets begin with a large amount of hydrogen on them, as well as helium, the two
most common elements in nature but also the lightest.
The colder a planet is and the stronger its surface gravity and magnetosphere, the easier
it is for those elements to remain.
Left to its own devices, a planet like Earth will leak away all its helium and most of
its hydrogen, some hydrogen will remain bonded to oxygen to form water, but not much.
When you consider that our planet is almost entirely covered in water kilometers deep,
it's worth remembering that is but a tiny remnant of the hydrogen we used to have.
A planet would not need to be much more massive to potentially have a gravity well and magnetosphere
strong enough to seriously diminish losses in hydrogen, so that a planet might be covered
in water and a much thicker atmosphere.
If it is much higher, it may have retained all its hydrogen and helium and be a gas giant
instead.
You spot a planet that is twice as wide as Earth and appears to be about the same density,
and composition, and even has a 24 hour day, too.
What's different?
First off, being twice as wide but having the same density, it has 8 times the mass
and four times the surface area.
That last sounds great, 4 times the living room, except if you landed on it you'd find
the gravity was twice as strong as Earth.
Mass rises with the cube of distance, if the object has no change in density, whereas gravity
falls off as the square of distance.
For such an object, the strength of gravity at the surface rises linearly with the distance
of that surface to the center, the radius.
Double the radius, double the gravity.
I wouldn't want to live in a place where I weighed twice as much and even a slip down
the stairs could shatter bones, but there's unlikely to be any land to live on anyway.
Being bigger it also started with more hydrogen, and will have lost a smaller portion of it
due to its increased magnetosphere and increased gravity, so odds are any land it has is buried
under kilometers of ocean under even more kilometers of atmosphere.
Needless to say we don't want that, and of course this is a Megastructures episode
so we are not interested in naturally occurring planets.
We are interested in building our own.
If you can build artificial planets and your goal is to make them as Earth-like as possible,
just bigger or smaller, there's a lot more to it than just dumping excess matter into
some big heap.
Since they are artificial, we can construct planets of different sizes that have the same
surface gravity as Earth.
The surface gravity increases linearly to radius, but that's only true if the density
remains the same.
If we constructed a planet the same size as Earth but twice as dense, if it were made
mostly of lead, it would have twice the mass, and so would generate twice the gravitational
force, undiminished by a larger radius.
So its surface gravity is the same as our example Super Earth a moment ago of 8 times
Earth's mass.
Its escape velocity though is not double, but just the square root of 2 or 41% higher
than Earth's.
If we went the other direction and lowered the density, to half, gravity at the surface
would drop to half and escape velocity would drop to 71% of Earth's.
It might be too low to hold a thick atmosphere.
But we can always find a specific density for a given planetary volume or radius that
will give the exact same gravity as Earth on the Surface.
And it's easy to remember, as it is inverse to radius or diameter.
If you want a planet that has the same gravity as earth but twice as wide, it simply needs
to be half as dense.
Ten times as wide, one-tenth as dense, one tenth as wide, tens times more dense.
Earth has an average density of 5.51 grams per cubic centimeter, water is just one gram
per cubic centimeter, and we use the term specific gravity to skip the mass per volume.
Being 5.51 times as dense as water, we know a planet composed entirely of water would
be 5.51 times wider to have the same density as Earth, and would have 30.4 times the surface
area.
Which is quite large.
It would also contain 30.4 times as much mass.
That's a handy scaling factor when you are keeping to the same surface gravity, it takes
an identical amount of mass to create the same living area at the same gravity.
If you want a million times the living area, at normal gravity, you need a million times
the mass.
Such a giant sphere would also need to be a thousand times wider than Earth and a thousand
times less dense.
The air we breathe is actually less dense than the sphere itself, and an air-filled
balloon or ball is reasonably sturdy.
Nor does the density have to be constant.
If you had a big thick shell around a point-like black hole, it wouldn't matter that the
intervening space was empty vacuum.
Now there are some obvious downsides to building planets this way.
