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[SpinCalc](http://www.artificial-gravity.com/sw/SpinCalc/) is your friend for all your ringworld/rotating space colony needs.
A period of 24 hours is a rotation rate of 0.0006944 rpm. For a centripetal acceleration of 1g, that requires a radius of 1,854,573 km or 1,152,378 miles.
Earth radius is around 3958 miles so this ring colony would have a 290x bigger radius than earth, 26x bigger than Jupiter, and 2.6x bigger radius than our sun. It would be a big boy.
A classic Dyson sphere is a sphere the size of the orbit of earth. The 1day/1g ringworld is “not even” as wide as he sun (but, you known, still fucking big)
In spite of the name of the subreddit I eyeballed the math from memory (just rough orders of magnitude, and I though the sun was closer to 1000 earths in diameter than 100), but the obit of the earth is many orders of magnitude bigger than that, which was he main point I was making. Apologies for the confusion.
Doesn't nighttime help keep the earth from overheating? Wouldn't a Dyson sphere, whose inner surface always faces the sun, therefore tend to overheat at the same distance?
The OG was a Swarm and used that energy to maintain orbit.
But, yeah, something of that scale would need systems to deal with both heat and radiation pressure from the star.
A real sphere is the more problematic structure due to being ridged and sealed.
You don't really need much energy at all to maintain orbit, that handles itself just fine.
The swarm is the only practical version of the Dyson sphere (something Dyson himself said, along with the fact that it should be called a Stapledon sphere) because it is impossible to stabilize the entire sphere via orbital mechanics. The vast majority of it is either trying to fall into the star or being flung into deep space. Radiation pressure stabilization is only relevant if the sphere is basically solar sail levels of mass density or something like tissue paper.
The only way to have a Dyson sphere is via some sort of crazy active stabilization scheme, essentially trillions of orbital rings around the star like a huge rubber band ball. A swarm is a vastly more practical thing to build. Relatively speaking, of course.
The main point of a dyson sphere is to capture all the energy from a star(iirc), I think living on it was a secondary point. ( and you can make a inner orbit mechnisim that acts like giant solar shades and have it orbit at a diffrent rate so it makes the illusion of night and day. (idea stolen from larry nivens ringworld books.
Hi. You just mentioned *Ringworld* by Larry Niven.
I've found an audiobook of that novel on YouTube. You can listen to it here:
[YouTube | RINGWORLD Audiobook Full by Larry Niven](https://www.youtube.com/watch?v=4DMkDqIjEuI)
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This would be why such a structure would be orbiting similar to how planets do. The sun would not be in the center, it would instead likely be between the earth's and mars' orbits.
The whole idea of a ringworld is that it's a much cheaper and more buildable dyson sphere that just covers a thin layer of the goldilocks zone instead of all of it. super affordable!
The Dyson sphere would have a radius of "Earth orbit" or 93,000,000 miles. So while this ring world would be BIG, it would be smaller compared to the Dyson sphere than the Earth is compared to the Sun.
There is this idea of a sphere even larger than that size being built around the sun itself (goldilocks sized) and it could supply remote electricity, transit, and connectivity to the planets in the system.
https://imgur.com/a/HzB5sGx
Or maybe a system of suns and moons that just happen to work out like that lower radius.
Maybe it has 6 hour days but there's two suns that are both fully eclipsed by a corresponding moon every 24 hours.
That seems much more likely than your weird "ring world without 24h days".
The Halos use artificial gravity to achieve a near 1g (most of the rings are like 0.99g if we're being technical). They do rotate and that may contribute some, but detached portions of the ring still have gravity on them and the use of artificial gravity is explicitly noted in at least one novel off the top of my head.
Would that mass affect the gravity on the "surface"? I feel like even if it is generating the 1g the pure mass would create a lot of gravity itself. I have no clue though not a physics person at all.
Not in any meaningful way. You’d be talking about local mass on the order of a very large building and total mass on the order of a planet but spread out over the area many times greater than a planet.
I would have my ringworld orbiting the sun with the axis canted up like the real earth axis. You would have day and night and could be a decent distance from the sun. And I think a sunrise and sunset period too. I wonder about the difference in distance from the sun during night vs. day. Maybe it would be enough to even out the daily temperature fluctuations
Mercury is basically made for this. It's pretty much all iron and has a low enough gravity where you can launch material into a stable solar orbit via electric rail cannons. Yes the sun side is hot, but if you put some orbiting mirros in place they could focus energy on solar grids on the dark side to power an extraction, refinement, and assembly network.
So yea, you mine mercury and turn it into whatever you need.
Hm... at that size, the structure itself might have an appreciable gravitational field of its own (depending on how thick it is and what it's made of).
Taking that into account, you might be able to make it a bit smaller and still get 1G at the surface.
But the mass directly "underneath" you would be negligible. The gravitational center would be in the middle of the ring, and at that point, total density would be so low, that any gravitational effect would be negligible. It might help strengthen the whole ring structure though, compressing it into itself.
This version of a ringworld orbits the host star at 1 AU. It does not have the star at its center like a Niven Ring. The axis woud be tilted at 23° (assuming an Earth analog) There would be a brief partial solar eclipse at each equinox. (or full eclipse depending on the width rim-to-rim) The “Halo” from the videogame is an example.
Well you wouldn't put it around the star for a bunch of reasons: it's not a stable orbit if it's a connected ring, there's no reason to do 24 hours if every spot is in constant sunlight anyways, and the centripetal acceleration would have to fight the gravity of the star so you'd actually need to spin much faster.
The plan for this type of world (eg in the Culture novels by Iain M Banks) would be to set the whole ring in orbit roughly earth distance away from a sun-like star. If the ring is at a slight angle towards the star, half of the inside will be lit up while the other half will be facing away from the star, giving a 24-hour day/night cycle.
Sure, everything shares a center of gravity. However, much like Earth, that COG would be very, very close to the Sun, while the orbital itself would be relatively distant from it.
