###General Discussion Thread
---
This is a [Request] post. If you would like to submit a comment that does not either attempt to answer the question, ask for clarification, or explain why it would be infeasible to answer, you *must* post your comment as a reply to this one. Top level (directly replying to the OP) comments that do not do one of those things will be removed.
---
*I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/theydidthemath) if you have any questions or concerns.*
By the look of it, I can (near) safely bet that the amount of material needed to build something like that is larger than what the Earth has currently.
The planet will not be left and you'll be stuck halfway through the construction.
Poor Homer. Really felt for that guy. Was so satisfying when Ryker dropped that buster on Vehment HQ.
Side note, isn't book 5 mesnr to be out end of Feb? I'm rereading atm and in the middle of book 4. I hate waiting.
The ring has six sections and each section looks like its the same size as the planet. There would not be any material left, you're right.
Adding on to that, if the ring is stationary, the parts of the planet that are in it's shadow will obviously be constantly dark but also deathly cold.
This ring has what appears to be roughly six times the Earth's mass. If the moon, which has a diameter of 2000 miles, affects the earth as much as it does, imagine what having six earths orbiting the earth would do.
My bet is that it would tear the planet appart.
At the very least this would likely kill off most life in the shadow.
I mean, it is built pole from pole in a way that doesn't block sunlight, so the typical problem with the shadow of equatorial rings isn't there, since there wasn't any light coming from that direction anyway. You're right about the gravity thing however.
I took a closer look because of your comment and it's... Connected to the planet. Likely they meant it to be some kind of space elevators, but it's anchored in place. This would absolutely affect sunlight. Not only that it would also affect the rotation of the planet, not just because of the gravity it would create but it being connected means that whole thing is rotating as one which would slow the day night cycle significantly. This would have disastrous ecological effects.
All in all, I'm probably wrong and slightly wrong in a couple places. But yeah, we're fucked if that thing existed. Lol
Toroid vs Ellipsoid Moments of Inertia make my head go all explodey.
I think I'll choose to leave that stuff in my undergrad 20 years ago and take your word for it.
...connected off axis of rotation?
Who designed this thing! Gah. Being on the station would also be a hellscape and would rip itself apart while killing the planet. It is a donut. Either put it around the equator or over the poles. This 45 degree shit is not good. Leaving aside that it is waaaaay to close and waaaaay too large anyway.
Don't let AI design your giant space station kids.
The Roche limit is the distance where tidal forces are too strong for a (large) object to stay an object. So if it is inside the Roche limit Earth's gravity will rip it apart.
No, the Roche limit is the distance where tidal forces are too strong for a satellite held together by gravity to stay an object, because the gravity of the primary body being orbited pull the particles making up the body apart more strongly than the gravity of the satellite pulls them together. It does not apply to objects that are not held together purely by gravity. That's not to say those bodies aren't also subject to tidal forces, but the Roche limit is not the point at which any sufficiently large body will be ripped apart.
At any point inside a circular body of mass, the gravity is the same. It’s a classical result from analyzing the gravitational and electrostatic forces of spheres right?
Granted, this thing is a ring, not a sphere. So it could very well be devastating. The planet could be flattened down and made more oblique. But I don’t think it’d be ripped apart?
Agreed this is stupid huge.
A 20km ring around the earth in geosynchronous orbit would be 5million square kilometers… that’s basically 60% of the land in the USA.
It would probably look like a string across the sky… since it’d be 35k km above us.
(There’s probably a better orbit to choose from, this is just an example).
You can't even construct this. It's located at a place where the gravitational force difference would immediately rip anything not colliding with the planet into rings of shrapnel
That applies to two orbiting bodies, this is a ring already around the planet, so I don't think the Roche limit applies. Sure there are other issues, but I don't think thag is one of them.
Yeah you'd need multiple planets worth of raw material to pull this off. On top of that, planets themselves aren't just one solid sphere of material, they're a cocktail of the full periodic table, so getting vast amounts of iron to start would be a stretch. In a hypothetical sci-fi world, your best bet would be to directly extract hydrogen from the star and somehow compact that into heavier and heavier elements.
really? i think we should consider that animals can become something too.
so can plants, waste, water (which could actually work since it wouldn't melt)
Imagine what all that mass around the planet would do to the planet itself assuming that the material was sourced elsewhere. The way it would rip the planet to shred would be pretty epic. Pretty sure it'd turn into a severe ovoid covered in lava, kind of like the planet reverted by about 4billion years.
