Weather and climate on a "realistic" discworld

[Altair_the_Vexed]

Let's assume we have a disc-shaped world, that somehow has what seems like normal gravity acting toward one surface of the disc (we'll call the the ground, and the other surface is the "underneath"), and has a day-night cycle of close enough to 24 hours, and mean temperatures similar to Earth - i.e. we have a global mean of about 15C.
Let's assume it somehow has continents of rocky stuff, oceans of water, and an atmosphere thick enough for weather <EDIT> that's retained on the disc somehow.

Let's also assume that other than these factors, our usual understanding of physics is working entirely as normal for this discworld. (If we need to express why this is the case, let's say the gods did it - then they ran out of power to do anything else supernatural. This left us with an improbable world, trying to exist in an otherwise normal universe.)

With these parameters, what the heck would the weather be like? How would the climate divide up over the disc, if at all? How would we get seasons?

How similar to our familiar Earth could such a world be, and what would its star system need to be like to make it so?
How different from Earth could it be, if we made different assumptions?

[Khedrac]

One problem is that with just gravity acting "down" then the rotation of the disc would start the air moving with the spin (friction etc.) which then would follow Newton's laws of motion and fly off the edge of the disk - I think fairly quickly (certainly by geological standards).

Once the atmosphere goes, the hydrosphere follows - anything that doesn't freeze first boils off into space. Most of that does freeze probably sublimes off slowly afterwards.

You might have small pockets of air/water in deep canyons where the rim-side wall is steep enough that it doesn't just flow over it, but any atmosphere will be very diffuse and probably safe to ignore.

Building a wall around the edge (similar to Larry Niven's "Ringworld") doesn't work very well - you would end up with an ocean at the base of it with a thin atmosphere above it that reaches up to the top of the wall and then slants diagonaly down to the disk a little way in from it (distance depends on height of wall and rate of spin). The centre of the disk will be airless and dead.

[factotum]

Even ignoring Khedrac's excellent point, weather would be nowhere near as strong, IMHO. The main reason for weather on Earth is due to differential heating of the surface causing convection currents in the atmosphere--that effect is going to be severely diminished on a disc, because every part of the surface is going to get pretty much the same incident sunlight due to the atmosphere being a consistent thickness over the whole thing. Therefore, the only thing that could cause differential heating is different ground surfaces, which is nowhere near as strong an effect.

[DavidSh]

Could you explain the day-night cycle? I see Khedrac is assuming that the axis of rotation is perpendicular to the plane of the disc, which would not generate a day-night cycle. You could still have a day-night cycle, but the duration of the cycle would be the period of orbit around the sun. (Subject to precession.)

Alternatively, although I think this would require divine intervention to keep it stable, you could generate a shorter day-night cycle by having the axis of rotation in the plane of the disc.

[Altair_the_Vexed]

One problem is that with just gravity acting "down" then the rotation of the disc would start the air moving with the spin (friction etc.) which then would follow Newton's laws of motion and fly off the edge of the disk - I think fairly quickly (certainly by geological standards).

Once the atmosphere goes, the hydrosphere follows - anything that doesn't freeze first boils off into space. Most of that does freeze probably sublimes off slowly afterwards.

You might have small pockets of air/water in deep canyons where the rim-side wall is steep enough that it doesn't just flow over it, but any atmosphere will be very diffuse and probably safe to ignore.

Building a wall around the edge (similar to Larry Niven's "Ringworld") doesn't work very well - you would end up with an ocean at the base of it with a thin atmosphere above it that reaches up to the top of the wall and then slants diagonaly down to the disk a little way in from it (distance depends on height of wall and rate of spin). The centre of the disk will be airless and dead.

Good point - but that wasn't really my intent for the puzzle / thought experiment / post.
I asked that we assume that the atmosphere is thick enough - to me, "is" implies that one of our god-sourced forces is keeping it that way. I suppose I should update my post to clarify that.

Secondly, related to your point: Why is the disc spinning? Where did this angular momentum come from? I assumed that the spin of planets is due to their formation from an accretion disc, whereas this discworld was been created out of nothing, or assembled in situ... So it seems to me that unless you made it spin, it would be stationary - which I know would have its own implications for climate and weather.
Is there something else that would make it spin?

[Altair_the_Vexed]

Could you explain the day-night cycle? I see Khedrac is assuming that the axis of rotation is perpendicular to the plane of the disc, which would not generate a day-night cycle. You could still have a day-night cycle, but the duration of the cycle would be the period of orbit around the sun. (Subject to precession.)