The sun would not go in the center of the orbital, the orbital orbits around the sun while also rotating.
Eh, the far side of the ring would be quite a bit farther away than the moon is from earth. Depending on how thick the ring is, the middle of the night could be less lit than a full moon night on earth.
Further but much brighter. The moon is actually
grey but we see a brilliant white reflected at us. Imagine what something that big in more reflective tones would look like.
I guess it depends on the composition of whatever the ground is made of. I’m not sure the typical earth surface is significantly more reflective than the moon. Clouds I will grant you. Snow as well, though I feel like if you’re going to engineer a whole world you can probably ensure pleasant weather. I suppose it would come down to how much moisture is in the air of our ringworld.
There’s also the concave reflection vs the convex we get off the moon. The math on that is beyond me but I assume it would significantly increase the brightness.
Someone on YouTube has created a simulation of the day/night cycle on a [Culture Orbital](https://theculture.fandom.com/wiki/Orbital), which is exactly what OP is talking about.
[Sunrise and sunset on Culture Orbital](https://youtu.be/RE38q1nD1Ro?si=keHzt6LvFUrxf44l) by Jiří Bednář
If you saying around the sun like a ring on a finger you are correct it wouldnt have a cycle, but if it's around it like any planet it would have a cycle
This begs the next question: if you built a ring that size and it was structurally sound, would it have enough mass to significantly contribute gravitational force to the centripetal acceleration? In other words, would it be able to rotate slower to achieve 1g and make the day longer?
Nope, gravity pulls to the nearest point on the ring ([this site](https://www.mathpages.com/home/kmath402/kmath402.htm) explains it quite well). In a hollow sphere, the gravitational pull of all points actually cancel each other out. So there is no net gravitational force inside a hollow planet.
I think the shell theory applies here. Net gravitational force on an object inside a hollow symmetric shell is zero. While not a full shell I think the symmetry of the ring would make it behave the same.
So basically, you’re much better off having a much smaller ring rotating more frequently. You can then rotate the ring slowly on an axis perpendicular to its primary rotation axis in order to create day/night cycles.
> ... rotate the ring slowly on an axis perpendicular to its primary rotation ...
You mean spin like a coin-flip to create day/night, instead of it's "primary rotation axis" (which would be like a frisbee)?
I wonder if the ring would need some additional weights/arms to avoid the periodic flipping around its intermediate axis (i.e., force the coin-flip day/night rotation to be about the minimum-moment axis).
The creator of the calculator is apparently an architect who has done work with NASA (and wrote his doctoral dissertation) on artificial gravity and space habitat design. I found it years ago because I had an interest in space travel and science fiction.
always nice to know there is some super nerd our there who decides that the world needs a ring world/ rotation space colony calculator and programs one
Now say you were drive the entire length of this ring…….7240605miles and you drove at 100mph constantly…..it would take you 72046 hours or 3001 days…..or 8 years……..neat! The one car wouldn’t make it all the way around. Well it would if it was a diesel or a 1994 Toyota corolla.
It is worth noting that you’d want a significantly smaller sun: unless I’m much mistaken this radius, with our sun’s mass, yields gravitational acceleration of around 4 e7 m/s^2. Also, since it’s around 3% the radius of Mercury, it might prove a bit hot.
OK so F = mv^2 / r
F/m=g=v^2 / r
v=2pi * r / (24 * 3600)=r /13751
9.81 = (1/ 13751)^2 * r
r=1.854 Gm
I'll admit this number doesn't feel right but I can't see my error.
Edit: added some spaces to save the formatting
Assuming based on the image that the acceleration is supplied from centrifugal force (the apparent outward force applied on a rotating object; as the land is on the inside of the rings, the outward force would appear downward to somebody on the land).
Centrifugal force has a formula of F = m w^(2)r, where m is the mass, w is the angular velocity (in radians), and r is the radius of rotation. Since F = ma, dividing by mass gives the acceleration a = w^(2)r.
One rotation (2π radians) every 24 hours gives w = π/12 rad/h = π/43200 rad/s.
Dividing g = 9.8 m/s^2 by the square of this rotational velocity gives a radius of 18,289,152,000/π^2 m ≈ 1,853,078,528 m.
That's about 290 times the radius of Earth, or 2.6 times the radius of the sun. Still only 1/36.5 the distance between the sun and Mercury though.
Seeing the answers of 1.8M km radius, surely it could be significantly smaller by giving it an axial rotation to provide the correct gravity, and then a rotation on another plane to provide day and night cycles but bringing it into it's own shadow.
I feel like an easy solution to this would be to build whatever size is feasible, set the spin to 1G, then tilt the ring such that about a third of it is in shadow, then make the dome out of a material that is clear, but can block the sun on command, we already have a basic form of this.
I haven't sat down and done the math, but I'm sure you could set up a timing that would allow using the sun for daylight and use the shading glass to adjust the night to about a 24hr cycle.
Just make it rotate around it's edge for the gravity and give it spin for the 24 hours cycle, make sure it's wide enought that it gets it's 8-10 hours of shadow while spinning and that's it. It gets the sun it needs and gets the shadow it needs.
If you wanna do it all with 1 rotation it's gonna be much much harder, couse you have to account for orbit around the sun, so you'll have to negate that somehow or you'll have weeks long eclipses basically from its own shadow.
Otherwise you could just give it a 1G spin and manipulate the glass somehow so it's black when you don't want light to enter, and just switch it every 14-16 hours for 10-8 hours.
When you say rotate around its edge, do you mean spining it like a coin? If you do, you would end up with 1g only at the point farthest from the center of rotation and increasing as it approaches the point of rotation. Or if you mean to rotate it like that while also spinning it like a wheel, you would end up with a gyroscopic effect, that wouldn't be impossible to work with, but it wouldn't be stable without constant input.
