Birch World

[Werner]

Black Hole
Mass: 1,537,268,497,607 Suns
Radius: 0.48 light years
Surface gravity: 9.896 meters per second squared.

https://www.omnicalculator.com/physics/schwarzschild-radius
This is an almost black hole, the figures above are for a black hole this size. Notice the gravity is just above that for the surface of the Earth. The actual value is 9.81 meters per second squared.
9.81/9.896= 0.99130962

Birch World
Mass: 1,523,909,050,200.7 Suns
Radius: 0.48 light years
Surface Gravity: 9.81 meters per second squared.
The radius in astronomical units is 30,294.46 AU.

What if we had a hollow shell and put our Solar system in its center? Yes it is also a Dyson Sphere with the mass of over one thousand galaxies. (1.5 quadrillion Suns) yet at a radius of 0.48 light years, the thickness of the shell need only about equal to the thickness of our planet to equal that much mass. How do we support it? Using orbital rings, lots of them! The orbital rings are spinning at slight greater than orbital velocity, and remember, the gravity diminishes the deeper you go under the surface of the Birch World, util you go completely inside the birch shell, (where we assume its mass is evenly distributed) where all the shells mass gets cancelled out, you are still at the bottom of an enormous gravitational well and the gravitational time dialation effects with the rest of the universe are quite significant. We'll assume there are fusion reactor built into the shell, the actual shell's thickness is about the diameter of Saturn. (1/10th the density of the Earth), there are corridors one can fly through to get to the surface of the birch World, and daylight is provided by an outer shell supported by air pressure underneath at an altitude of 10 km above sea level.

A fake Sun image is projected onto the inner surface of this shell. If one were to get above this ceiling, there is a trace atmosphere above it, more substantial air pressure underneath, and the trace atmosphere consists mostly of nitrogen and oxygen which diminishes to a vacuum with further altitude. The outer shell is transparent at night, but at night, there is nothing to see. The sky above is black. If parabolic dish telescopes are trained on it cosmic microwave background radiation is detected which was blue shifted from radio waves. The universe surrounding the birch World is extremely ancient, there are no stars, and it may be trillions to quadrillion of years old. The birchworld on the other hand has enormous habitable area.

 

[Werner]

Take the entire map of Charted space, all 11,000 worlds of it, this would be but a tiny portion of the birch world in terms of living space. The surface would look much like the surface of Earth, it would be a type IV civilization, the only kind of type IV civilization possible in a setting without FTL drives, you need to cannibalize the mass of one thousand galaxies to build a birch World, most of the material would be hydrogen, you only need the upper crust to be solid.

If you have a setting where there are gates to other universes, this one would be an interesting one to visit. This works best in a very ancient universe, one of the motivations for building one of these is to survive well into the cold and dark era of the universe, as time moves much more slowly on the surface of a birch World as it is almost a black hole itself.

 

[aramis]

Keep in mind: Dyson's shell wasn't a sphere... it was a cloud of separate sats, since the strain of a proper shell would preclude actually having the poles covered; no material known would handle the strain. (Later authors conflated Dyson's Swarm with solid shells.)

Given practical gravitics, if you include that, you CAN float a solid shell, but if there's a major outage, only the tropical belt is likely to survive. (the poles will be drawn down into the center mass.

So, you need gravitics in your setting. Either that, or restrict the birch world to a probably 30 degree wide belt,

 

[Werner]

Keep in mind: Dyson's shell wasn't a sphere... it was a cloud of separate sats, since the strain of a proper shell would preclude actually having the poles covered; no material known would handle the strain. (Later authors conflated Dyson's Swarm with solid shells.)

Given practical gravitics, if you include that, you CAN float a solid shell, but if there's a major outage, only the tropical belt is likely to survive. (the poles will be drawn down into the center mass.

So, you need gravitics in your setting. Either that, or restrict the birch world to a probably 30 degree wide belt,

What makes it a birch World is that it is almost a black hole, the escape velocity to climb out of its gravitational well is almost the speed of light. This setting is another Universe or our own universe in the distant future, when the universe is almost dead. It is basically a pocket Universe in it's own right, as there is nothing outside of it that matters. Anything that falls toward it from outside would be falling at nearly the speed of light by the time it hit its surface, if it punched a hole in the sky roof, the atmosphere can't escape, there is just too much gravity, it will just sit on top of the roof and can be pumped back underneath while the roof is being repaired.

As far as the PCs are concerned, this world may as well be flat, they are never going to explore all of it, it might make a good base for a time travel campaign or a parallel universe campaign. This world is not abandoned, it requires active management and maintenance to exist, those in charge may as well be gods, and they don't concern themselves with the affairs of mortals, they are concerned with maintaining the structure of this world not with who lives on it. Humans are just part of the scenery along with everything else. This is pretty much a world at the end of time, which is why I think it might make a good base for a time travel campaign.