Alternatively, although I think this would require divine intervention to keep it stable, you could generate a shorter day-night cycle by having the axis of rotation in the plane of the disc.

Well that's kind of my point - what would we need to give us a day-night cycle of about 24 hours?
We can have a tiny sun orbit the disc, like Pratchett, but that's not a natural star system, so we'd need the gods to intervene again, and my origina lidea was to avoid that as much as possible.
Is there a way we could have a natural star system and get a 24 hour diurnal cycle - say, by having the plane of the disc perpendicular to the star and orbiting the star really fast - but without ripping the disc to bits with tidal forces?

[DavidSh]

We have detected exoplanets with orbital periods as short as 11 hours, orbiting various stars, so a 24-hour orbit is not out of the question. The star would have to be a red (or even brown) dwarf, for the temperature to be reasonable for life as we know it.

[factotum]

Secondly, related to your point: Why is the disc spinning? Where did this angular momentum come from? I assumed that the spin of planets is due to their formation from an accretion disc, whereas this discworld was been created out of nothing, or assembled in situ

If someone is capable of assembling this discworld or creating it out of nothing, that someone is also capable of giving it a spin. I was personally thinking it would be spinning like a coin does when you flip it, rather than about the perpendicular axis, although that would lead to some interesting effects--there would be two points during the year where the disc would be edge-on to the sun and thus wouldn't really get any sunlight. In fact, those two points would be "winter", with summer presumably being when the disc is at 90 degrees to its primary and thus getting the maximum available sunlight--so you'd still get seasons, even though the weather would be significantly calmer than on a sphere.

It does have to be said, though--as soon as you start talking about having some magic force that keeps the atmosphere flat and prevents it spinning off into space, you've left reality behind and started into "anything goes" territory.

[Lvl 2 Expert]

If someone is capable of assembling this discworld or creating it out of nothing, that someone is also capable of giving it a spin. I was personally thinking it would be spinning like a coin does when you flip it, rather than about the perpendicular axis, although that would lead to some interesting effects--there would be two points during the year where the disc would be edge-on to the sun and thus wouldn't really get any sunlight. In fact, those two points would be "winter", with summer presumably being when the disc is at 90 degrees to its primary and thus getting the maximum available sunlight--so you'd still get seasons, even though the weather would be significantly calmer than on a sphere.

It does have to be said, though--as soon as you start talking about having some magic force that keeps the atmosphere flat and prevents it spinning off into space, you've left reality behind and started into "anything goes" territory.

You could flip the coin in the same direction as the disk's orbit around the sun (or the exact opposite). That way any day-night cycle has a moment with the sun straight overhead and one with the sun directly below. You could make a semblance of seasons by tilting the disk a bit. The "north" of the spinning axis points slightly towards the sun when you release it, but it won't keep pointing towards the sun rather it retains its absolute direction as the disk completes its orbit. At two moments in a solar cycle there would be a moment when the sun is straight overhead, and two moments in the year achieve maximum tilt.

What you lose is most of the climate zones as we know them. If the sun is realistically far away all parts of the disk get the same cycle of sunlight. There might be a very strong climate zone effect at the edges of the disk, but we'd have to know more about how the disk retains its air for that. If we assume a forcefield that completely boxes in the atmosphere but lets sunlight and heat through the center of the disk would probably be the warmest region. Even though heat loss to space is slow, it's warmer to be surrounded by land that gets warmed than by the big nothing. This in turn would create some sort of wind system. Heating happens near the ground, but warm air rises, so I'd expect high up winds going towards the edge of the disk, and cooler air blowing inwards at lower levels. In the cold seasons there might be a difference between the east-west and the north-south directions as far as wind goes, but I think that's actually not the case, or a minimal effect. The winds would be stronger in the warm season, because more heating.

With this climate system you might see rain forests in the center, surrounded by savannes, steppes and desert, similar to our tropics. But whether that would actually happen depends on so many details of the weather system and water cycle. But some versions of this setup could very well end up having all of that, plus temperate and cold regions around the edges. Although I don't have too much of a clue how their water supply would look in a climate dominated by the outward blowing wind. It might just be desert all the way until the point where you'd call it tundra.

[Kato]

I don't follow you guys... For the most part. :smallconfused:

First: If we assume the disc has some (magic) gravity, then that is also strong enough to keep an atmosphere, the same way Earth's one is not ejected by centrifugal force (if you want to fight me on using the term, bring it :smalltongue:)
Fine, the direction of force is slightly different but if it also keeps the disc intact, this should not be an issue.

