1 Light Year Diameter Planet

Question

Suppose a species has limitless resources and the ability to construct megastructures of an astronomical scale.

Would it be possible, given antigravitational technology (hypothetical), to create a planet with the diameter of a light year? Suppose there is an internal structure inside the planet that enables the gravity of the planet to be cancelled at correct points to ensure stability. This would stop the planet from collapsing in on itself?

Perhaps without antigravitational technology the planet would turn into a blackhole due to the massive mass (assuming relative composition to that of the earth)?

Answer 1

As mentioned, anti-gravity and or gravity generators will let you pull magic out of thin air, but let's try it without magic. I can't imagine why anyone would bother doing it, but I decided to see what happens and ended up with a totally insane project that uses a lot of carbon nanotube (CNT) and crazy amounts of energy. But, you don't need unproven technologies like anti-gravity or unobtanium. $\ddot\smile$

Creating the Beast

The Schwarzschild radius of a black hole is $r_s<{2MG\over c^2}$. Solving that for mass, given a ½ ly radius, we get $M<3.19\cdot 10^{42}kg$ to avoid being a black hole.

The surface area of a sphere is $A=4\pi r^2$. The volume of spherical shell is $V\approx A\Delta r$ for $r\gg\Delta r$. The mass of the shell is $M=V\rho\approx A\Delta r\rho=4\pi r^2\Delta r\rho$. Solving that for thickness, given ½ ly radius, the mass given above, and the density of CNT (about $1.3 {g\over cm^3}$), we get $\Delta r<8727 km$.

The compressive strength of CNT is around 416 MPa. The inside of the sphere feels the pressure of the entire mass weighing down on it. The force is given by $f=Ma$, where $a$ is acceleration at the surface. $a={MG\over r^2}$, so $f={M^2G\over r^2}$. Pressure is $p={f\over A}={{M^2G\over r^2}\over 4\pi r^2}={M^2G\over 4\pi r^4}$. Rearranging gives $M=\sqrt{4p\pi r^4\over G}=r^2\sqrt{4p\pi\over G}$. Solving for mass, given 416 MPa and ½ ly radius, we get $1.98\cdot 10^{41}kg$, which is not a black hole, yay.

Using that mass, we can calculate a thickness of 55 km, surface acceleration of 0.0061 g (about $1\over 164$ Earth gravity), not a black hole, and the CNT construction can withstand the pressures. Of course, getting 10 billion solar masses of carbon nanotubes is a bit of a feat, but it's not outside the realm of just-possible.

You wouldn't be able to cover the entire thing with people, dirt, etc., and you'd need some source of energy (maybe a Dyson sphere surrounding a super-massive star in the center of your CNT planet?), but it's doable without magic.

Add some "Gravity"

As Zsolt Szilagy points out, pretty much any kind of rotation you can actually notice is going to wreak havoc with shear forces, but you might be able to spin it just fast enough to get some normal Earth gravity along the equator if you put your people on the inside. Wikipedia says the breaking length of CNT is around 4700 km under 1 g, so the CNT should stay together while being flung outward at 1 g. Centripetal acceleration is given by $a={v^2\over r}$ for uniform circular motion. Solving for speed, given 1 g and ½ ly radius, we get 0.718 c at the equator. Not impossible, but it's going to take a long time to get there.

Notes

Also, angular kinetic energy is $E={1\over 2}I\omega^2$, and $I={2\over 3}Mr^2$ for a thin, spherical shell. $\omega={v\over r}$, so $E={1\over 2}{2\over 3}Mr^2({v_\text{equator}\over r})^2={1\over 3}Mv_\text{eq}^2$. Solving for energy, given mass of $2\cdot 10^{41}kg$ and $0.718c$ speed, we get $3\cdot 10^{57}J$, which means converting about 8% of the Milky Way's mass to kinetic energy over some insanely long time period to do it.

Of note, if you're going to spin the "planet" and put people on the inside, you might as well save a bunch of material and just make it a Ringworld-style ring (it's still going to be insane though). Also, at 0.7 c, we're getting into relativistic territory, so the Newtonian equations aren't perfect, but I don't think it's anything sufficiently advanced scientists can't handle if they made it to this point. I'd be more worried about extrapolating CNT strengths from $\mu m$ scales to $km$ scales. And rogue stars.

Answer 2

Given anti-gravity and a big enough power source, yes, a planet like that is possible But, really, by introducing anti-gravity, an author can do pretty much whatever they want as long as the universe rules stay consistent.

Without anti-gravity, the amount of mass required to make a 1 light year sphere out of iron would have long ago turned into a very large black hole.