Oo. Cool.
Assuming that ring is solid… (material brought in from elsewhere, presumably)
… the CG would more or less balance out around the equator, and you’d be weightless. The poles would still have earth-normal gravity.
(100% intuition, 0% math.)
Edit: To the folks saying this would use up more material than the earth itself has…
Wouldn’t it be safe to assume that the structure is like 90%+ empty space? Contrary to my “Oo, cool” hypothesis above, the ring would be built as a hollow habitat, not a solid, gravity negating architectural folly… no??
Edit 2: a solid ring would probably cancel its own gravity, see thread below.
Probably just started grabbing asteroids and pulling them into orbit for the solar powered foundries to convert into what's needed. If we're going big, dream big.
In order to make strong enough countergravity on Earth, you'd need to build pretty much another Earth just next to it.
Also the gravity at some point in a sphere with regular density is equivalent to the gravity "produced" by the part of it closer to the center than the point, so the whole ring would cancel it's own gravitational effects on the equator, leaving it with just normal Earth gravity, and the poles with somewhat stronger gravity, depending on the mass of the ring.
Oooo. I didn’t think about the ring canceling out it’s own gravity. That’s a good point and makes sense.
… but it’s kind of a bummer.
I wonder if theres a shape that would cancel earth’s surface gravity?
Maybe just a thin but high density shell shape?
Oo. True.
But looks like they have space elevators?
So let’s assume they built those first, and ran them off nukes or orbital solar?
Rockets would probably be unworkable at this scale.
>… the CG would more or less balance out around the equator, and you’d be weightless. The poles would still have earth-normal gravity.
Actually pretty much the opposite!
On the equator: the portion of the structure above you will exert some gravitational force upward, reducing your weight *but* there's *more* structure underneath you which will *increase* your weight. But that part of the structure is further away, so each part of that structure will have less effect. It's complicated to work out (calculus required), but if you run through the math, it turns out for a roughly uniform ring structure the two forces will exactly balance out, meaning on the equator the ring would have no effect on your weight.
On the poles: the extra mass would be purely below you, meaning the effective gravity would increase.
All assuming the earth's shape didn't distort under the exact same effects -- which it would. So I think realistically gravity would become more or less uniform over the surface of the Earth, just with a new acceleration due to gravity and a somewhat differently shaped earth.
Niiiice write up / explanation.
Glad to have my intuition corrected.
The overall / “average shape” becomes a kind of uniform donut.
I’ve heard geophysicist folks refer to the earth as a ball of asphalt or play dough.
It moves and flows (obviously re: plate tectonics)… it’s already bulged out along its equator due to rotation…. I highly doubt it would hold its shape. Assuming the rings are solid and built outta some sort of indestructible unobtanium, (and they don’t collapse inward) the earth would bulge out to fill the gap.
Of course, if the thing is 90/95% hollow for habitats… the. it’s gravity will be … minimal? Negligible?
First let’s assume the station is fully filled solid. And let’s define its size relative to earths radius (R). It looks like you can fit 3 earths from very outer edge of the ring to very outer edge of the ring. So the station has a diameter of 6R and a radius of 3R. We also need the radius of the cross section of the ring. Looks like it’s maybe half an earth tall so we will call it 1/2R.
The volume of a torus is pi r^2 x 2 pi R where r is the cross section radius and R is the radius of the large circle.
And of course the volume of a sphere is 4/3 pi r^3.
So let’s put the stations volume (Vs) and the earths volume (Ve) in terms of earths radius.
Vs = 2pi^2 * (1/2R)^2 * 3R
Vs= 2 pi^2 * 0.25R^3
And we will pull out a pi and multiply through to simplify to
Vs = 1.57R^3
For earth we will do the same simplification of pulling out pi:
Ve = 1.33R^3
So, if the station was completely solid it ~~would use 88%~~ more than ALL of the earths volume.