Second: what keeps the discs day and night / seasons from working mostly the same as with us? Op didn't ask for a Discworld, so we can have a normal sun / star with the disc spinning about its axis to make nights and tilt it to give it seasons,pretty much like we have.

You'd have an equator with mostly constant temperatures and northern and southern hemispheres with opposite and depending on the tilt extreme seasons.
At least ignoring all other factors.. Earth's regional weather / climate is strongly dependent on the shape of oceans, continents, mountains... Giving an indication on that would be more difficult.

Also, it's kind of important how thick the atmosphere is and how the underneath looks like. I guess the assumption is just boring rock, no atmosphere, nothing (?)

[Lord Torath]

If we assume the planet is Earth-like in that it has a 23.5o tilt and is "flipping" around the same axis Earth is relative to its orbit and the sun, you will still get seasons similar to Earth's, but they will be half as long. Summer on the disc will occur and the vernal and autumnal equinoxes (the flat of the disc is perpendicular to the sun), and winter will occur at the solstices. The entire surface of the flat will experience the same seasons at the same time, rather than how we get summer in the North when it's winter in the South.

How thick is this disc? Because the edges of the disc will have seasons very similar to Earth's seasons (3 months per season, and alternating between northern and southern halves). If the disc is fairly thin, the weather on the edges will be dominated by weather on the flat, and the edge seasons will be negligible. The thicker the disc, the greater the effect of the "edge" seasons.

[DavidSh]

Assuming Newtonian mechanics applies for the most part, we have to consider both the orbit of the disc around its sun, and the rotation of the disc around some axis. There are two angles of importance: (1) the angle between this axis and the plane of the orbit, and (2) the angle between this axis and the plane of the disc. If the rotation axis is perpendicular to the orbital plane, and also perpendicular to the plane of the disc, then the sun is always on the horizon. If the rotation axis is 23 degrees off perpendicular to the orbital plane, and at angle theta to the plane of the disc, then from the surface of the disc the sun appears to behave just like it behaves from a point on Earth with latitude theta. If the rotation axis is in the plane of the disc, theta is zero, and the sun behaves like it behaves from the equator on Earth.

[factotum]

Second: what keeps the discs day and night / seasons from working mostly the same as with us? Op didn't ask for a Discworld, so we can have a normal sun / star with the disc spinning about its axis to make nights and tilt it to give it seasons,pretty much like we have.


Where does the shadow come from that creates the "night" if the disc is spinning about its axis? We get night because our sphere's spin naturally carries us onto the side where the planet itself blocks the sun, but if you think about it for a minute, you'll see that can't happen with a disc.

[Lvl 2 Expert]

Where does the shadow come from that creates the "night" if the disc is spinning about its axis? We get night because our sphere's spin naturally carries us onto the side where the planet itself blocks the sun, but if you think about it for a minute, you'll see that can't happen with a disc.

Think "coin flip" spinning, not "pizza dough" spinning. The axis is north south rather than up down.

[halfeye]

This is not possible with mechanics and gravity as we know them.

https://en.wikipedia.org/wiki/Hydrostatic_equilibrium

The gravity of the moon is pretty weak, but it's still enough to pull the shape into a sphere. Ceres is smaller and lighter still, but it's still almost exactly spherical. Rocks just aren't that strong against gravity.

I love Terry Pratchett's discworld, but it's a fantasy.

The overall gradient of Everest is a lot less than 10 degrees, maybe less than two degrees if you count all the way down to sea level.

[Tvtyrant]

I say make it a cup-world, with colossal walls compared to the livable part at the bottom. The bottom of the cup is pointed at the sun, which is much closer then Earth's, and the sun-as-seen by natives is actually a very bright moon which orbits diagonally near the top of the cup, so the cold parts are where the angle provides less light and the warm parts where it provides the most.

[Altair_the_Vexed]

This is not possible with mechanics and gravity as we know them.
Yes, I know that - but if we magic up the disc and gravity and atmosphere, what happens next? The reason I'm asking is that I'd like to discuss what it would take to make a livable discworld, if we just handwave the fundamental parts.

That's the point of the question, not "Can there be a discworld?" - because obviously no, there can't, not with anything like normal physics.

---

To answer a few other questions that have cropped up - how thick is the disc, how fast is it spinning, what axis is it spinning on, is there atmosphere underneath? Let's explore the different possibilities!