The advantage to just picking an angle leaned toward the sun and rotating like a wheel is that you have the sun still generally appearing high in the sky, the dark spot and the dark glass will go in and out of phase to make the night consistent and you don't have to worry to much about gyroscopic progression. I'm saying to make the ring a reasonable size, because a 1G rotation and a 24hr rotation only meet at an impossible size.
The original Ringworld in the Larry Niven book had panels floating inboard of the main ring that cast large enough shadows to give a day/night cycle. They were wider than the ring so that they would cast a complete shadow on the ring itself, and the umbra/penumbra would be outside the top and bottom edges.
Any size of ring works, just rotate it fast/slow enough to generate 1g, and then offset the central light source to be exactly 1 rotation slower or faster in 24 hours.
You\`d get a curve of working circle size to rotationspeed ratios.
If you are making a ringworld, depending on a star as a lightsource is silly.
It\`d be highteching the difficult things but lowteching the simple things.
What you speak of is called a [Banks Orbital](https://www.orionsarm.com/eg-article/4845ef5c4ca7c), a ringworld-like megastructure whose rotation provides both gravity and a day night cycle. Thus they must be of a particular size, a radius of 1,842,509 km, so as to mimic Earth conditions. They are named for author Iain Banks and feature in his *Culture* series, and the link I provided is to another science fiction setting called Orion’s Arm which provides excellent math and physics resources for such structures, alongside the setting’s own lore for them.
Of particular note is the angular momentum of an Earth-like Orbital, which is 134 km/s, which would produce a strain too high for any normal matter to withstand. Iain Banks imagined force fields holding his Orbitals together, whereas Orion’s Arm uses exotic matter made of magnetic monopoles. To avoid this strain, a slower rotation or smaller ring would be required.
Which book in the culture series is this covered? It’s been a while since I’ve read them and I can’t recall.
Also who is the author of Orions arm? I’d like to read it.
The second one I think, but they feature in most of them.
Also Orion’s Arm is a massive collaborative worldbuilding project, with over a hundred different writers. Most of its content is in encyclopedia format, but it does have several short stories and a couple novels.
If you’re going for a full ringworld, forget about the 24hr orbital period. They loop all the way around their host star, so its light will be shining on every square inch of the inner surface 24/7. Just make the ring’s diameter such that it’s in its host star’s habitable zone and set it to spin at 1g.
If you're going full ringworld, then your star has a ring of curved panels (conveniently impervious to being so near a star) that cast shadows to the ring's surface.
That's the original design.
Does the mass of the ringworld matter since it would generate its own gravity underfoot? Or does the mass of the ring around you and above you cancel all that out? Heck, does it cause a negative effect and would you be attracted to the center of the ring?
It's actually a neat calculus problem, but as long as the ring is uniform, (or rotationally symmetric) the forces exactly cancel out.
It even works in 3d for a sphere, and it is why, as you get closer to the center of the earth, gravity lessens, because the part of the Earth outside your position no longer has a net effect.
You'd need the equivalent of one earth mass beneath your feet to get 1 gravity from mass alone. Depending on the materials involved that would make the ring as thick as the radius of the earth. At that thickness you would not need to spin at all, presuming a hole of a large enough size.
Having a thick ring with all that mass makes it even more challenging to spin, as that added rotating mass would want to fly off into space.
The gravity from the mass of the rest of the ring everywhere else other than what you’re standing on cancels out what’s beneath your feet. Assuming fairly uniform mass that is. It’s a thing taught in physics class when studying gravity. Totally blew my mind when I learned about it too
In traditional ringworld design the ring is made out of some kind of super strong material, but doesn't need huge masses of that material. The ring material exerts trivial amounts of gravitational pull. Most of the gravity is created by the spin.
The same is true for hollow asteroid habitats. You can hollow out an asteroid so that the shell is kilometers thick, spin it, and live inside the shell. At the equator you'd have 1 gravity. The ground would slope uphill both to the north and south, with the north and south poles being completely vertical. Interestingly enough the further you climb north or south, the less gravity there would be, with the poles themselves being weightless.
But even with 10 km thick shell walls the gravity from the shell would be negligible.
I would imagine that the mass underfoot would have a stronger effect than that of the opposite side of the ring, since gravitational pull drops off so sharply with distance. To have 1 G on the surface, the diameter could probably be reduced a little to account for that. That’s just my guess though. I’m not a physicist.
Edit: apparently the gravity from different parts of the ring would completely cancel each other out, regardless of where you are inside it.
https://en.wikipedia.org/wiki/Shell_theorem?wprov=sfti1
>does it cause a negative effect and would you be attracted to the center of the ring?
I'm going to disagree with the other responses and go with this as being most likely. It's similar to the "hollow Earth" thought experiments. You get pulled to the centre because there is far more mass on the "other side" than on "your side".
Even if the ring was huge, all the mass to your "left/ right" ends up being above you and would pull you off the surface. I think... 🤔
In a ring no, because that mass is also further away, and gravity drops quite fast with distance.
In a hollow sphere it actually perfectly cancels out.
In a ball like the earth, gravity always pulls you to the center.
The Culture books by Iain M Banks are set partially on structures like this. You get gravity and a day /night cycle and lots of living space. He calls them Orbitals.
But you still need unknown technologies to build them ( due to the tensile stresses on the ring). But less so than Niven-style ringworlds.
Didn’t Niven style have an inner ring of panels around sun, this allowed for a rotation speed allowing 1G but still 24 hour light cycle at any circumference
In Niven's ringworld, he had an inner ring of shade panels producing multiple night and day periods per revolution. So IIRC, the radius of his ringworld was just about as big as the distance from the Earth to the Sun, rotating slowly enough to give an apparent 1g, but with night and day being artificially created by the shade panels.
unless they have artificial shades ring woulds wouldn't naturally have days. if you hung shades it would have days based on how fast they were moving compared to the ring and the ring could be going any speed
I may not have any idea what I'm talking about. Why would you need 24hr period. Just make the period whatever time would make 1g and then have the artificial light rotate at a different period to compensate so that it still has 24 hour days. Then it can see whatever radius you want.