Firstly, regardless of size you have to spend the same amount of mass for each amount of
living area, which for earth gravity is 12 billion kilograms or 12 megatons per square
meter of living space.
You could build a very sturdy chunk of rotating habitat exterior shell for only a ton per
square meter, and give yourself a nice thick layer of dirt and water for, say, 120 tons
per square meter, maybe 50 meters deep, far deeper than we tend to dig, and use 1/100,000th
the mass you would need to make the same living area with a classic spherical planet.
The supermajority of the universe is hydrogen and helium, which aren't too useful by themselves,
but could be used to generate gravity just fine.
And when we say supermajority, we are actually excluding dark matter, which - if you could
ever collect and confine it - outweighs all the rest of the matter in the universe several
times over.
Just because your artificial planet needs a lot of mass, does not mean you need the
rock and soil to go any deeper than our classic rotating habitat does.
Our second issue is how you could possibly build something strong enough to act as a
shell?
You do not necessarily need one though.
Saturn for instance, has almost the same surface gravity as Earth, and a shell built around
it, like a balloon, could be kept up simply by balancing the internal pressure of the
gas against the external pressure of the rocks and water sitting on the balloon shell.
We have no material strong enough to act as a rigid shell.
We have discussed doing that with active support in the past.
I've talked about that enough this year, and indeed all the way back to the original
Shellworld's episode, that I won't repeat that explanation again.
See the Orbital Rings episode for a discussion of the mechanics involved.
Such planets resemble a soccer ball.
Underneath the exterior of rock and dirt is an immense series of windings around a bladder
of gas, or even vacuum, and those windings are endless magnetic accelerators pushing
materials around at orbital velocities inside themselves.
Sounds fragile, but it is in fact is a lot sturdier than what we stand on already on
Earth, floating atop a sea of hot magma.
Artificial things make folks worry about failure, compared to the natural systems, but carefully
designed, sturdy and well-maintained machines can easily survive a long time and, unlike
natural systems, because you created them you know what to expect and how to fix them
when tell-tale signs of things going wrong happen.
Now there are limitations as to how big, or small, you can build these things, but it
depends on type and some other factors.
For type, you can define three: a rigid one held up by a network of orbital rings, the
balloon kind held up by an equilibrium of internal and external pressure, and a raw
dumping of matter, like is the case with Earth.
Rocks, soil, and water are a good deal less dense than Earth's average is, so you could
build a bigger planet just by skipping on dense elements like iron and uranium in the
planet's core.
This version is the one with the least variation, you can't build much bigger than our Ocean
planet, 5.5 times wider with 30 times the surface area, and presumably with floating
islands for land.
You can't go much smaller either, your densest materials are stuff like Osmium, Tungsten,
Gold, Platinum, Uranium, and Plutonium, none of which are particularly abundant and are
only 3-4 times denser than Earth, thus allowing you to miniaturize only to about 3-4 times
skinnier and about a tenth less land.
The balloon type has size limitations too, you can't really go smaller than Earth with
one, but you can certainly go larger.
Again, Saturn is practically ideal to be made one, however, you can't go much larger,
because these things begin to contract under their own mass, so that you'd have no pressure
pushing back against the balloon at the Earth-gravity radius, and eventually they get massive enough
to form their own sun, which you don't want underneath you…
usually.
We'll get to using exotic stars inside shell worlds like white dwarfs, or neutron stars
another time.
Now the episode is titled Mega-Earths, which by common prefix means millions, and if you
want a planet a million times bigger than Earth you need to use the orbital ring shell
approach.
This is the type I usually mean when I say Shellworld, though you will also hear them
referred to as Supramundane planets, but this indicates size, not what is keeping the thing
from falling in on itself.
Shellworlds have the greatest size range.
They can be made either much smaller or larger than Earth, and the smallest you can make
one is essentially the point at which its escape velocity is so low even room temperature
gas will fly away into the void, for all that gravity feels the same.
The largest size we will save for last, but happens to be when the escape velocity is
the same as the speed of light.