If the disc is a couple of dozen miles thick (like Earth's crust), does that produce an edge effect for the weather systems?

Spin speed and axis are interrelated, I think: do we want to make it spin to produce night and day, or can we do that with the orbit?
Let's say the disc is spinning perpendicularly to its horizontal plane, like a spinning coin on a table, so that the diurnal cycle is caused by the spin - does that give us polar regions, or is the general flatness going to mean we get even enough insolation to lose the whole climate zoning effect? My gut instinct is that there'd be no difference between the concentration of energy hitting at different parts of the disc, because of the flatness - unlike the near spherical planets.
Or what if the disc always faces one way with respect to its orbital path, so that day and night are caused by the orbit around the star (one cycle per orbit) - does that mean you don't get seasons? It seems to me that you wouldn't, as any tilt that might cause seasons is drowned out by the far greater effect of the day-night cycle of the orbit.
Or - if the disc spins in the same plane as its horizon, like a frisbee in flight, how do we get our day and night?

If there was an atmosphere underneath, what would change?

[Khedrac]

If the disc is a couple of dozen miles thick (like Earth's crust), does that produce an edge effect for the weather systems?
- - - -
If there was an atmosphere underneath, what would change?
The problem with these questions is that when you hand-wave the reason why the atmosphere and hydrosphere stay put we now cannot answer the questions without knowing more about the hand-wave. So edge effects and double-sidedness will have effects, but what they might be depend on what is keeping the atmosphere there in the first place.

[Lord Torath]

You will only get polar regions along the edges of the disc. The flat of the disc is flat, therefore it sees the same relative angle of light from the Sun across the entire face.

I suspect that a 20 mile thick disc would have pretty negligible edge weather effects. The Earth is big, and if we flattened it out into a two-sided disc, the diameter would be about 1.414 times larger than current (area of sphere is 4 pi r2 => half area on each side of disc, so each side has 2 pi r2 , which means increase radius by square root of 2). Our current diameter is roughly 8,000 miles, so flattened with the same surface area, our diameter would be about 11,300 miles. Edit: Only surface area is conserved in the magical squishing process here. Volume is not conserved.

20 miles is pretty thin compared to 11,300 miles. I think your disc would need to be several hundred miles thick before the edge effects would be significant.

I think a critical assumption to make for this case is that gravity acts universally perpendicular to the face or edge of the disc at a value of 9.807 m/s2 and "wraps" around the corners evenly. This would apply to the disc itself, not any mountains or canyons in or on the disc. So the air and water will flow around the edges of the disc without flowing off into space.

[factotum]

Thinking about it, if you somehow managed to create a disc planet with the same mass as Earth (and made it so it didn't just collapse back into a sphere under its own gravity, which would require materials with enormous compressive strength), it could maintain a spherical atmosphere using just regular gravity. That would have some interesting effects--for instance, there'd probably be a fairly narrow ring on the surface where conditions were habitable, with areas outside that having thin, barely breathable air and regions inside having extremely high pressures. It would also mean that everywhere away from the centre of the disc would be effectively uphill from it, so you might end up with a situation where all the rivers flow inwards into the high-pressure centre, where there might be a sea or the water might just evaporate into the general atmospheric circulation. (Would the high pressures in the centre also mean higher temperatures? Really not sure about that).

[Altair_the_Vexed]

The problem with these questions is that when you hand-wave the reason why the atmosphere and hydrosphere stay put we now cannot answer the questions without knowing more about the hand-wave. So edge effects and double-sidedness will have effects, but what they might be depend on what is keeping the atmosphere there in the first place.

That's part of the discussion - how does the magic need to work in order to achieve these things? If the environment is preserved by a force barrier around the edge of the disc, what would that mean? Or if it's preserved by some other means, what properties would it need to have, and what would emerge from those properties?

Let's start with thinking of the environment being kept in place by a magical force field, approximately 100km from the surface on average, as that's the generally agreed threshold of space. We've also got a magical gravity giving us a uniform direction for "down" - towards the surface of the disc, instead of towards its more Newtonian centre of gravity.

[Lvl 2 Expert]

We've also got a magical gravity giving us a uniform direction for "down" - towards the surface of the disc, instead of towards its more Newtonian centre of gravity.

Yet we have it orbiting a star. So the fake gravity is some sort of localized phenomenon, or a force that loses power over a shorter distance than true gravity.

The good news is the disk itself probably doesn't need to weigh all that much, so there isn't a lot of true gravity that our fake gravity needs to compensate for. Ceres has near negligible gravity and is around 1000 km across.