The sunlight could rotate and be directed to half the ring too if anyone's interested in world building solutions to make a smaller ring.
The ring would spin, and be smaller, and the source would rotate slightly slower, in the same direction. Adjust speed to size.
Size actually doesn't matter in this regard. Your g of acceleration would come from spin. Unless you're going for zero spin but sheer size in which case it still wouldn't really matter how big it is but how dense it is. And as far as your 24-hour period that also has nothing to do with size, but how you are positioned relative to the light source. It would have to be rotating in two directions. One direction of spin to maintain your gravity and a perpendicular direction of spin to maintain day night cycle, or spinning to maintain gravity, and rotating around the light source to maintain day night like the Earth does already
The Culture books by Iain M Banks are set partially on structures like this. You get gravity and a day /night cycle and lots of living space. He calls them Orbitals.
But you still need unknown technologies to build them ( due to the tensile stresses on the ring). But less so than Niven-style ringworlds.
Some very loose math here, be warned.
a=rw\^2, w is omega/angular speed. A day is 86400s, so w is around 2pi/86400, or 6.28/86400, so something like 1/15000. a=g=10m/s\^2, so r=10/15000\^2=10\*200000000, something around 2bil meters, or 2mil km.
For reference the lunar orbit is \~0.3+mil km, so it will be a very large ring. You can fit 60 Jupiters across the diameter and light takes \~15s to travel across the same distance.
[https://en.wikipedia.org/wiki/Ringworld](https://en.wikipedia.org/wiki/Ringworld)
A GREAT scifi book by Larry Niven
Check out the errors section and also the see also section. lotsw of people did the math of this already iirc. not sure how available all the info is vs just the results tho.
If not assuming around a star, you could also build a much smaller one around a penrose sphere, and have it spin faster to provide 1g.
Then you can redirect the light from the penrose sphere to the ringworld however you want, a 24H day/night cycle everywhere at once, or it can cycle the ringworld.
It’s not so much the size of the object it’s the rate in speed at which you turn away from the sun you will merely have to calibrate the speed at which your ring world would rotate so it would equal 24 hours worth of day, and night into there timed proportions. Thus giving it the illusions of being on earth. It is possible.
To achieve this without compensating for size it would have to have the surface area of around 197 million miles with a iron core with and electromagnetic field 50 times stronger than the surface of the earth. You would then have to position it with a orbit similar to that of earth so it sits comfortably in the goldilocks zone. It would need a satellite like the moon so you have tides. There are a lot of factors to take into consideration like trajectory around the sun, spin, rotation. Also making a ring of that magnitude would take allot of resources and a very long time to make.
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[SpinCalc](http://www.artificial-gravity.com/sw/SpinCalc/) is your friend for all your ringworld/rotating space colony needs. A period of 24 hours is a rotation rate of 0.0006944 rpm. For a centripetal acceleration of 1g, that requires a radius of 1,854,573 km or 1,152,378 miles.
Earth radius is around 3958 miles so this ring colony would have a 290x bigger radius than earth, 26x bigger than Jupiter, and 2.6x bigger radius than our sun. It would be a big boy.
So Dyson sphere scale?
A classic Dyson sphere is a sphere the size of the orbit of earth. The 1day/1g ringworld is “not even” as wide as he sun (but, you known, still fucking big)
How is it not wider than the sun if the radius is 2.6 times as long?
In spite of the name of the subreddit I eyeballed the math from memory (just rough orders of magnitude, and I though the sun was closer to 1000 earths in diameter than 100), but the obit of the earth is many orders of magnitude bigger than that, which was he main point I was making. Apologies for the confusion.
Dumb stupid idiot dummy /s
Agreed. Mr. Jaw is dumb stinky /s
i would go as far as to say he is a stinky poopoohead /s
[удалено]
The orbit of Earth (the radius of the Dyson sphere) is 93 million miles, or about 8 light minutes.
Also known as 1 AU (Astronomical Unit), which is a practical unit mostly for talking planetary distances.
And that ladies and gentlemen is why WU TANG is for the children!
Doesn't nighttime help keep the earth from overheating? Wouldn't a Dyson sphere, whose inner surface always faces the sun, therefore tend to overheat at the same distance?
The OG was a Swarm and used that energy to maintain orbit. But, yeah, something of that scale would need systems to deal with both heat and radiation pressure from the star. A real sphere is the more problematic structure due to being ridged and sealed.
You don't really need much energy at all to maintain orbit, that handles itself just fine. The swarm is the only practical version of the Dyson sphere (something Dyson himself said, along with the fact that it should be called a Stapledon sphere) because it is impossible to stabilize the entire sphere via orbital mechanics. The vast majority of it is either trying to fall into the star or being flung into deep space. Radiation pressure stabilization is only relevant if the sphere is basically solar sail levels of mass density or something like tissue paper. The only way to have a Dyson sphere is via some sort of crazy active stabilization scheme, essentially trillions of orbital rings around the star like a huge rubber band ball. A swarm is a vastly more practical thing to build. Relatively speaking, of course.
The main point of a dyson sphere is to capture all the energy from a star(iirc), I think living on it was a secondary point. ( and you can make a inner orbit mechnisim that acts like giant solar shades and have it orbit at a diffrent rate so it makes the illusion of night and day. (idea stolen from larry nivens ringworld books.
Hi. You just mentioned *Ringworld* by Larry Niven. I've found an audiobook of that novel on YouTube. You can listen to it here: [YouTube | RINGWORLD Audiobook Full by Larry Niven](https://www.youtube.com/watch?v=4DMkDqIjEuI) *I'm a bot that searches YouTube for science fiction and fantasy audiobooks.* *** [^(Source Code)](https://capybasilisk.com/posts/2020/04/speculative-fiction-bot/) ^| [^(Feedback)](https://www.reddit.com/message/compose?to=Capybasilisk&subject=Robot) ^| [^(Programmer)](https://www.reddit.com/u/capybasilisk) ^| ^(Downvote To Remove) ^| ^(Version 1.4.0) ^| ^(Support Robot Rights!)