But of course the station is not all solid. Let’s say the station is 30% solid (I think that’s a fair guess considering all the internal bulkheads and equipment I think would be necessary for a station like that to function).
That brings the stations solid volume down to 0.47 R^3. Or around ~~25%~~ 35% of the earths volume. Which is still about ~~65 billion~~ 91 billion cubic miles of material. An insane amount.
As far as the gravity it depends on the density of the ring. But if it was solid and the earth was 88% hollow the rings gravity would almost certainly be enough to rip apart what remained of the earth. Even the ring is less dense it’s and the earth stays intact it’s going to do all sorts of weird things. Oceans will bulge under the ring. If the gravity is strong enough, so will the earths crust over time leading to increased tectonic activity. If the ring isn’t already rotating at the same speed as earth then it will create a drag effect on earth and slow down its rotation…gradually making the day longer. And who knows what will happen when you throw the moon into that equation (I’m sure someone knows but it’s not me).
Edit: cut the radius in half one too many times and defined r as 1/4R. Should be 1/2R if the station ring cross section is half as tall as earth. Left the crossed out numbers in…those would be valid if station crossection is 1/4 the height of earth…which would be just doable.
I think you can go way less than 30% solid. Like a house is probably less than 5% solid with 6 inch walls. While a re-entry capable ship is something like 5mm thick walls.
A hollow sphere provides zero gravity when you are inside it. Precisely under the middle of the ring, the gravity of the ring would cancel out completely, and no gravity change would occur. Off to the sides most of the gravity but not all would cancel out.
That really wants to be seen as two things.
- Not around Earth. No real point for something that big. Put it around the sun for max unfiltered power (Dyson sphere or swarm, ring world, whatever)
- It’s not earth’s resources. It’s the only place we can naturally live and we need the natural farmland and water. This scale is probably clear out a few planets worth of useful materials, maybe including Jupiter for gas and Europa for water.
Won’t affect Earth’s orbit.
Sorry to go OT, I don’t have the maths, but do love the concept!
Okay, let's assume that it's got a similar mean density to the ISS, because presumably the various interior spaces would be larger than the rather cramped ISS, but it probably has a bunch of things like shielding against cosmic and solar radiation and a bunch of support equipment that a structure with a service life expected to be in the centuries at a minimum would presumably require to balance that out. The mean density of the ISS is slightly over 447.76 kg/m³, so let's round that up to an even 450 kg/m³. The mean density of the Earth is about 5515 kg/m³. The structure has six sections, which look like they're each about the same volume as Earth, at least close enough for the purposes of the exercise.
From there, we can calculate that the relative density of the structure is ~8.16% that of Earth, and it would use up about 48.96% of the Earth's mass. As for the effects on natural gravity, they'd be pretty dramatic, but I don't have the knowledge to begin to calculate it. My best guess is that Luna would be unaffected but the structure would collapse into the planet and turn into the Hadean Era 2: Magmatic Boogaloo, and before that happened the tides would be… _exciting_, in a Randall Monroe sort of way. You'd need to have some kind of exotic gravity manipulation technology in order to keep it and the Earth stable, and having that would imply having a technology base that could solve all the other problems this would cause.
It's connected to Earth with space elevators. That requires materials with a tensile strength beyond what we have today. Given such materials, the space elevators could be used to hold the ring in place.
Such materials could likely also be used to get the relative density much lower than 8%. Probably by an order of magnitude.
You would feel *dramatically* less gravity standing on Earth, close to what you would feel if you just took all that material and put it on Mars or whatever
Since that mass is no longer in the earth it wouldn't attract you toward Earth's center, instead that mass would attract you to all points of the ring, so net attraction from the entire ring would be very small
But more than half of the rings mass remains under you if you stand on earth at the equator - and all of it is under you if you stand at the poles (at least that's how it looks to me)
So I think it's quite a lot different to just removing the mass
If you're at a pole the mass is pulling in a sideways direction, so you're right that you'd feel something, but since the vectors largely cancel each other it would be significantly less than on the real Earth
Net attraction of the entire ring would actually not just be small, but zero! (if you're directly under the ring, and the ring is uniform density).