At this point I was going to say: "The same volume packed into a disk around the thickness of the Earth's mantle, say 20 km or so, would give a living surface the size of..."

But I did the calculation, and I'm ending up at the impossible situation where it says the living space from that project would only be slightly larger than the Netherlands, while the actual amount of surface on present day Ceres is the size of Kazakhstan or Argentina, while being a lot thicker than 20km. Can anyway see where I's missing a zero?

V=4/3*pi*r^2=4/3*pi*500^2~1,000,000 km^3, /20~50,000 km^2, /pi=r^2~16,666, r=129.1 km

After that I would have argued that the true gravity on a disk would at least in most places be less then the gravity on a sphere of the same size, and in those places where it's strongest it points roughly down. (Or up, on the underside.)

[Tvtyrant]

You could also revert to Greek theories: the whole thing is built along nested invisible superstructures.

[Lord Torath]

Yet we have it orbiting a star. So the fake gravity is some sort of localized phenomenon, or a force that loses power over a shorter distance than true gravity.

The good news is the disk itself probably doesn't need to weigh all that much, so there isn't a lot of true gravity that our fake gravity needs to compensate for. Ceres has near negligible gravity and is around 1000 km across.

At this point I was going to say: "The same volume packed into a disk around the thickness of the Earth's mantle, say 20 km or so, would give a living surface the size of..."

But I did the calculation, and I'm ending up at the impossible situation where it says the living space from that project would only be slightly larger than the Netherlands, while the actual amount of surface on present day Ceres is the size of Kazakhstan or Argentina, while being a lot thicker than 20km. Can anyway see where I's missing a zero?

V=4/3*pi*r^2=4/3*pi*500^2~1,000,000 km^3, /20~50,000 km^2, /pi=r^2~16,666, r=129.1 km

After that I would have argued that the true gravity on a disk would at least in most places be less then the gravity on a sphere of the same size, and in those places where it's strongest it points roughly down. (Or up, on the underside.)Got your error: Volume of a sphere is 4/3 pi r3. You've got 4/3 pi r2.

At a radius of 500 km, Ceres has a volume of 523,598,776 km3.

Divide that by 20 km, you get an area of 26,179,938 km2.

Divide that by pi, you get 8,333,333 km2.

Square Root of that gives you a radius of 2886.75 km, or a diameter of 5774 km. A fair bit smaller than Earth's diameter of 12,756 km.

Edit: Surface area of a sphere is 4 pi r2, so Earth's current surface area is 511,000,000 km2.
Surface area of your squished Ceres is 52,700,000 km2 (2 pi r2+20*2 pi r), an order of magnitude smaller than Earth's.

[Lvl 2 Expert]

Nice, thanks.

So with the same thickness (we'll reinforce the disk with space-rebar) we'd need ten times the volume to get to an Earth sized living space, which means a bit over twice the diameter. So we'd need to cannibalize Pluto, where the current gravity is about twice as strong as Ceres' negligible pull.

[factotum]

Nice, thanks.

So with the same thickness (we'll reinforce the disk with space-rebar) we'd need ten times the volume to get to an Earth sized living space, which means a bit over twice the diameter. So we'd need to cannibalize Pluto, where the current gravity is about twice as strong as Ceres' negligible pull.

I think you're ignoring something here--namely, that your compressed Pluto is much thinner than the real one, so you'd expect the gravity to be proportionally much higher toward the middle of the disc? That's assuming that the gravity of this object will act as if it's all focused in the middle, which is probably not going to be the case (and I have no idea how you'd calculate it).

In fact, I think that's a critical thing we're missing here. If you had a solid disc of rock the sort of size we're talking about, just how would regular gravity work on it? Is there any reasonable way to work that out?

[Manga Shoggoth]

Yet we have it orbiting a star. So the fake gravity is some sort of localized phenomenon, or a force that loses power over a shorter distance than true gravity.

On the Diskworld, the star orbits the disk. It's occasionally awkward for the elephants.


In fact, I think that's a critical thing we're missing here. If you had a solid disc of rock the sort of size we're talking about, just how would regular gravity work on it? Is there any reasonable way to work that out?

I 'aint going to do the maths, but if you have the inhabitable part of the disk as a substrate on top of an extremely dense disk to provide sufficient gravity you would have a number of forces in play.