As a fun little addendum, let's look at the surface gravity of this planet. Earth's surface gravity is $1~\text{g}=9.8~\frac{\text{m}}{\text{s}^{2}}$. The density of iron is $7874~\frac{\text{kg}}{\text{m}^{3}}$.

$$M = V\cdot D$$ $$r = 0.5~\text{ly} = 4.73025 \cdot 10^{15}~\text{m}$$ $$V = \frac{4}{3}\pi \cdot \left(4.73025\cdot 10^{15}~\text{m}\right)^{3} = 4.43348 \cdot 10^{47}~\text{m}^{3}$$ $$D = 7874~\frac{\text{kg}}{\text{m}^{3}}$$ $$M = 4.43348 \cdot 10^{47}~\text{m}^{3} \cdot 7874~\frac{\text{kg}}{\text{m}^{3}} = 3.49092 \cdot 10^{51}~\text{kg}$$ $$g = G \frac{M}{r^{2}}$$ $$g = 6.67\cdot10^{-11}~\text{N}\frac{\text{m}^{2}}{\text{s}^{2}} \cdot \frac{3.49092 \cdot 10^{51}~\text{kg}}{\left(4.73025 \cdot 10^{15}~\text{m}\right)^{2}}$$ $$g=1.04\cdot10^{10}~\frac{\text{m}}{\text{s}^{2}} = 1.06\cdot10^{9}~\text{g}$$

Answer 3

I am not making fun of you but given the tremendous ability to manipulate their environment demonstrated by constructing this thing (the ability to move the mass of many solar systems, redirect the energy of many stars to illuminate it, and generally technology indistinguishable from magic), doing all this this no problem. But if they were able to harness these vast capabilities to make your structure, what sort of problems might a race like this encounter? Would anything be a "problem" to them at this point?

When you add anti gravity and gravity generating technology to hold everything in place and manipulation of vast amounts of energy to provide heat, your race may not be bound by the law of conservation of energy too.

So my question is, "Why do you want to put such a thing in you story?" Putting such a fantastic thing in your story should serve a narrative purpose. If we knew that purpose we may be able to answer your question better.

"If your race has the ability to create such a thing, what would such a race not be able to do?".

Both of these questions have profound implications for your story.

Answer 4

You probably need to make it empty inside (like a ball) to avoid immediate gravitational collapse. Also, this makes obtaining the required amount of building material more realistic.

A body so large still would require some very advanced technologies to use, but may be manageable then.

You could then use some strong light source in the center that would keep the planet blown up like a huge solar sail. But this should be some special technology; no solar sail would work in such a distance from the ordinary star.

Answer 5

The black hole bit is the majority of the problem.

The density needed to become a black hole goes down as the radius of object increases. For the planet that you're talking about, if it had a density of $0.00000001488~\frac{\text{g}}{\text{cm}^{3}}$, it would collapse into a black hole. The density of the Earth is around $5.51~\frac{\text{g}}{\text{cm}^{3}}$.

You would need this planet to be something like a shell of unobtanium, or a lot of antigravity devices to stop from collapsing.

Answer 6

As the others have said, without anti-gravity it won't work, with anti-gravity you can pretty much do whatever you want.

Just a few things to think about

With a diameter of 1 light year ($5.879 \cdot 10^{12}$ miles) you get a circumference of $1.85 \cdot 10^{13}$ miles, and a surface area of $1.09 \cdot 10^{26}$ square miles.

The Earth only has a surface area of $1.969 \cdot 10^{8}$ square miles, so this thing is going to be really really big. If you took a big bag of Earths and skinned them like oranges, you would need $5.535805 \cdot 10^{17}$ Earths to cover this monster.

The point is that heating and lighting the place is going to be hard. You'd essentially want fleets of Sun-sized stars orbiting the planet in order to keep things warm and to provide enough light to grow things.

If you only put them around the equator, one AU away from the surface and spaced them 2 AUs apart, you'd need $99,505$ suns to circle the planet. However you'd need more than one band to keep the place warm, so maybe 2 bands at the 45th parallels too...

Just to put the numbers in normal notation instead of scientific notation:

surface area of $1.09 \cdot 10^{26} = 109,000,000,000,000,000,000,000,000$ square miles

$5.535805 \cdot 10^{17} = 553,580,500,000,000,000$ times the surface area of Earth

Answer 7

So long as you abandon the notion of "planet" and will accept a sphere of the requisite size this could be built although I can't imagine it being done by anything less than a K3 civilization.