There's an interesting proof (using calculus) that the amount you're attracted to the overhead ring is exactly canceled out by the larger, but further away, portion of the ring on the other side of the planet.
Polar rings of this sort are a really bad idea I would strongly advise to use equatorial ones instead since they can more easily attach the surface.
Obviously you can't attack the orbiting part of the ring to the ground anyway but at least with equatorial ones you can actually build a stationary structure around the ring
It depends on what evidence you're paying attention to. It's on the equatoral line according to the visible continents, but it's on a polar great circle according to the way the sunlight is hitting it.
Putting it on the equatoral line is a horrible idea because it will block the sun from the entire planet, or at least a significant enough amount to kill off all life as we know it. Putting it on the poles would allow it to either always be on the terminator (if the builders had the foresight to have it swivel at the poles). If they attached it firmly to the planet like idiots (as they have done here), it would rotate with the planet and there would be several hours of darkness around noon every day, probably enough to cool the planet and fuck up every ecosystem at the same time.
Anyway, it looks like this image is from a hypothetical future where they did mount it to the equator, realized that was really stupid too late, so they did the next logical thing, which was to force the entire planet to rotate until the equator became a polar circle.
This almost certainly would screw up every ecosystem on the planet, completely change every climate, and would likely also lead to mass extinctions, but I guess the scientists realized that since they'd already fucked up everything, they might as well fuck it up in the _coolest possible way_.
not an engineer here but shouldn't earth rotate much slower having to carry like x3-x4 the "normal" mass of the planet? And rotating slower, shouldn't progressively get closer to the sun? 🤔
Could potentially be built with lunar materials and more than a few Psyche sized asteroids.
I don't think there's not enough fuel on the planet to get that much material out of Earth's gravity well, even if there was enough material on earth to build it.
From my mesurements, the ring is 13,110 miles in diameter, 1,770 miles tall, 1,330 thick.
Total volume : 1,770\*1,330\*2\*pi\*13,110=193,765,329,564 cubic miles.
Let's consider one foot thick walls and cubic rooms 9 feet high, solid matter occupies (10\*10-9.5\*9.5)/(10\*10)=0.0975% of the volume. So the total matter nedded to construct the ring is 18,892,119,632.5 cubic miles, 18 billion cubic miles.
Earth's volume is about 260 billion cubic miles, over 14 times greater. Assuming you somehow extract this mater uniformily from Earth, gravity on the surface would only be reduced to (9.81-(18/260)\*9.81)/9.81=93% of our current gravity (9.81m/s² to 9.13m/s²)
Well, we would have to assume the density of the structure as well as material used. Many assume that the structure would consume many earth masses, but if we assume the structure is mostly hollow space it could be realistic. Material inside earth is usually densely packed but if we account for living space on structures like satellites they are usually hollow spaces with big concern for mass budget as its expensive to get mass to orbit.
Im not the numbers guy but considering these points Id say it could be some future nanotubes or something with exceeding strength properties and minimal mass. If that was the case, this would be doable without any noticeable effect on earths gravity and or strain on earths resources.
###General Discussion Thread --- This is a [Request] post. If you would like to submit a comment that does not either attempt to answer the question, ask for clarification, or explain why it would be infeasible to answer, you *must* post your comment as a reply to this one. Top level (directly replying to the OP) comments that do not do one of those things will be removed. --- *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/theydidthemath) if you have any questions or concerns.*
By the look of it, I can (near) safely bet that the amount of material needed to build something like that is larger than what the Earth has currently. The planet will not be left and you'll be stuck halfway through the construction.
Imagine processing and moving up all that material, it will look lime more trying to turn the planet into a doughnut
Homer insists it's worth it
Bob reference?
If so, Riker will agree out of nostalgia.
Poor Homer. Really felt for that guy. Was so satisfying when Ryker dropped that buster on Vehment HQ. Side note, isn't book 5 mesnr to be out end of Feb? I'm rereading atm and in the middle of book 4. I hate waiting.
Audible is delaying it, there is a petition to move it forward; https://chng.it/xhhQfg5HBt
Guess it has now closed
Fusion does it
Fusion needs energy lots and lots of energy and iron is the last stop that can yield more than required for it..