A naive list is as follows:


The gravitational pull of the base material below you (the vertical component if the gravity), which would you to the disk.
The gravitational pull of the material around you (the horizontal component of the gravity), which would pull you towards the center of the disk if you were standing on the rim, and cancel out completely at the center of the disk. Because it cancels out at the center a larhe structure like Core Celesti would be possible.
Centrifugal (centripetal for pedants) force due to the spinning of the disk. This would add an apparent outward force that increases as you move towards the edge of the disk. This would cancel out the pull due to the horizontal component of the gravity. To allow for the rimfall, this force would have to be slightly larger than the horizontal component at the edge of the disk.
Coriolis force from the spinning disk would then drive wind and weather patterns.


Incidentally, Vsauce looks at the real-world issue here (https://www.youtube.com/watch?v=VNqNnUJVcVs).

[Lvl 2 Expert]

On the Diskworld, the star orbits the disk. It's occasionally awkward for the elephants.

But this was about a flat world which is situated in a universe as close to ours as possible. So many of us assumed the most "real" solution was having it orbit a star. That way at least we don't have to figure out how to make a tiny body create light or how to have a giant body orbit the disk. Although I guess combining a slow lunar and fast solar orbit we could lock the disk behind a gas giant with a smaller companion feeding the disk "moonlight" from a bright main star...

[GeorgeFowell]

Climate change can agitate sustenance openness, reduce access to nourishment, and impact sustenance quality. For example, foreseen increases in temperatures, changes in precipitation outlines, changes in incredible atmosphere events, and the lessening in water openness may all result in reduced provincial gainfulness. Climate play the important role for agriculture.

[Sean Mirrsen]

The only way I can think of having a world like this, is an invisible tether.

By which I mean of course nothing like a tether. It'd be a slab of rock that undergoes constant acceleration in its "upward" direction, creating apparent gravity. If this construct were to rotate slowly around its "north/south" axis, the constant acceleration would cause it to describe a circular orbit around a point in space, as if it were spun around it on an invisible tether, the acceleration of the object itself replacing the tension of the tether.

If this rotation had a precisely controlled rate, matching to a precisely controlled orbital velocity around a star, the discworld could describe an accelerated orbit around it, albeit forced to always face towards it, resulting in constant day and likely not very pleasant living conditions.

I'm not sure about the dynamics involved, what additional forces there would be at the east/west edges of the disc, and how significant they would be.

However, theoretically, I think it's possible for a system like this to continue a circular pattern in a spiral, rotating around nothing in particular with a period roughly similar to a day, while also being in a regular orbit around a star. I can't say how possible that is exactly, and how stable the resulting system would be (not very, I'd assume), but it's the most scientifically plausible way of having a "discworld" in a regular solar system. The plausibility of an enormous slab of rock capable of indefinite constant acceleration aside. If the day-cycle spin trajectory were slightly inclined, the resulting changes in daylight strength over a "year" would cause something approximating seasons, but it's hard to say what they would look like.

[factotum]

The plausibility of an enormous slab of rock capable of indefinite constant acceleration aside.

I think we waved goodbye to plausibility as soon as we started talking about a discworld, to be honest with you. :smallwink: I mean, we were talking about some magical force field that holds the atmosphere earlier on!

This constant acceleration idea--could the disc essentially orbit the star, but constantly accelerate in a circle around the actual orbit point? If it took 24 hours to make a full circle then you get the day/night cycle you need. (Is that what you meant when you were talking about a spiral?).

[Sean Mirrsen]

This constant acceleration idea--could the disc essentially orbit the star, but constantly accelerate in a circle around the actual orbit point? If it took 24 hours to make a full circle then you get the day/night cycle you need. (Is that what you meant when you were talking about a spiral?).

Yes. Drawing on my wealth of orbital mechanics experience (via screwing around in Kerbal Space Program), I see it as basically a rocket at thrust in a constant-rate spin. Since it spends an equal amount of time applying an equal amount of force in any given direction, then the net acceleration of the rocket per 'revolution' is zero, absent the usual rocket phenomena such as losing mass over time. At the same time it's still subject to gravity, so it can, thus spinning, follow an orbit, describing a spiral along the orbital path as if it were a satellite of something. And the crew on board still primarily experience just the apparent gravity from thrust.

What I don't know is if the size of the discworld is going to introduce some interesting forces into the mix, with the spinning, even if it's as slow as one revolution per 24 hours. It may be that oceans, and atmosphere, will be inclined to collect towards the east/west edges, and the actual direction of gravity felt on the world will only be strictly "down" along the north/south axis of rotation. It will probably be a comparatively minor effect, though.