 

[BackworldTraveller]

I'd be interested to see what the maths says about the pressures on the surface given the mass and size. Would the pressures be large enough to collapse the matter into something fluid like? If so, the whole collapses all too quickly into that black hole.

I'd also disagree about the statement about the gravity well. The gravity peaks at the surface - the exact centre has equal mass at equal distance in all directions and is thus in zero-g!

Finally, the body can't be treated as a point mass at the centre when calculating surface gravity. That assumption requires a solid body of uniform density.

The distance to each place varies and the pull exerted is dependent on the inverse of the square of that distance. So that portion of mass directly below a point is twice the distance away that a point mass at the centre would be...Thus it has only 1/4 of the effect.

 

[Werner]

I'd be interested to see what the maths says about the pressures on the surface given the mass and size. Would the pressures be large enough to collapse the matter into something fluid like? If so, the whole collapses all too quickly into that black hole.

I'd also disagree about the statement about the gravity well. The gravity peaks at the surface - the exact centre has equal mass at equal distance in all directions and is thus in zero-g!

Finally, the body can't be treated as a point mass at the centre when calculating surface gravity. That assumption requires a solid body of uniform density.

The distance to each place varies and the pull exerted is dependent on the inverse of the square of that distance. So that portion of mass directly below a point is twice the distance away that a point mass at the centre would be...Thus it has only 1/4 of the effect.

Yes, at 1 light year from the center, the gravity is 1/4 g, at 2 light years it is 1/16 g, at 4 light years it is 1/64 g, this is over one thousand galaxies worth of matter packed into one cubic light year of space, it is kept from forming a black hole by centrifugal force from within, there are spinning belts inside the shell moving at just below the speed of light, communication between any two points is just under 2 years to send a message and to receive a response, still it is possible to have a government. The surface area with a radius 30,300 times the radius of a 1 au dyson sphere is one quintillion times the surface area of the earth or a one followed by 18 zeroes.

 

[BackworldTraveller]

As I said, the gravity profile isn't what you'd expect.

Earth has a column of material under each point that is treated as (on average) 6370(ish) km away.

Birch has a tiny column of material very near followed by empty space followed by another tiny column of material at 0.96 LY away. Gravity directly towards the centre is thus tiny at any point. How the vectors for every point add up to act on any other point I don't know but it isn't the same as a solid body. 50% of the mass is over 0.48LY away and is acting at an angle. Nearby mass is mostly pulling sideways and doesn't exactly offset the far points because of the variation in distance.

Spinning the surface at something near C means that any incoming particles are incoming at near C. That makes them very dangerous to life!

The circumference is almost exactly 3 light years. Which means that centrifugal force experienced is about 0.5m/s2 (relativistic effects not calculated).

A sphere will be in trouble because the poles have no centrifugal force and thus fall towards the centre. Here they quickly exceed the mass required for a black hole to form. And the whole thing then collapses.

The great circle has the mass of 1,523,909,050,200.7/2 suns spread along a line 3LY long. That is .000027 MSol per metre. More than enough to make any material malleable. So the radius slumps, collapses and...big black hole.

 

[Werner]

Sun towers are an alternative to a roof for self-illumination of the birch World, the taller the towers are the fewer you would need. Another idea is to use parabolic arches to replicate the Sun's path across the sky. You need something called a space fountain to support such tall structures. We will probably need multiple artificial suns, as a single sun to illuminate a hemisphere of the birch would and have a 24-hour day would be impossible.

One can have multiple Suns in orbit turning on and off, perhaps powered by black holes to get something that can illuminate a hemisphere at a time, it probably needs to be a light year away at a minimum.

One alternative would be an array of lasers, and an orbiting ring of illuminators the full 360 degrees around the birch World, with individual pixel elements turning on and off to present an image of the sun rising and setting. The whole thing could not orbit in 24 hours (as it is a light year in radius, but it can time its pixels to go on an off producing a pseudo-motion visible from the birchworld surface creating an image of a sun rising and setting, though such actual motions would be physically impossible as they would have to be FTL.

 

[Werner]

As I said, the gravity profile isn't what you'd expect.

Earth has a column of material under each point that is treated as (on average) 6370(ish) km away.

Birch has a tiny column of material very near followed by empty space followed by another tiny column of material at 0.96 LY away. Gravity directly towards the centre is thus tiny at any point. How the vectors for every point add up to act on any other point I don't know but it isn't the same as a solid body. 50% of the mass is over 0.48LY away and is acting at an angle. Nearby mass is mostly pulling sideways and doesn't exactly offset the far points because of the variation in distance.

Spinning the surface at something near C means that any incoming particles are incoming at near C. That makes them very dangerous to life!