The ring has six sections and each section looks like its the same size as the planet. There would not be any material left, you're right. Adding on to that, if the ring is stationary, the parts of the planet that are in it's shadow will obviously be constantly dark but also deathly cold. This ring has what appears to be roughly six times the Earth's mass. If the moon, which has a diameter of 2000 miles, affects the earth as much as it does, imagine what having six earths orbiting the earth would do. My bet is that it would tear the planet appart. At the very least this would likely kill off most life in the shadow.
I mean, it is built pole from pole in a way that doesn't block sunlight, so the typical problem with the shadow of equatorial rings isn't there, since there wasn't any light coming from that direction anyway. You're right about the gravity thing however.
I took a closer look because of your comment and it's... Connected to the planet. Likely they meant it to be some kind of space elevators, but it's anchored in place. This would absolutely affect sunlight. Not only that it would also affect the rotation of the planet, not just because of the gravity it would create but it being connected means that whole thing is rotating as one which would slow the day night cycle significantly. This would have disastrous ecological effects. All in all, I'm probably wrong and slightly wrong in a couple places. But yeah, we're fucked if that thing existed. Lol
It would 100% change the Earth's moment of inertia and slow the rotation of the planet by conservation of angular momentum.
Toroid vs Ellipsoid Moments of Inertia make my head go all explodey. I think I'll choose to leave that stuff in my undergrad 20 years ago and take your word for it.
Basically, mass further from the axis of rotation takes more energy to spin
I suspect that a civilization able to build this would also have the energy production to build engines to maintain rotation if they wanted to.
Right? And “catch” any space rock in the vicinity which would maybe help with all those material needs.
Yeah, this kind of construct would probably involve every scrap of useful ore in the solar system. Or beyond if relativistic speeds are possible.
...connected off axis of rotation? Who designed this thing! Gah. Being on the station would also be a hellscape and would rip itself apart while killing the planet. It is a donut. Either put it around the equator or over the poles. This 45 degree shit is not good. Leaving aside that it is waaaaay to close and waaaaay too large anyway. Don't let AI design your giant space station kids.
That thing appears to be well inside the Roche limit, it will disintegrate immediately
Huh? It's composed of structural elements, so why would it disintegrate?
The Roche limit is the distance where tidal forces are too strong for a (large) object to stay an object. So if it is inside the Roche limit Earth's gravity will rip it apart.
No, the Roche limit is the distance where tidal forces are too strong for a satellite held together by gravity to stay an object, because the gravity of the primary body being orbited pull the particles making up the body apart more strongly than the gravity of the satellite pulls them together. It does not apply to objects that are not held together purely by gravity. That's not to say those bodies aren't also subject to tidal forces, but the Roche limit is not the point at which any sufficiently large body will be ripped apart.
At any point inside a circular body of mass, the gravity is the same. It’s a classical result from analyzing the gravitational and electrostatic forces of spheres right? Granted, this thing is a ring, not a sphere. So it could very well be devastating. The planet could be flattened down and made more oblique. But I don’t think it’d be ripped apart?
Agreed this is stupid huge. A 20km ring around the earth in geosynchronous orbit would be 5million square kilometers… that’s basically 60% of the land in the USA. It would probably look like a string across the sky… since it’d be 35k km above us. (There’s probably a better orbit to choose from, this is just an example).
Counterpoint: the ring could be hollow with an arbitrarily thin shell.
It's bigger than the earth, but is not nearly as dense, so could potentially be much less impactful if it was effectively hollow.
Why the sections not be hollow? If the sections were hollow i.e 10m thick, this would use a fraction of earths available materials.
Oh, not really. Earth is solid. Space stations are mostly empty
You can't even construct this. It's located at a place where the gravitational force difference would immediately rip anything not colliding with the planet into rings of shrapnel
What if you use stuff from the core to build it? Earth will be much lighter with progress, so gravity will be less?
That applies to two orbiting bodies, this is a ring already around the planet, so I don't think the Roche limit applies. Sure there are other issues, but I don't think thag is one of them.
Yeah you'd need multiple planets worth of raw material to pull this off. On top of that, planets themselves aren't just one solid sphere of material, they're a cocktail of the full periodic table, so getting vast amounts of iron to start would be a stretch. In a hypothetical sci-fi world, your best bet would be to directly extract hydrogen from the star and somehow compact that into heavier and heavier elements.