A shellworld does not rely on mass providing the gravity to keep it as a sphere rather
than collapsing, so we can circumvent the maximum size issue at which something will
ignite and turn into a star by using a black hole instead.
In theory, those can be made of any size or mass.
Our sun is not quite a million times more massive than Earth though, so if you want
an actual MegaEarth, you either need to use a black hole or use a material that won't
undergo fusion at that mass.
Helium might do the trick, dark matter should, and any element above helium will.
Each will have a maximum total mass though, and if you build any bigger you will get a
star, and probably a very short lived and explosive one at that.
All this gravity and stuff though isn't the only issue.
Once you start building planets bigger than Saturn for instance, the rotation rate at
the equator to produce normal 24-hour days starts exerting a rather noticeable centrifugal
force acting in the opposite direction of gravity.
You might not mind a little lower gravity at the equator, but it will get worse the
bigger the planet gets.
We can curb this by abandoning it being a pure sphere, indeed planets generally are
not, being wider at the equator than the poles exactly because they spin, but in our case
we do this backwards.
We make equator more narrow, so when you are on it you are closer to the center of the
planet's stronger gravity, and moving slower, therefore having less centrifugal force.
At some point, even this stops being viable though, even by the time you are getting to
Jupiter size your planet is looking decidedly egg-shaped.
Fortunately, at this size you are also getting near the maximum before something turns into
a star anyway.
Now, we say a day is 24 hours and how long the planet takes to spin around once, actually
that only take 23 hours and 56 minutes, the sidereal day, 360 degrees of spin, but it
needs to spin for another 4 minutes to get facing back toward the Sun since the planet
moved.
A day is not how long the Earth takes to spin once, but how long a day-night cycle takes
to repeat.
Now before you jump ahead and say "ah-ha, we'll go geocentric and have a planet so
big the Sun orbits it!", let me head you off.
To orbit something as massive as the Sun once a day means only being 3 million kilometers
from it, Earth is 50 times further away, and an object at that distance would get 50-squared
or 2500 times the sunlight per area, it would flash-fry you!
That distance increases if the orbiting object is more massive, a pair of binary solar mass
stars would orbit daily at 4 million kilometers.
It also goes up if the central mass is much heavier, but a mass would need to be 100,000
times as massive as our sun to produce a daily orbital period 1 AU out, the distance Earth
is, and if we want the same gravity on the surface, a Mega-Earth 100,000 times as massive
as our Sun, or 30 billion times more massive than Earth.
Meaning 30 billion times the surface area and 180,000 times the diameter of Earth, and
would thus be over a billion kilometers wide, so you wouldn't be scorched by the Sun if
you were standing on the surface, but only because it would be deep inside the planet.
If we took the very weakest of stars, those with a luminosity only one ten thousandth
of our sun, we could be a 100 times closer to it and not get scorched, just 1.5 million
kilometers away, and such a star could orbit once every 24 hours around a Mega-Earth just
20,000 times the mass of Earth.
But that would be about a million kilometers wide itself.
So even here you are getting pretty scorched, and the light coming in is almost entirely
infrared and more like what an old incandescent bulb gives off.
Now, we could spin such a planet backwards, letting us place the Sun a bit further out,
giving it a longer sidereal day than sunset length, and contracting around the equator
to deal with that fast spin issue, egg-shaping the planet.
You also have a lot more distance to the poles so they are more habitable than on Earth.
And you could get away with making the day a bit longer too, say 25 hours, so you could
sleep in.
Also, you can play with the albedo of the planet or even set up shades and mirrors around
the Sun to block some of the light and redistribute some of that light to those poles.
This lets you get your sun a bit bigger and whiter, but it's hard to get above 100,000
times the size of Earth and that's about it.
Technically not a mega-Earth, as again that would be a million.
This is pretty much our boundary even with an artificial sun, one that's just a big
light bulb of a brightness of our choosing, because once you get over a hundred thousand
Earth's worth of planetary mass, you can't have an object spread out wide enough to only
have normal Earth gravity on the surface that also have any orbits of 24 hours around it,
rather than inside it.