As others have shown a solid mass is out of the question. A thin shell is the only possible way to do this--which leaves the problem of how to support it. Fortunately, we can do this without any handwavium.

The inside surface of the sphere is a huge collection of maglev tracks. Each track is occupied by a super-train--they are 6.28 light years long, the head coupled to the tail. They are moving far above orbital velocity and thus exert an outward force. Enough trains going fast enough and you can support your sphere. (We can't calculate the speed without knowing the ratio between the mass of the trains and the mass of the shell. I would not be surprised to learn that the speed needs to be relativistic.)

Answer 8

Once you cancelled gravity and made sure you have enough energy sources, tectonics might become an issue. Make sure that planet does not rotate (like almost every known planet does). The centrifugal forces would need a year to cascade through - without beeing able to provide the math, I could imagine the planet would rip apart when the surface rotates at considerable fractions of the speed of light, or when parts of it have a differing momentum.

Answer 9

I would say that there are many levels of "no" beyond gravitational considerations.

You've identified one obvious reason why a 1 LY planet wouldn't exist - gravity.

If in theory somehow something were possible to make a sphere 1 LY across made of something that somehow has a stable anti-gravity effect over such, then there are still many other basic conflicts with reality to consider, such as:

• Have you really considered how large 1 LY is in comparison to any other known physical object in the universe, and in comparison to Earth and other planets in the solar system?

• What is the thickness of the crust and the density of the interior that you have in mind? Any answer for this that even involves an earth-like surface over that distance, I would expect to add up to more matter than exists in multiple galaxies. What process is going to gather, transform and assemble your planet?

• Given the scale of effort and ability needed to build such a thing, why would anything that advanced and powerful ever choose to use all that power to do that?

• There are many ways in which the thing you are talking about is not going to be a planet, for many things we commonly think of as a planet.

• For example, it won't rotate. Rotating something that large at any noticeable speed is practically impossible in a variety of ways due to several considerations from physics. For example, it will involve ridiculous amounts of shear force that would rip it apart. For another example, the resulting speeds at the surface would be relativistic, since the planetary circumference is 3.14159 Light Years - so there would be crazy time dilation effects between latitudes, and even if somehow the equator could go near the speed of light, one day would be over three years long. (Rotation relative to the direction of a bright light source is what provides days to planets.)

• Also, things won't orbit around it (and it won't orbit around things) like Earth's moon and sun do, because it would take ridiculous amount of time for them go around the planet or vice versa, and they'd not be at scale with the planet or else they'd me even more ridiculous and impossible than the planet itself is. Even if you wanted a moon to go around as fast as possible, skimming near the surface of the outer atmosphere at nearly the speed of light (maybe you can project all that gravity onto the moon?), it's still going to take over three years to make one orbit, and the time visible overhead is going to be a small fraction of that. The geometry alone is off by a huge amount.

• Given that you probably have no sun, what's going to provide surface heat and light?

• As AndyD273 pointed out, you'd need something like "fleets of suns" to keep the surface heated, but again those multiply the impossibility of the construction project, and then there's the impossible task of getting them arranged in some sort of movement pattern that somehow regularly covers a sphere without problems. There probably exists no orbital pattern that would work, so you probably need the ability to control the movements of an astronomical number of suns all the time.

Answer 10

Without thinking too much (sorry) they could construct it:

• Empty inside (like buckminsterfullerene) and inside the surface (like bridges forming a mega-structure).
• Made with a super-material (like fullerenes)
• Rotate the "planet", which araises interesting paradoxes.

Answer 11

Though it might not be impossible, it might be too problematic.

Not even space is a perfect vacuum. There are forces, gravity included, pushing, pulling, oscillating, etc., and the larger an object in space, the more these forces will act upon it.

Imagine a mile wide ball of leaves. Imagine said ball floating around our atmosphere about three miles up. Now, imagine the inconsistent wind blowing half the ball from the north and half the ball in the south... blowing twice as fast on the top of the ball as on the bottom. Imagine the flocks of birds, airplanes and debris from space colliding with it. Imagine the clouds passing through, oftentimes heavy with precipitation, oftentimes thunderous and lightning...ous... and then, finally, there's the gravity. All these forces acting on your ball of leaves would tear it apart, and the larger the ball, the more area it occupies, the more forces will act on it. The wind alone would be coming from so many diverse directions at so many diverse speeds that it would break your leaf ball into a million pieces. This is true for our atmosphere, for our ocean and, yes, even for the vacuum of space.