[factotum]

I don't think it needs to spin in the mentioned scenario. The day/night cycle will be provided by the thing flying around in a circle--essentially, it's the "coin flip" rotation already mentioned in this thread, only the thing is under constant acceleration.

[Sean Mirrsen]

The "flying in a circle" still necessitates a spin, which will still generate some kind of force.

Helpful visualization chart:
https://i.imgur.com/VXtSgTu.jpg

edit: I suppose that's what you mean by "coin flip rotation", but that's also a spin, just a different axis, and it creates an acceleration on the opposing ends of the disc all the same. Just on a specific axis, instead of radially towards the edges, and is thus easier to counteract.

It would also create interesting weather conditions, since the tops of the two "bulges" of atmosphere at the east/west walls would cool faster, creating a constant flow of air. And the slight incline in the day-cycle orbit would create seasonal areas of permanent night/"dark winter" at either the north or the south wall, creating another source of cold air to flow and mix with the rest, inverting twice per year, from north to south.

Unfortunately I'm not a meteorologist, so I can't really tell what weather patterns that would form.

[Sean Mirrsen]

There is, admittedly, a far simpler solution to this, which merely requires that the discworld be accelerating straight forward, without any rotation, on a precalculated trajectory towards some far-away galaxy. Essentially, it would be a massive generation-ship.

In this case, the "sun" would not be a star, but a either a highly luminous satellite, or some kind of holographic/hardlight phenomena generated by whatever is powering and controlling the generation-ship. If it is a satellite, it is likely to be the powersource of the whole system, supplying power to the "constant-acceleration engine", and emitting light and heat as a useful byproduct. It likely also has its own propulsion then, and probably never stays directly overhead, instead describing an inclined circular orbit around the discworld. It might even be that the light and heat is the byproduct of the "engine" itself, and the discworld is riding a pillar of annihilation fire of some description. Or the "sun" is another discworld, shining too brightly to ever be discerned as such, flying in parallel, the two worlds circling one another, each being the other's "sun". The possibilities are endless.

[Altair_the_Vexed]

There is, admittedly, a far simpler solution to this, which merely requires that the discworld be accelerating straight forward, without any rotation, on a precalculated trajectory towards some far-away galaxy. Essentially, it would be a massive generation-ship.

In this case, the "sun" would not be a star, but a either a highly luminous satellite, or some kind of holographic/hardlight phenomena generated by whatever is powering and controlling the generation-ship. If it is a satellite, it is likely to be the powersource of the whole system, supplying power to the "constant-acceleration engine", and emitting light and heat as a useful byproduct. It likely also has its own propulsion then, and probably never stays directly overhead, instead describing an inclined circular orbit around the discworld. It might even be that the light and heat is the byproduct of the "engine" itself, and the discworld is riding a pillar of annihilation fire of some description. Or the "sun" is another discworld, shining too brightly to ever be discerned as such, flying in parallel, the two worlds circling one another, each being the other's "sun". The possibilities are endless.

A discworld as a generation ship - that's an interesting concept!

- But I like how you say that the constant acceleration is a "simpler solution" and then go on to invent a whole swathe of new technologies necessary to make it work. I'm not criticising the concepts, just slightly amused that a host of new imaginary tech is the "simple solution".

---

In case it'll make any difference to the now mature and independent discussion going on here, remember I said in the OP that gravity on the disc was a given? We don't need to account for how gravity works. I'm fine with the idea that it just does.
Of course, if you're all having fun inventing and solving gravity puzzles, feel free! I love this sort of chatting.

[Sean Mirrsen]

A discworld as a generation ship - that's an interesting concept!

- But I like how you say that the constant acceleration is a "simpler solution" and then go on to invent a whole swathe of new technologies necessary to make it work. I'm not criticising the concepts, just slightly amused that a host of new imaginary tech is the "simple solution".It's a, heh, "mechanically simpler" solution. :P

It just means that instead of figuring out the effects of rotation, seasonal sun exposure, orbital periods, instability, etc, all you have is an accelerating object with an artificial sun. So your weather can be anything you want, as it's obviously managed.


In case it'll make any difference to the now mature and independent discussion going on here, remember I said in the OP that gravity on the disc was a given? We don't need to account for how gravity works. I'm fine with the idea that it just does.
Of course, if you're all having fun inventing and solving gravity puzzles, feel free! I love this sort of chatting.