It does let you get just a little bigger than a dim red dwarf of a sun permits, and also
lets you spread your light out better to not have a far wider spectrum of temperatures
between equator and pole than Earth has, so it is better, but doesn't let you get much
bigger for size.
This does not mean you have to stop.
You just have to abandon lighting by a normal object you are orbiting or the reverse.
For instance I could stick a huge mega-Earth around an actual sun and use all that power
to light its surface by giant towers over it, streetlamps on an epic scale.
Or I could build an orbital ring around the planet and have a fake sun race around that,
rather than orbit, or forego that to just have light all over that ring that turned
on and off, in each its own turn, so it looked like a sun was moving through the sky below
even though it was series of massive light bulbs just turning on and off.
There's no size limit on this, but once you switch to an artificial source of lighting,
you might want to start asking why you don't just build more layers?
After all a second thin shell a few hundred kilometers above the first is a whole new
free planet, costing you very little extra mass.
There's not even much drop in gravity since you aren't much further away, and indeed
you can tweak the distance and mass of the next shell to add to the gravity at its own
surface to keep it the same as the lower one.
Successive concentric shellworld's, what I usually label a Matrioshka Earth or Matrioshka
Shellworld -- not to be confused with a Matrioshka Brain -- let you add each new layer for a
mass cost parallel to rotating habitats, and indeed, I see this as one likely future scenario
for Earth, as you could mine out lower layers of Earth to add new layers above and just
add extra mass stolen from places like Jupiter.
Your top layer is still entirely natural but your lower layers are artificially lit.
Since you want your spacing between layers ideally bigger than the atmosphere is high,
so you aren't getting stupidly high air pressures on the lower levels, you could just
slather the bottom of the next higher layer in black paint and some fake stars and an
artificial sun ring and it will feel decently Earth-like.
So in order to build a Mega-Earth, you have to be willing to go for artificial lighting,
but once you accept that option you can jump even bigger by just adding more layers, though
trying to do more than maybe ten is going to give you big issues getting rid of all
the waste heat your artificial sunlight produces even if you are tweaking the spectrum to optimize
for photosynthesis and human comfort.
You could have almost countless dim twilight cavern layers full of mushroom forests or
storage facilities though.
Before we get to the biggest example, though, let's go the other way and consider how
small you can make them.
There's no limit as to how small a shell world could be made if you can use a black
hole as the gravity source, but it eventually becomes more logical to use a traditional
rotating habitat, because you need to start doming things under to keep your air in.
Though you can build one just 100 meters in diameter whose Hawking Black Hole radiation
would be enough to power a comfortable homestead on what would be about 7 acres, a bit over
3 hectares, of land.
You'd need domes or force fields to keep the air in, but it lets you own your own planet.
If you go much smaller, you have issues with gravity being noticeably different from head
to toe and that black hole in the basement giving off too much energy for the planet
to dissipate.
Way back in the original episode on the channel at the end I mentioned that the largest megastructure
I'd ever heard of was one of these artificial planets built around a galactic mass black
hole, with multiple concentric layers.
The notion was given to us by Paul Birch, who unsurprisingly also designed the original
Orbital Ring concept, as well as the trick for cooling down Venus we discussed a couple
months back in Colonizing Venus.
An interesting feature of the original one is that being that close to that much mass
seriously slows down time, so that the folks living on the lower levels have time pass
much more slowly than on the higher levels.
And you might be able to have a lot of levels since beyond being massive power sources,
it is sometimes thought you can use black holes, especially bigger ones, as a place
to dump waste heat.
So you could potentially have folks from the top layer, level 1000, go visit levels 1 or
2 for an afternoon and come back to find out that your watch is quite off.
Our own galaxy's central black hole is 4.5 million times more massive than the Sun or
1.5 trillion times Earth's Mass, which means that each layer has 1.5 trillion times the
living room Earth has, and a thousand times what even a Full Kardashev 2 Dyson Sphere
has.