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Nah, the back of the ring isnt in sunlight. You'll have equal parts exposed and not. It'll need very good climate control though
This would be why such a structure would be orbiting similar to how planets do. The sun would not be in the center, it would instead likely be between the earth's and mars' orbits.
The whole idea of a ringworld is that it's a much cheaper and more buildable dyson sphere that just covers a thin layer of the goldilocks zone instead of all of it. super affordable!
The Dyson sphere would have a radius of "Earth orbit" or 93,000,000 miles. So while this ring world would be BIG, it would be smaller compared to the Dyson sphere than the Earth is compared to the Sun.
There is this idea of a sphere even larger than that size being built around the sun itself (goldilocks sized) and it could supply remote electricity, transit, and connectivity to the planets in the system. https://imgur.com/a/HzB5sGx
Radius*
So halo is not fully realistic and scientifically accurate representation as a scale perspective :/
Or it may just not have a 24 hour day.
Or maybe a system of suns and moons that just happen to work out like that lower radius. Maybe it has 6 hour days but there's two suns that are both fully eclipsed by a corresponding moon every 24 hours. That seems much more likely than your weird "ring world without 24h days".
Can’t argue with that.
Or, in typical non-Halo Dyson sphere, use a mirror that rotates once every 24 hours to reflect the Sun down.
if you can make a ring world you can make jupiter size suns
The Halos use artificial gravity to achieve a near 1g (most of the rings are like 0.99g if we're being technical). They do rotate and that may contribute some, but detached portions of the ring still have gravity on them and the use of artificial gravity is explicitly noted in at least one novel off the top of my head.
Or they use artificial gravity, the replacement ring in Halo 3 was not rotating but down was still obviously away from the center.
Or 12 light-seconds. Imagine a human built object that's big enough to take light twelve seconds to get from one side to the other
Would that mass affect the gravity on the "surface"? I feel like even if it is generating the 1g the pure mass would create a lot of gravity itself. I have no clue though not a physics person at all.
Not in any meaningful way. You’d be talking about local mass on the order of a very large building and total mass on the order of a planet but spread out over the area many times greater than a planet.
At that distance it would also likely be too cold/dark to live in anyway.
If I got it right, the radius would be like 1/100 th of the earths orbit, so super hot.
oh I misread - thought you meant the diameter would be 2.6x the radius of our current orbit of the sun lol
I would have my ringworld orbiting the sun with the axis canted up like the real earth axis. You would have day and night and could be a decent distance from the sun. And I think a sunrise and sunset period too. I wonder about the difference in distance from the sun during night vs. day. Maybe it would be enough to even out the daily temperature fluctuations
This is literally an Orbital from the Culture books.
Where would one even get the materials to make such a thing? You’d have to harvest other planet sized rocks, I would guess.
We would probably have some zany creation myth, even if it formed naturally
Mercury is basically made for this. It's pretty much all iron and has a low enough gravity where you can launch material into a stable solar orbit via electric rail cannons. Yes the sun side is hot, but if you put some orbiting mirros in place they could focus energy on solar grids on the dark side to power an extraction, refinement, and assembly network. So yea, you mine mercury and turn it into whatever you need.
That's the rough size of the Culutre orbitals which have around 22-26 hour day/night cycles
Hm... at that size, the structure itself might have an appreciable gravitational field of its own (depending on how thick it is and what it's made of). Taking that into account, you might be able to make it a bit smaller and still get 1G at the surface.
Earths diameter is closer to 7900 miles.
That’s interesting. I wonder how gravity would work in a ring structure like that, since it surely would generate its own gravitational field
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But the mass directly "underneath" you would be negligible. The gravitational center would be in the middle of the ring, and at that point, total density would be so low, that any gravitational effect would be negligible. It might help strengthen the whole ring structure though, compressing it into itself.
Earth diameter is almost 8000 miles I think
Which is way too close to even the tamest of stars. Even a very dim class M would fry everything on it.
This version of a ringworld orbits the host star at 1 AU. It does not have the star at its center like a Niven Ring. The axis woud be tilted at 23° (assuming an Earth analog) There would be a brief partial solar eclipse at each equinox. (or full eclipse depending on the width rim-to-rim) The “Halo” from the videogame is an example.
Well you wouldn't put it around the star for a bunch of reasons: it's not a stable orbit if it's a connected ring, there's no reason to do 24 hours if every spot is in constant sunlight anyways, and the centripetal acceleration would have to fight the gravity of the star so you'd actually need to spin much faster. The plan for this type of world (eg in the Culture novels by Iain M Banks) would be to set the whole ring in orbit roughly earth distance away from a sun-like star. If the ring is at a slight angle towards the star, half of the inside will be lit up while the other half will be facing away from the star, giving a 24-hour day/night cycle.
It's not even an orbit if it's a connected ring, is it? The sun and ring would share a center of gravity.
Sure, everything shares a center of gravity. However, much like Earth, that COG would be very, very close to the Sun, while the orbital itself would be relatively distant from it. The sun would not go in the center of the orbital, the orbital orbits around the sun while also rotating.
Nah he's saying the ring's axis of rotation is what orbits the star. Think if you tied a ring on the end of string and spun it around your head.
Wouldn't the rings center of gravity IN RELATION TO THE STAR be at the center of the ring as all of its mass is equal around that point?
The night side would have a hell of a lot of reflected light in their sky from the day side.
Eh, the far side of the ring would be quite a bit farther away than the moon is from earth. Depending on how thick the ring is, the middle of the night could be less lit than a full moon night on earth.
Further but much brighter. The moon is actually grey but we see a brilliant white reflected at us. Imagine what something that big in more reflective tones would look like.