The circumference is almost exactly 3 light years. Which means that centrifugal force experienced is about 0.5m/s2 (relativistic effects not calculated).

A sphere will be in trouble because the poles have no centrifugal force and thus fall towards the centre. Here they quickly exceed the mass required for a black hole to form. And the whole thing then collapses.

The great circle has the mass of 1,523,909,050,200.7/2 suns spread along a line 3LY long. That is .000027 MSol per metre. More than enough to make any material malleable. So the radius slumps, collapses and...big black hole.

For one thing the Universe this Birch World exists in is extremely old, the builders of this world had to gather the materials of over a thousand galaxies when this universe was much younger, as they foresaw the end coming, they knew the stars would not shine forever, this Universe is hundreds of trillions of years old, maybe quadrillion of years old. Anyway when this Birch World was built the universe was much younger, they created a void buy mining out local galaxies until there was nearly nothing left, since they built it, those living on its surface were under its gravitational time slowing effects, so maybe for every year spent on the Birch World one thousand years pass for the external universe and this universe just keeps on getting bigger, darker, and emptier, there are black dwarfs out there. The Birch World has billions of years supply of hydrogen and other light elements to run its fusion reactors and with gravitational time dialation that is trillions of years passing in the external universe, escaping the gravity of the birch World requires an antimatter drive and once out there, there is not much, a few black holes. The birch World builders had little use for those stellar sized black holes, as they couldn't build anything out of them.

There is little reason to rotate the birchworld anyway, parts of it spin to counteract the pull of gravity, but not the whole thing. Having gravity is kind of the point. The surface gravity is 9.81 meters per second squared, the escape velocity however is nearly the speed of light. One can go above the atmosphere of course, but it takes continuous thrust to stay up there. As for whatever engineering magic is required to keep this structure stable, I leave it to minds far more ancient and smarter than my own. You just have to take a leap of faith that this thing is possible, just like you do for artificial gravity generators and the Jump drive.

As for the Jump Drive itself, it just won't work anywhere out to a radius of 100 light years, so they are pretty useless, inside the shell is another story, you can make a jump from 12,800,000 km inside the shell to the star system in the center. Inside this shell is flat space, you can jump to any but the innermost planet in the star system, or from there back to the shell, in each case the Jump will take one week in Jump space. Perhaps the PC's have misjumped their Starship and ended up in this strange and ancient parallel universe. At the center is a model of Earth's Solar System, it is not certain whether it is the original Solar System or just a copy. All the planets are there from the Sun all the way out to the Oort cloud, there is Earth, the continents are in an unfamiliar arrangement, the Sun looks to be 5 billion years old, it is clear that this birch world was built by the descendants of humans. There are the images of stars projected on the inside of the birch world shell, its surface reflects radar, so its nature is obvious to the right detection instruments, to the naked eye it just looks like normal space, so any PC starship that ends up trapped here will become immediately familiar with the situation once they attempt to jump out of system. Naturally the Birch world builders left a device that could send the PC's starship back where it came from, they just have to find it.

 

[Werner]

The way out is via the fourth dimension, the birch world builders have invented a time machine, they knew their universe was dying and their building this birchworld was only putting off the inevitable, so they have developed a time warp drive and wormhole technology. The timewarp sends their wormhole openings back in time to whatever time period they want all the way back to the big Bang. Of course nothing they send to the big Bang will survive, so they can send wormholes almost to the big bang.

Go back far enough in time and all the multiple universe's merge back into a single one, and from there, the PCs can find their own universe and return to their present in that Universe. The builders will be happy to send the PCs back in time, but from there it's up to the PCs to move forward in time back to their present. Since the builders were once human, they can send the PCs back to a historical era, to a point where the PC's historical timeline is identical to the builders. The builders' timeline and the OTU's merge at some point before Alexander the Great's empire fell, for the builder's Alexander's children survived and ruled that Empire for several centuries before it fell much like the Roman Empire did, so one possible way for the PC's to get back to their own timeline would be to kill Alexander the Great by poisoning him, then with some further course corrections the PCs will be on their way back to their own universe.

 

[Krikkitone]

Issue with living “inside the shell”

Gravity will only naturally come from layers you are outside, once you are in the inside surface, the only gravity will be from the system in the middle which will pull you (and all the inside atmosphere) into the central star.

What I would have it do is
people live outside Most of the shells, but there is one thin shell encompassing the rest (a ceiling shell) at a distance of a few 1000 km, that provides the “sunlight”.
(that way the “living space gravity is natural rather than artificial.

 

[Werner]

Might need occasional pillars to hold it up, at 1000 km. If its 10 km up you can rely on the difference in air pressure between top and bottom, at 1000 km there would be just vacuum. One can go with arches and pillars.