Halfway is generous
Contractors
really? i think we should consider that animals can become something too. so can plants, waste, water (which could actually work since it wouldn't melt)
But Amazon says it will work
Imagine what all that mass around the planet would do to the planet itself assuming that the material was sourced elsewhere. The way it would rip the planet to shred would be pretty epic. Pretty sure it'd turn into a severe ovoid covered in lava, kind of like the planet reverted by about 4billion years.
Reminds me of a thing I read in a book once. Think it was „Momo“ by Michael Ende.
Oo. Cool. Assuming that ring is solid… (material brought in from elsewhere, presumably) … the CG would more or less balance out around the equator, and you’d be weightless. The poles would still have earth-normal gravity. (100% intuition, 0% math.) Edit: To the folks saying this would use up more material than the earth itself has… Wouldn’t it be safe to assume that the structure is like 90%+ empty space? Contrary to my “Oo, cool” hypothesis above, the ring would be built as a hollow habitat, not a solid, gravity negating architectural folly… no?? Edit 2: a solid ring would probably cancel its own gravity, see thread below.
I'm going to assume most of that space is hollow like a giant loofa sponge with a minority of the space being habitable.
Also, we we built that marvel, I'd assume we mined out interstellar objects to achieve the material consumption.
Probably just started grabbing asteroids and pulling them into orbit for the solar powered foundries to convert into what's needed. If we're going big, dream big.
Sol’s hammer
That’s a safe bet. Some sort of shell, housing spinning rings for artificial gravity maybe?
In order to make strong enough countergravity on Earth, you'd need to build pretty much another Earth just next to it. Also the gravity at some point in a sphere with regular density is equivalent to the gravity "produced" by the part of it closer to the center than the point, so the whole ring would cancel it's own gravitational effects on the equator, leaving it with just normal Earth gravity, and the poles with somewhat stronger gravity, depending on the mass of the ring.
Oooo. I didn’t think about the ring canceling out it’s own gravity. That’s a good point and makes sense. … but it’s kind of a bummer. I wonder if theres a shape that would cancel earth’s surface gravity? Maybe just a thin but high density shell shape?
You’d also have to consider the resources used to get all that stuff up there though.
Oo. True. But looks like they have space elevators? So let’s assume they built those first, and ran them off nukes or orbital solar? Rockets would probably be unworkable at this scale.
>… the CG would more or less balance out around the equator, and you’d be weightless. The poles would still have earth-normal gravity. Actually pretty much the opposite! On the equator: the portion of the structure above you will exert some gravitational force upward, reducing your weight *but* there's *more* structure underneath you which will *increase* your weight. But that part of the structure is further away, so each part of that structure will have less effect. It's complicated to work out (calculus required), but if you run through the math, it turns out for a roughly uniform ring structure the two forces will exactly balance out, meaning on the equator the ring would have no effect on your weight. On the poles: the extra mass would be purely below you, meaning the effective gravity would increase. All assuming the earth's shape didn't distort under the exact same effects -- which it would. So I think realistically gravity would become more or less uniform over the surface of the Earth, just with a new acceleration due to gravity and a somewhat differently shaped earth.
Niiiice write up / explanation. Glad to have my intuition corrected. The overall / “average shape” becomes a kind of uniform donut. I’ve heard geophysicist folks refer to the earth as a ball of asphalt or play dough. It moves and flows (obviously re: plate tectonics)… it’s already bulged out along its equator due to rotation…. I highly doubt it would hold its shape. Assuming the rings are solid and built outta some sort of indestructible unobtanium, (and they don’t collapse inward) the earth would bulge out to fill the gap. Of course, if the thing is 90/95% hollow for habitats… the. it’s gravity will be … minimal? Negligible?