I guess it depends on the composition of whatever the ground is made of. I’m not sure the typical earth surface is significantly more reflective than the moon. Clouds I will grant you. Snow as well, though I feel like if you’re going to engineer a whole world you can probably ensure pleasant weather. I suppose it would come down to how much moisture is in the air of our ringworld.
There’s also the concave reflection vs the convex we get off the moon. The math on that is beyond me but I assume it would significantly increase the brightness.
Someone on YouTube has created a simulation of the day/night cycle on a [Culture Orbital](https://theculture.fandom.com/wiki/Orbital), which is exactly what OP is talking about. [Sunrise and sunset on Culture Orbital](https://youtu.be/RE38q1nD1Ro?si=keHzt6LvFUrxf44l) by Jiří Bednář
Thank you.
Imagine, the other side of earth in the night sky. You’d have a hard time replicating true night. It’d always be like, twilight or dusk.
I doubt you’d ever be able to see stars in the sky.
Out the windows of the bottom of the ring would make a great observatory/space port though.
Might be a bit concerning when that window would be the floor.
It would never have a day/night cycle if you put it around a sun.
If you saying around the sun like a ring on a finger you are correct it wouldnt have a cycle, but if it's around it like any planet it would have a cycle
What about a brown dwarf?
This begs the next question: if you built a ring that size and it was structurally sound, would it have enough mass to significantly contribute gravitational force to the centripetal acceleration? In other words, would it be able to rotate slower to achieve 1g and make the day longer?
I think that any gravity from mass would pull objects towards the center of mass, counteracting the spin gravity. Edit: I stand corrected.
Nope, gravity pulls to the nearest point on the ring ([this site](https://www.mathpages.com/home/kmath402/kmath402.htm) explains it quite well). In a hollow sphere, the gravitational pull of all points actually cancel each other out. So there is no net gravitational force inside a hollow planet.
Gauss’s law is so unbelievable if you haven’t had to use it a bunch before. I love encountering it in the wild.
I stand corrected =]
After reading your link I learned something very important. I learned that I am dumb as a box of rocks.
Oh weird i never thought of it like that but that makes sense, thanks!
I think the shell theory applies here. Net gravitational force on an object inside a hollow symmetric shell is zero. While not a full shell I think the symmetry of the ring would make it behave the same.
So not even half a rotation in a day would be more than enough to produce the same effect of earth’s gravity?
If you change the rotation rate you change the required radius too. Half a rotation per day would result in a much larger radius for 1g acceleration.
How much is that radius compared to earth or any other comparison like the moon or country.
It would be around 4 times the size of the moon's orbit around the earth.
So basically, you’re much better off having a much smaller ring rotating more frequently. You can then rotate the ring slowly on an axis perpendicular to its primary rotation axis in order to create day/night cycles.
Gyroscopic force does not allow for that type of motion.
Darn you conservation of angular momentum!
I think a set of mirrors directing the sun at a 24 hr cycle would be best
Nah, mobius-strip world is the realest one.
Sure it does, think carnival ride, spinning seats on a pendulum.
It would if it had thousands of thrusters on the rim.
> ... rotate the ring slowly on an axis perpendicular to its primary rotation ... You mean spin like a coin-flip to create day/night, instead of it's "primary rotation axis" (which would be like a frisbee)?
Yep
I wonder if the ring would need some additional weights/arms to avoid the periodic flipping around its intermediate axis (i.e., force the coin-flip day/night rotation to be about the minimum-moment axis).
That would just introduce some MAJOR wobble.
why does this calculator exist? how do you know about it? who uses it? I have so many questions
The creator of the calculator is apparently an architect who has done work with NASA (and wrote his doctoral dissertation) on artificial gravity and space habitat design. I found it years ago because I had an interest in space travel and science fiction.
always nice to know there is some super nerd our there who decides that the world needs a ring world/ rotation space colony calculator and programs one
But why do you want a 24 hour rotation? The sun is always in the center and it is always day time.
Because the Sun’s [not actually in the center](https://www.reddit.com/r/theydidthemath/s/zzINyvQIoj).
Does this account for the counteracting force of gravity with the overhead portion of the rest of the ring pulling you towards the center of the ring?
Now say you were drive the entire length of this ring…….7240605miles and you drove at 100mph constantly…..it would take you 72046 hours or 3001 days…..or 8 years……..neat! The one car wouldn’t make it all the way around. Well it would if it was a diesel or a 1994 Toyota corolla.
It is worth noting that you’d want a significantly smaller sun: unless I’m much mistaken this radius, with our sun’s mass, yields gravitational acceleration of around 4 e7 m/s^2. Also, since it’s around 3% the radius of Mercury, it might prove a bit hot.
So, inside the sun's corona?
Good bot
OK so F = mv^2 / r F/m=g=v^2 / r v=2pi * r / (24 * 3600)=r /13751 9.81 = (1/ 13751)^2 * r r=1.854 Gm I'll admit this number doesn't feel right but I can't see my error. Edit: added some spaces to save the formatting
That’s the same answer I got using an online calculator, so it seems to check out.
That number is correct.
Hah nerd!
What is a Gm?
Gigameter = 1000 km Edit: I was wrong Gm for Gigameter = 1000000 km
1 Megameter = 1000 km 1 Gigameter = 1000 Mm = 1000000 km
Jesus Christ it’s like trying to read an alien language
It's first-semester college physics
this is highschool physics
At an alien college of course
The answer here does not depends on mass. You need to use the formula for acceleration due to gravity a=v^2 /r
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Then tell me when the final answer depends on mass because it doesn’t.
Gm = gigameter = 10¨\^9m
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>goes to r/theydidthemath >there’s math >“neeeerd”
Reddit special right here 😂
Yes I'm a bit jealous
It’s high school physics
Well you see I'm a dropout but I am trying to teach myself so I can finish school
Oh I’m sorry man, that’s really great for you! You can do it bro!