Even if you only had a dozen layers it would have about 20 trillion times the living room
and you might be able to have hundreds or thousands of layers.
Like I said though, we can go a bit bigger.
That structure we just mentioned is so big it would occupy the entire volume out to Saturn,
but the black hole itself would be much smaller, not even a hundredth as wide.
The bigger a black hole gets, the weaker the gravity near its surface gets, which is why
you get torn to ribbons approaching a normal one but can get a lot closer to the bigger
ones before tidal forces rip you apart.
Is there a black hole size so large that the gravity at its surface is the same as Earth's
Surface?
Yes, a black hole with 1.5 trillion times the mass of our sun, or 500 quadrillion times
the mass of Earth, has a diameter of nearly one-light year and a gravity at its event
horizon equal to Earth's own.
This is the absolute largest any structure of this type can be built since any bigger
and you would be inside the black hole.
A single layer of such a shellworld would be almost a billion times the living area
of a dyson sphere, and given a modest number of layers it would match in living area an
entire Kardashev 3, galaxy spanning empire.
Not one where every system has an inhabited planet, but where each one was its own Dyson
Sphere.
You can also build one with approximately the mass of a galaxy too.
Needless to say, time runs very slowly on the lowest layers and even the higher ones,
but that makes it a nice place to hide to pass the time and since you would harvested
your entire galaxy and maybe a bit more to build it, you don't have any reason to care
what is going on elsewhere.
It's basically the most massive structure you can build since firstly, anything bigger
will be inside the black hole and secondly, anything bigger requires harvesting material
from outside the area of the Universe gravitationally bound to you, rather than destined to fly
off over the cosmological event horizon one day.
Since Paul Birch is far less well-known than he deserves, and since this channel is big
enough I can coin names and expect them to stick, I am going to name this a Birch Planet.
The largest possible Earth-like megastructure you can build under known physics.
I will go ahead and include the smaller original version around a galactic center black hole
as a Birch Planet too, TeraEarth not sounding right compared to a mega-Earth or Giga-Earth.
Okay, why would you build these?
Any of these?
They use a ton of matter, and too much to really justify that they are more Earth-like
than a rotating habitat.
However, as I've mentioned before any galactic scale civilization, or even just a decently
long-lived interstellar one, needs to think on timelines of more than one classic human
lifespan to continue to exist or even come to be in the first place.
So the amount of mass one person needs for one lifetime stops being a good path for determining
the stockpiles of resources you need to keep around.
When you engage in starlifting and other stellar engine creation, you often will have a ton
of useless mass leftover, hydrogen and helium for instance, which has little value except
for its mass or mass-energy for fusion or matter to energy conversion.
You still want to store that stuff so you can use it later, and you might want to take
advantage of the gravity it produces.
If you've got some big fuel bunker in space shaped like a sphere, as it presumably would
be, you might want to just dump some dirt, water, and air on it and build some houses
too.
In the long term you want to harvest the entire galaxy, and even further if you can, because
the raw materials of the Universe are not stored well.
A solar system you leave sitting around untouched for a million years instead of harvesting
is losing value that whole time, burning hydrogen, having solar wind escape, having valuable
rocky asteroids and comets crash into their sun, and so on.
If you are harvesting and storing all that for eventual use, you might as well make use
of its gravity now.
And if you are thinking on those timelines, you aren't interested in how many centuries
or even millions of years some rotating habitat could run its fusion reactors off its tanks
of hydrogen fusion fuel, but how many trillions or quadrillions of years a hollow planet stuffed
full of hydrogen can run its lighting off that hydrogen, slowly lowering gravity or
even contracting the planet as the fuel gets used.
We will talk about some of those scenarios more when we do our next installment in the
Civilizations at the End of Time series.
Another big advantage of a Birch Planet relates to the scale of Kardashev 3 or K3 civilization.
A K3 civilization makes use of all of the energy put out by its galaxy.