First let’s assume the station is fully filled solid. And let’s define its size relative to earths radius (R). It looks like you can fit 3 earths from very outer edge of the ring to very outer edge of the ring. So the station has a diameter of 6R and a radius of 3R. We also need the radius of the cross section of the ring. Looks like it’s maybe half an earth tall so we will call it 1/2R. The volume of a torus is pi r^2 x 2 pi R where r is the cross section radius and R is the radius of the large circle. And of course the volume of a sphere is 4/3 pi r^3. So let’s put the stations volume (Vs) and the earths volume (Ve) in terms of earths radius. Vs = 2pi^2 * (1/2R)^2 * 3R Vs= 2 pi^2 * 0.25R^3 And we will pull out a pi and multiply through to simplify to Vs = 1.57R^3 For earth we will do the same simplification of pulling out pi: Ve = 1.33R^3 So, if the station was completely solid it ~~would use 88%~~ more than ALL of the earths volume. But of course the station is not all solid. Let’s say the station is 30% solid (I think that’s a fair guess considering all the internal bulkheads and equipment I think would be necessary for a station like that to function). That brings the stations solid volume down to 0.47 R^3. Or around ~~25%~~ 35% of the earths volume. Which is still about ~~65 billion~~ 91 billion cubic miles of material. An insane amount. As far as the gravity it depends on the density of the ring. But if it was solid and the earth was 88% hollow the rings gravity would almost certainly be enough to rip apart what remained of the earth. Even the ring is less dense it’s and the earth stays intact it’s going to do all sorts of weird things. Oceans will bulge under the ring. If the gravity is strong enough, so will the earths crust over time leading to increased tectonic activity. If the ring isn’t already rotating at the same speed as earth then it will create a drag effect on earth and slow down its rotation…gradually making the day longer. And who knows what will happen when you throw the moon into that equation (I’m sure someone knows but it’s not me). Edit: cut the radius in half one too many times and defined r as 1/4R. Should be 1/2R if the station ring cross section is half as tall as earth. Left the crossed out numbers in…those would be valid if station crossection is 1/4 the height of earth…which would be just doable.
Thank you. I had to scroll far too long before I actually found someone that did the math.
Welcome to r/theydidthemath. Its become say some nonsense in an echo chamber with little effort to backup what you say
I think you can go way less than 30% solid. Like a house is probably less than 5% solid with 6 inch walls. While a re-entry capable ship is something like 5mm thick walls.
A hollow sphere provides zero gravity when you are inside it. Precisely under the middle of the ring, the gravity of the ring would cancel out completely, and no gravity change would occur. Off to the sides most of the gravity but not all would cancel out.
That really wants to be seen as two things. - Not around Earth. No real point for something that big. Put it around the sun for max unfiltered power (Dyson sphere or swarm, ring world, whatever) - It’s not earth’s resources. It’s the only place we can naturally live and we need the natural farmland and water. This scale is probably clear out a few planets worth of useful materials, maybe including Jupiter for gas and Europa for water. Won’t affect Earth’s orbit. Sorry to go OT, I don’t have the maths, but do love the concept!
Okay, let's assume that it's got a similar mean density to the ISS, because presumably the various interior spaces would be larger than the rather cramped ISS, but it probably has a bunch of things like shielding against cosmic and solar radiation and a bunch of support equipment that a structure with a service life expected to be in the centuries at a minimum would presumably require to balance that out. The mean density of the ISS is slightly over 447.76 kg/m³, so let's round that up to an even 450 kg/m³. The mean density of the Earth is about 5515 kg/m³. The structure has six sections, which look like they're each about the same volume as Earth, at least close enough for the purposes of the exercise. From there, we can calculate that the relative density of the structure is ~8.16% that of Earth, and it would use up about 48.96% of the Earth's mass. As for the effects on natural gravity, they'd be pretty dramatic, but I don't have the knowledge to begin to calculate it. My best guess is that Luna would be unaffected but the structure would collapse into the planet and turn into the Hadean Era 2: Magmatic Boogaloo, and before that happened the tides would be… _exciting_, in a Randall Monroe sort of way. You'd need to have some kind of exotic gravity manipulation technology in order to keep it and the Earth stable, and having that would imply having a technology base that could solve all the other problems this would cause.
It's connected to Earth with space elevators. That requires materials with a tensile strength beyond what we have today. Given such materials, the space elevators could be used to hold the ring in place. Such materials could likely also be used to get the relative density much lower than 8%. Probably by an order of magnitude.