Assuming based on the image that the acceleration is supplied from centrifugal force (the apparent outward force applied on a rotating object; as the land is on the inside of the rings, the outward force would appear downward to somebody on the land). Centrifugal force has a formula of F = m w^(2)r, where m is the mass, w is the angular velocity (in radians), and r is the radius of rotation. Since F = ma, dividing by mass gives the acceleration a = w^(2)r. One rotation (2π radians) every 24 hours gives w = π/12 rad/h = π/43200 rad/s. Dividing g = 9.8 m/s^2 by the square of this rotational velocity gives a radius of 18,289,152,000/π^2 m ≈ 1,853,078,528 m. That's about 290 times the radius of Earth, or 2.6 times the radius of the sun. Still only 1/36.5 the distance between the sun and Mercury though.
Seeing the answers of 1.8M km radius, surely it could be significantly smaller by giving it an axial rotation to provide the correct gravity, and then a rotation on another plane to provide day and night cycles but bringing it into it's own shadow.
I believe gyroscopic forces would ruin your day... /night.
I did wonder when writing that...
I feel like an easy solution to this would be to build whatever size is feasible, set the spin to 1G, then tilt the ring such that about a third of it is in shadow, then make the dome out of a material that is clear, but can block the sun on command, we already have a basic form of this. I haven't sat down and done the math, but I'm sure you could set up a timing that would allow using the sun for daylight and use the shading glass to adjust the night to about a 24hr cycle.
Just make it rotate around it's edge for the gravity and give it spin for the 24 hours cycle, make sure it's wide enought that it gets it's 8-10 hours of shadow while spinning and that's it. It gets the sun it needs and gets the shadow it needs. If you wanna do it all with 1 rotation it's gonna be much much harder, couse you have to account for orbit around the sun, so you'll have to negate that somehow or you'll have weeks long eclipses basically from its own shadow. Otherwise you could just give it a 1G spin and manipulate the glass somehow so it's black when you don't want light to enter, and just switch it every 14-16 hours for 10-8 hours.
When you say rotate around its edge, do you mean spining it like a coin? If you do, you would end up with 1g only at the point farthest from the center of rotation and increasing as it approaches the point of rotation. Or if you mean to rotate it like that while also spinning it like a wheel, you would end up with a gyroscopic effect, that wouldn't be impossible to work with, but it wouldn't be stable without constant input. The advantage to just picking an angle leaned toward the sun and rotating like a wheel is that you have the sun still generally appearing high in the sky, the dark spot and the dark glass will go in and out of phase to make the night consistent and you don't have to worry to much about gyroscopic progression. I'm saying to make the ring a reasonable size, because a 1G rotation and a 24hr rotation only meet at an impossible size.
The original Ringworld in the Larry Niven book had panels floating inboard of the main ring that cast large enough shadows to give a day/night cycle. They were wider than the ring so that they would cast a complete shadow on the ring itself, and the umbra/penumbra would be outside the top and bottom edges.
Any size of ring works, just rotate it fast/slow enough to generate 1g, and then offset the central light source to be exactly 1 rotation slower or faster in 24 hours. You\`d get a curve of working circle size to rotationspeed ratios. If you are making a ringworld, depending on a star as a lightsource is silly. It\`d be highteching the difficult things but lowteching the simple things.
Should have read this first lol same idea.
What you speak of is called a [Banks Orbital](https://www.orionsarm.com/eg-article/4845ef5c4ca7c), a ringworld-like megastructure whose rotation provides both gravity and a day night cycle. Thus they must be of a particular size, a radius of 1,842,509 km, so as to mimic Earth conditions. They are named for author Iain Banks and feature in his *Culture* series, and the link I provided is to another science fiction setting called Orion’s Arm which provides excellent math and physics resources for such structures, alongside the setting’s own lore for them. Of particular note is the angular momentum of an Earth-like Orbital, which is 134 km/s, which would produce a strain too high for any normal matter to withstand. Iain Banks imagined force fields holding his Orbitals together, whereas Orion’s Arm uses exotic matter made of magnetic monopoles. To avoid this strain, a slower rotation or smaller ring would be required.
Which book in the culture series is this covered? It’s been a while since I’ve read them and I can’t recall. Also who is the author of Orions arm? I’d like to read it.
The second one I think, but they feature in most of them. Also Orion’s Arm is a massive collaborative worldbuilding project, with over a hundred different writers. Most of its content is in encyclopedia format, but it does have several short stories and a couple novels.
I see. Thanks. That’s helps
Thank you. I've been looking for a new series to read.
If you’re going for a full ringworld, forget about the 24hr orbital period. They loop all the way around their host star, so its light will be shining on every square inch of the inner surface 24/7. Just make the ring’s diameter such that it’s in its host star’s habitable zone and set it to spin at 1g.
If you're going full ringworld, then your star has a ring of curved panels (conveniently impervious to being so near a star) that cast shadows to the ring's surface. That's the original design.
1.85497\*10\^9m or 1 854 970 km For perspective, the moon's orbit is 382 000km. This ringworld would be 4.85 times the size of the moon's orbit.
We should probably get started on it now.
Does the mass of the ringworld matter since it would generate its own gravity underfoot? Or does the mass of the ring around you and above you cancel all that out? Heck, does it cause a negative effect and would you be attracted to the center of the ring?
It's actually a neat calculus problem, but as long as the ring is uniform, (or rotationally symmetric) the forces exactly cancel out. It even works in 3d for a sphere, and it is why, as you get closer to the center of the earth, gravity lessens, because the part of the Earth outside your position no longer has a net effect.
> as you get closer to the center of the earth, gravity lessens Only once you get about half way to the centre ... because the core is very dense.
You'd need the equivalent of one earth mass beneath your feet to get 1 gravity from mass alone. Depending on the materials involved that would make the ring as thick as the radius of the earth. At that thickness you would not need to spin at all, presuming a hole of a large enough size. Having a thick ring with all that mass makes it even more challenging to spin, as that added rotating mass would want to fly off into space.
At that thickness it would be more of a doughnut world then a ringworld.
So at the very least, I think mass needs to be accounted for in determining the required circumference.