 

[aramis]

Might need occasional pillars to hold it up, at 1000 km. If its 10 km up you can rely on the difference in air pressure between top and bottom, at 1000 km there would be just vacuum. One can go with arches and pillars.

if the area is sufficiently deep as to have significant dilation, it's sufficiently deep that people will be turned to jam.

The difference between 0.9G and 1G is measured in centiseconds per year. And a year is roughly 31536000 seconds.

To have livable for humans, the G's can't exceed 2 by much... and that's still only going to be no more than single digit seconds per year.

you're not going to get humans surviving significant gravitational dilation without having significant centrifugal pseudo-force... but that's got other issues, as well, since the gravitational gradient over 2m with significant time dilation is going to be enough that your speed won't save you from spaghettification.

 

[Werner]

if the area is sufficiently deep as to have significant dilation, it's sufficiently deep that people will be turned to jam.

The difference between 0.9G and 1G is measured in centiseconds per year. And a year is roughly 31536000 seconds.

To have livable for humans, the G's can't exceed 2 by much... and that's still only going to be no more than single digit seconds per year.

you're not going to get humans surviving significant gravitational dilation without having significant centrifugal pseudo-force... but that's got other issues, as well, since the gravitational gradient over 2m with significant time dilation is going to be enough that your speed won't save you from spaghettification.

Here are two real world examples. Earth and Saturn, surprisingly, Saturn has 95 times the mass of Earth, but at its "surface" the gravity is the same as Earth, although its escape velocity is much higher. If you continue increasing the radius of a sphere by the square root of its mass as its mass increases, then its surface gravity will remain the same as its escape velocity continues to increase. In order to do this, the density of the object must decrease, if you continue this trend until the radius equals 0.48 of a light year, that is a birch world, at that point the escape velocity approaches the speed of light, it is the largest possible World you can build that is held together by it's own gravity.

Gravity obeys the inverse square law with distance, and it also increases proportional to mass so is you have a planet with 1 Earth mass and 1 Earth radius you will get 1 Earth gravity on its surface. If you double the radius but keep the mass the same the gravity on its surface will be 1/4 g, and if you quadruple its mass within that same volume you are back to having 1g on its surface. Now normally if you double a planet's radius while keeping the density the same the mass is proportional to the planet's volume so you would octuplets the planets mass, but since you are only quadrupling it, the density of the planet has to be halved each time your double the planet's radius to keep the surface gravity at 1g.

 

[BackworldTraveller]

Gravity obeys the inverse square law with distance, and it also increases proportional to mass so is you have a planet with 1 Earth mass and 1 Earth radius you will get 1 Earth gravity on its surface. If you double the radius but keep the mass the same the gravity on its surface will be 1/4 g, and if you quadruple its mass within that same volume you are back to having 1g on its surface. Now normally if you double a planet's radius while keeping the density the same the mass is proportional to the planet's volume so you would octuplets the planets mass, but since you are only quadrupling it, the density of the planet has to be halved each time your double the planet's radius to keep the surface gravity at 1g.

n.b. Only applies if the body is solid and (for hollow bodies) is small enough for R-squared not to be significant.
Birch is neither solid nor small

Take a planet the mass of earth...1G
Take two planets each half the mass of earth and separate them by 1 diameter...No longer 1G at any point on either surface.

 

[Werner]

n.b. Only applies if the body is solid and (for hollow bodies) is small enough for R-squared not to be significant.
Birch is neither solid nor small

Take a planet the mass of earth...1G
Take two planets each half the mass of earth and separate them by 1 diameter...No longer 1G at any point on either surface.

Solid is a relative term, a white dwarf is much more solid than the Earth.
A typical white dwarf has the mass of our Sun and the radius of Earth. Since our Sun has 333,000 times as much mass as the Earth, its surface gravity will be 333,000g in direct proportion to its mass, and it will also be 333,000 times as dense as the Earth. The Earth and this hypothetical white dwarf both have the same radius, 6400 km. Now let's say we wanted to blow up this white dwarf to a large enough size so that it has 1g on its surface. The radius of the new object is the square root of its mass multiplied by an Earth radius 6400 km. The new radius is 3,693,194 km. The surface area is 333,000 times that of Earth, it's volume is 192,161,487 times that of Earth. We can find its density relative to Earth by 333,000/192,161,487=0.0017 times that of Earth, if the mass is uniformly distributed under its shell, meaning that every square kilometer has the same amount of mass under it, it doesn't matter whether its hollow or filled with a diffuse gas, it will still be 1g on its surface, if more mass is packed towards one side of the sphere, obviously the uniform gravity won't hold. One can have an expanding sphere and so long at added mass distributed uniformly equal the increasing surface area, the gravity will remain the same.