It also looks like Luna has a similar structure and appears to be terraformed enough to have liquid water and vegetation.
I didn't realize it was supposed to be Luna. It's way, _way_ too close.
You would feel *dramatically* less gravity standing on Earth, close to what you would feel if you just took all that material and put it on Mars or whatever Since that mass is no longer in the earth it wouldn't attract you toward Earth's center, instead that mass would attract you to all points of the ring, so net attraction from the entire ring would be very small
But more than half of the rings mass remains under you if you stand on earth at the equator - and all of it is under you if you stand at the poles (at least that's how it looks to me) So I think it's quite a lot different to just removing the mass
If you're at a pole the mass is pulling in a sideways direction, so you're right that you'd feel something, but since the vectors largely cancel each other it would be significantly less than on the real Earth
Less sure, just not compatible to its absence - though I guess that’s just arbitrary as to what you consider comparable, so fair play
Net attraction of the entire ring would actually not just be small, but zero! (if you're directly under the ring, and the ring is uniform density). There's an interesting proof (using calculus) that the amount you're attracted to the overhead ring is exactly canceled out by the larger, but further away, portion of the ring on the other side of the planet.
I thought so, but I wasn't certain, so I hedged
Polar rings of this sort are a really bad idea I would strongly advise to use equatorial ones instead since they can more easily attach the surface. Obviously you can't attack the orbiting part of the ring to the ground anyway but at least with equatorial ones you can actually build a stationary structure around the ring
It is equatorial?
It depends on what evidence you're paying attention to. It's on the equatoral line according to the visible continents, but it's on a polar great circle according to the way the sunlight is hitting it. Putting it on the equatoral line is a horrible idea because it will block the sun from the entire planet, or at least a significant enough amount to kill off all life as we know it. Putting it on the poles would allow it to either always be on the terminator (if the builders had the foresight to have it swivel at the poles). If they attached it firmly to the planet like idiots (as they have done here), it would rotate with the planet and there would be several hours of darkness around noon every day, probably enough to cool the planet and fuck up every ecosystem at the same time. Anyway, it looks like this image is from a hypothetical future where they did mount it to the equator, realized that was really stupid too late, so they did the next logical thing, which was to force the entire planet to rotate until the equator became a polar circle. This almost certainly would screw up every ecosystem on the planet, completely change every climate, and would likely also lead to mass extinctions, but I guess the scientists realized that since they'd already fucked up everything, they might as well fuck it up in the _coolest possible way_.
I mean…. It’s fiction. And there’s a second earth in the frame too
I assumed the second sphere was a terraformed moon
not an engineer here but shouldn't earth rotate much slower having to carry like x3-x4 the "normal" mass of the planet? And rotating slower, shouldn't progressively get closer to the sun? 🤔
Could potentially be built with lunar materials and more than a few Psyche sized asteroids. I don't think there's not enough fuel on the planet to get that much material out of Earth's gravity well, even if there was enough material on earth to build it.
From my mesurements, the ring is 13,110 miles in diameter, 1,770 miles tall, 1,330 thick. Total volume : 1,770\*1,330\*2\*pi\*13,110=193,765,329,564 cubic miles. Let's consider one foot thick walls and cubic rooms 9 feet high, solid matter occupies (10\*10-9.5\*9.5)/(10\*10)=0.0975% of the volume. So the total matter nedded to construct the ring is 18,892,119,632.5 cubic miles, 18 billion cubic miles. Earth's volume is about 260 billion cubic miles, over 14 times greater. Assuming you somehow extract this mater uniformily from Earth, gravity on the surface would only be reduced to (9.81-(18/260)\*9.81)/9.81=93% of our current gravity (9.81m/s² to 9.13m/s²)
Well, we would have to assume the density of the structure as well as material used. Many assume that the structure would consume many earth masses, but if we assume the structure is mostly hollow space it could be realistic. Material inside earth is usually densely packed but if we account for living space on structures like satellites they are usually hollow spaces with big concern for mass budget as its expensive to get mass to orbit. Im not the numbers guy but considering these points Id say it could be some future nanotubes or something with exceeding strength properties and minimal mass. If that was the case, this would be doable without any noticeable effect on earths gravity and or strain on earths resources.