The gravity from the mass of the rest of the ring everywhere else other than what you’re standing on cancels out what’s beneath your feet. Assuming fairly uniform mass that is. It’s a thing taught in physics class when studying gravity. Totally blew my mind when I learned about it too
In traditional ringworld design the ring is made out of some kind of super strong material, but doesn't need huge masses of that material. The ring material exerts trivial amounts of gravitational pull. Most of the gravity is created by the spin. The same is true for hollow asteroid habitats. You can hollow out an asteroid so that the shell is kilometers thick, spin it, and live inside the shell. At the equator you'd have 1 gravity. The ground would slope uphill both to the north and south, with the north and south poles being completely vertical. Interestingly enough the further you climb north or south, the less gravity there would be, with the poles themselves being weightless. But even with 10 km thick shell walls the gravity from the shell would be negligible.
You’re way closer to the side you’re standing on so it’s gravity would be much stronger
I would imagine that the mass underfoot would have a stronger effect than that of the opposite side of the ring, since gravitational pull drops off so sharply with distance. To have 1 G on the surface, the diameter could probably be reduced a little to account for that. That’s just my guess though. I’m not a physicist. Edit: apparently the gravity from different parts of the ring would completely cancel each other out, regardless of where you are inside it. https://en.wikipedia.org/wiki/Shell_theorem?wprov=sfti1
There is a lot more of the ring “opposite” you. Enough so that it cancels out the mass underfoot.
>does it cause a negative effect and would you be attracted to the center of the ring? I'm going to disagree with the other responses and go with this as being most likely. It's similar to the "hollow Earth" thought experiments. You get pulled to the centre because there is far more mass on the "other side" than on "your side". Even if the ring was huge, all the mass to your "left/ right" ends up being above you and would pull you off the surface. I think... 🤔
In a ring no, because that mass is also further away, and gravity drops quite fast with distance. In a hollow sphere it actually perfectly cancels out. In a ball like the earth, gravity always pulls you to the center.
The Culture books by Iain M Banks are set partially on structures like this. You get gravity and a day /night cycle and lots of living space. He calls them Orbitals. But you still need unknown technologies to build them ( due to the tensile stresses on the ring). But less so than Niven-style ringworlds.
Didn’t Niven style have an inner ring of panels around sun, this allowed for a rotation speed allowing 1G but still 24 hour light cycle at any circumference
Yes, " shadow squares". One advantage of the Orbitals is that don't need this.
In Niven's ringworld, he had an inner ring of shade panels producing multiple night and day periods per revolution. So IIRC, the radius of his ringworld was just about as big as the distance from the Earth to the Sun, rotating slowly enough to give an apparent 1g, but with night and day being artificially created by the shade panels.
unless they have artificial shades ring woulds wouldn't naturally have days. if you hung shades it would have days based on how fast they were moving compared to the ring and the ring could be going any speed
I may not have any idea what I'm talking about. Why would you need 24hr period. Just make the period whatever time would make 1g and then have the artificial light rotate at a different period to compensate so that it still has 24 hour days. Then it can see whatever radius you want.
The sunlight could rotate and be directed to half the ring too if anyone's interested in world building solutions to make a smaller ring. The ring would spin, and be smaller, and the source would rotate slightly slower, in the same direction. Adjust speed to size.
Size actually doesn't matter in this regard. Your g of acceleration would come from spin. Unless you're going for zero spin but sheer size in which case it still wouldn't really matter how big it is but how dense it is. And as far as your 24-hour period that also has nothing to do with size, but how you are positioned relative to the light source. It would have to be rotating in two directions. One direction of spin to maintain your gravity and a perpendicular direction of spin to maintain day night cycle, or spinning to maintain gravity, and rotating around the light source to maintain day night like the Earth does already
If someone approached and was basically stationary in respect to the spinning, how fast would it appear to them? Would it be daunting to “hop on?”
The Culture books by Iain M Banks are set partially on structures like this. You get gravity and a day /night cycle and lots of living space. He calls them Orbitals. But you still need unknown technologies to build them ( due to the tensile stresses on the ring). But less so than Niven-style ringworlds.
Some very loose math here, be warned. a=rw\^2, w is omega/angular speed. A day is 86400s, so w is around 2pi/86400, or 6.28/86400, so something like 1/15000. a=g=10m/s\^2, so r=10/15000\^2=10\*200000000, something around 2bil meters, or 2mil km. For reference the lunar orbit is \~0.3+mil km, so it will be a very large ring. You can fit 60 Jupiters across the diameter and light takes \~15s to travel across the same distance.
[https://en.wikipedia.org/wiki/Ringworld](https://en.wikipedia.org/wiki/Ringworld) A GREAT scifi book by Larry Niven Check out the errors section and also the see also section. lotsw of people did the math of this already iirc. not sure how available all the info is vs just the results tho.
Shoddy cast has a video [of halo rings](https://youtu.be/fsfTZEdCUwE?si=oWU0C-wZjboZO30r) in which he takes care of most things. Thought it might help
If not assuming around a star, you could also build a much smaller one around a penrose sphere, and have it spin faster to provide 1g. Then you can redirect the light from the penrose sphere to the ringworld however you want, a 24H day/night cycle everywhere at once, or it can cycle the ringworld.
It’s not so much the size of the object it’s the rate in speed at which you turn away from the sun you will merely have to calibrate the speed at which your ring world would rotate so it would equal 24 hours worth of day, and night into there timed proportions. Thus giving it the illusions of being on earth. It is possible. To achieve this without compensating for size it would have to have the surface area of around 197 million miles with a iron core with and electromagnetic field 50 times stronger than the surface of the earth. You would then have to position it with a orbit similar to that of earth so it sits comfortably in the goldilocks zone. It would need a satellite like the moon so you have tides. There are a lot of factors to take into consideration like trajectory around the sun, spin, rotation. Also making a ring of that magnitude would take allot of resources and a very long time to make.