We know that the sun, moon and even the other planets have a significant-to-negligible gravitational pull on our planet. A light year wide planet would be subjected to the pull of who knows how many stars... including the one megastar or collection of lesser stars used to heat it. Speaking of heating it, what is the molten core situation for a planet like this? It seems there's only three options: virtually no molten core whatsoever when you get down to it, a thin crust of rock built on to of a sun (game over) or some magical, potentially impossible sweetspot that gives you a very large molten core that is both hot enough to stay molten while heating your planet AND not so hot that... well... one could only imagine. Hmh...

Long story short, the science and power needed to do something like this are so great that you'd have to be almost literally capable of anything in order to make it work. You'd have to be at the point where not only would creating the planet be no sweat, but handling every single problem that arises would be equally easy to solve, because you're like some kinda god or something. On that level, science would be irrelevant. It wouldn't be a matter of possible... it would be a matter of whether you wanted to or not.

Answer 12

Assuming basic science fails us (and it does), the BFP would have to be made one of several ways. 1.) Grown from a matrix that scavenges raw materials as it grows, extruding new material the same way a baby growing develops new skin. The "epidermis" would change structures at each stage to best support the newest pressures. The surface would have localized energy ports (self replicating) for harvesting new material from the surrounding system and be able to communicate shifts in spin to maintain the shape while still "flexible". Upon near completion all stored / harvested energy will have been distributed among all the sections to maintain balance and then the radiators would be launched on tethers as the rotation was slowed and the surface hardened. The entire innards of the sphere would be laced with slender ultralight cables much like a 3D bicycle wheel spoke system with the ends of the cables forming a sphere deep within the BFP (well 1/2 ly). These cables are only really needed to communicate and monitor stresses at first.

Once the radiators are launched (from every other section) they will serve multiple purposes. First, a specific radiation will be generated from the surface of each section using the matter harvesting generators and this will end the growth phase and start the unification phase. Each section will bond to its neighbor and use interlocking tendrils to help bind each plate to a perfect mating. Whatever the final geometric shape would be (boggles the mind) each section and it's immediate neighbors would be essentially a planetary surface and this is where the generators/radiators come into play.

The generators (the every other ones) would generate a beam of energy that struck the radiator spheres and those would release it as the most desirable visible frequency and a healthy modicum of infrared in alternating day night cycles tuned to each neighbor. The crust of the BFP would be roughly 12,750 km providing enough mass at every point to simulate 1g and provide structural integrity to the entire sphere, with a 500 m Earth like layer of organic topsoil. The rest of the 12,250 km would be layers of support structure, global and local supply/storage and automated repair facilities. This sectional mass would be insignificant to the size of the final construct, and too far away from other masses to cause problems. The side to side attraction of the sections would do little more than further strengthen integrity.

The harvesting generators not used for lighting would be responsible for gathering new matter and energy as needed and everything from asteroids to solar systems would be munched into what ever the BFP required, cutting swaths in whatever it encountered.

In this fashion, it would be 100% self sufficient and capable of travel by use of the same harvester energy beams used to power gravimetric engines. By no means could this ever be called a planet, it is more of a living machine.

2.) Genetically engineer some sort of bio-mechanical robotic creature(s) to build it, then consume it building on the outside of the existing structure and grow each cycle leaving your with a perfect honeycomb sphere made of whatever material you program it for and whatever depth is desired for best structure strength. You would also need to incorporate the same sort of energy harvesting beam technology.

In both cases, a holographic communication system would be used to defer delays in signaling, the light being transmitted via the fibers from each section and the data encoded in the holographic standing wave. The light might take 1 year to get from edge to center to all edges, but the standing wave should be affected instantaneously (in theory). Much like if you threaded a single glass rod from Chicago to Australia and tapped it, normal wave propagation comes into effect for the "tap" to be heard at the other end, but if you pull or push on the end, the other end moves at the same instant, no propagation needed.

I need to think this over when I've had more sleep...

Answer 13

Yes. And lighting it is possible without unobtainium. Sunlight is 1000W/m^2. Over a billion seconds (30 years) you will need 10^12J. Direct mass to energy transformations give 10^17J/kg so that is 10^17/10^12 x30 years =3,000,000 years per kilo per meter squared. So if it has enough mass per area to give earth gravity at 1.2*10^10 kg/m^2 then it can be lit for at most 1.2*10^10*3000000=3.6*10^16 years (earth years) (actually twice as much because of night) before all the mass has turned to energy. I would recommend the maglev track idea with large tanks of matter(any) underground. These are slowly fed to mini black holes whose hawking radiation is beamed up out a hole in the ground, bounces off a mirror kept aloft by the force of the light and illuminates the ground.