I've mentioned in other episodes that divergence will inevitably occur due to the timelines
involved in setting up and communicating in a K3 civilization that has no faster than
light travel or communications.
It takes potentially a million years to travel across the galaxy even when approaching relativistic
speeds.
Colonizing a galaxy takes millions of years and, even without technological tinkering,
folks on the other side of the galaxy might be as genetically different as we are to the
dinosaurs.
The consequence is that members of the K3 civilization across the galaxy are going to
be very alien to one another, even if they originally came from the same species.
If a K3 civilization wanted to make itself cohesive, then the Birch Planet is a solution
to the divergence problem.
A K3 civilization can install itself into a Birch Planet and will be able to communicate
to its entire population, a billion, billion times as many individuals as Earth holds,
in timelines of about a year.
Many an old empire from our own history existed within similar constraints and still remained
relatively cohesive.
You can also start building one and just keep making it bigger as more mass becomes available,
you don't have to build a Birch Planet all at once.
This also leads onto a possible solution to the Fermi Paradox I speak so much about on
this channel, which at its simplest is an apparent contradiction that despite a seemingly
high probability for the existence of space-faring aliens that there is no evidence that such
aliens actually exist.
Now, we've been actively looking for sentient alien life in our galaxy for decades, but
we've also been looking for signs of it in other galaxies.
If there were a K3 civilization, we would usually expect to be able to see it from the
tell-tale waste infrared heat that it would output, but possibly not if that K3 civilization
was on a Birch Planet.
Even if a Birch Planet put out the ferocious amount of heat that such a vast civilization
would produce, we wouldn't necessarily notice it since it would be concentrated.
The construction of one uses up an entire galaxy, and while it should be very visible
if you are looking at that spot, the odds of looking at that spot aren't very high.
What's more, a maximum sized one is hanging out just over the event horizon of a black
hole, so the light leaving it is going to be massively red-shifted, you won't spot
one of these, even the smaller ones, if you are just looking for the infrared signature
of an Earth temperature Dyson Sphere.
But moreover, as mentioned earlier, it is thought that you might be able to dump waste
heat into black holes, which you would want to do if that trick works, so a Birch Planet
might be incredibly hard to see since it is very far away from any other civilization,
very tiny compared to a galaxy, has all it's light red-shifted, and might be able to use
that black hole as a heat sink.
Now, construction of such a thing is not even vaguely covert, so the civilization that made
it isn't going be hiding, but they'd be hard to see and a Birch Planet, once constructed,
would be the perfect place for a K3 civilization to hide from us.
Perhaps this is the reason we have not seen a K3 Civilization, they build inwards, not
expand outwards, just dragging in matter to add to their single immense planet.
We had to do a lot of math today to discuss our topic, as usual, I did try to keep it
to the minimum and supplementary, so that folks who wanted to design artificial planets
of their own had the available tools.
I left out a lot of the math in this video… but to start doing your own research into
distant worlds you're going to need a toolbox… a perfect place for that is Brilliant.
It's a great place to improve your skill and comfort level with math and science so that
you can think like a physicist.
In Brilliant's Astronomy course, starting from simple beginnings, you can also learn
how to model the habitable zone around different stars, look for observational signatures of
distant worlds and analyze the logistics of sending probes to explore them.
With these basic skills, you can go on to explore places like we discussed today, or
even dream up new ones.
To support the channel and learn more about Brilliant, go to brilliant.org/IsaacArthur
and sign up for free.
As a bonus, the first 200 subscribers will get 20% off the annual Premium membership.
Next week, we return to the Outward Bound series for Colonizing Jupiter, and we will
look at the concept of a mini-solar system of gas giant moons along with oceanic colonies
on places like Europa, and how to colonize an actual gas giant itself.
The week after that we'll continue our look at Artificial Intelligence, and follow that
up with a look at the concept of Hive Minds.
For alerts when those and other episodes come out, make sure to subscribe to the channel
and if you enjoyed this episode, hit the like button and share it with others.
Until next time, thanks for watching, and have a great week!
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