If gravity is not an issue and you have something resembling a circular Tryslmaistan world-plate, the weather is not significantly different from the scenario with the accelerating discworld corkscrewing around a star. You just have a disc-shaped rock slab with raised walls, that rotates along a north/south axis like a coin. The walls keep in the atmosphere (with some electro-magical-netic assistance), and are raised in an arching bulge along the east and west edges to account for atmosphere collecting there due to the acceleration forces from the day-period rotation of the disc.

The atmosphere at the top of the bulges cools faster, creating a constant circulation of air, which from my limited understanding of weather would create a more or less constant pattern of winds as cold air cycles down and is warmed closer to the center of the disk, rising back up and towards the bulge.

On top of that, if the disk rotation axis is inclined relative to the orbital path, every year there would be alternating seasons of "northwinter" and "southwinter", as the atmosphere-retaining wall would cause the ground near either polar edge to stay in growing/shrinking areas of permanent dark, with two brief periods of "equilux" when the north and south retaining walls are parallel to the sunlight at noon, thus both getting equal light during the day. Helpful visual reference:
https://i.imgur.com/R1GQz4R.png

The effect of this on weather is that another, seasonal atmospheric cycle would be created, with cold air cycling in from the likely frozen polar region, either north or south, and warming closer to the center. This would also shift the constant east-center-west air cycle towards the opposite pole, shifting the weather patterns as more cold air comes towards that direction.

The exact weather patterns would take an actual meteorologist and possibly a very expensive weather simulation program to determine. But it's pretty much a given that they would not be anywhere near as strong as on Earth, where there's far more potential for temperature differential.

Still, acclimatization is a thing. Even if a cold day on this "discworld" wouldn't cause a typical Earthman to so much as shiver, to its regular inhabitants a "winter" would be just as cold as any winter to an Earthman.

[Lvl 2 Expert]

Is that realistically a thing, constant acceleration of around 1g on a generation ship? Even in a pure Newtonian universe where e is still mv^2?

It does really simplify some parts of the story.

[Sean Mirrsen]

Is that realistically a thing, constant acceleration of around 1g on a generation ship? Even in a pure Newtonian universe where e is still mv^2?

It does really simplify some parts of the story.

Accelerating a thing at a constant 1g, is theoretically easier on the laws of physics than generating artificial gravity at a uniform 1g over a large area.

With the wild forkery that is relativity, even though for the rocket the acceleration is always 1g, "in reality" it will never break lightspeed, so you're not putting infinite amounts of energy into it.

...

That's not to say it's not ridiculous amounts of energy.

Let's say this thing is riding on magical emDrives that convert every joule of energy into one Newton of thrust. Hell if I know if that's even absolutely possible. Let's say the disc is a massive slab of granite 6000km in radius and 500km thick. And finally, let's say that the source of energy for everything is a massive slab of magically-contained antimatter that constantly reacts with matter at a controlled rate, and feeds all of that energy into thrust.

In order to keep up the acceleration, the discworld would use up around ten thousand tons of reacting matter/antimatter. Per. Second.

The good news is that comes up to "merely" some 30 quadrillion tons of it per year. Which, with the size of the discworld, would only amount to around 1% of its total mass... in around 100 millenia. :P

Unless my math is off by a few orders of magnitude, which wouldn't surprise me in the least. :)
(if you factor in conversion losses, and somewhat more "realistic" thrusters, you would probably see around 1% of mass lost per a millenium at best, which would limit the effective "burn time" to maybe 10 millenia before the amount of stored antimatter would be completely improbable)

[factotum]

Let's say this thing is riding on magical emDrives that convert every joule of energy into one Newton of thrust.

I don't think that works that way? The definition of a joule is the amount of work required to move 1kg by 1m, so I don't think there's a nice simple relationship between that and thrust as you're saying here. If that's wrong then all your other calculations are wrong too, and they certainly sound off to me--to be able to accelerate continuously at 1g for thousands of years while only using a relatively tiny amount of fuel sounds utterly bonkers.

[Lvl 2 Expert]

Accelerating a thing at a constant 1g, is theoretically easier on the laws of physics than generating artificial gravity at a uniform 1g over a large area.

With the wild forkery that is relativity, even though for the rocket the acceleration is always 1g, "in reality" it will never break lightspeed, so you're not putting infinite amounts of energy into it.

...

That's not to say it's not ridiculous amounts of energy.

Let's say this thing is riding on magical emDrives that convert every joule of energy into one Newton of thrust. Hell if I know if that's even absolutely possible. Let's say the disc is a massive slab of granite 6000km in radius and 500km thick. And finally, let's say that the source of energy for everything is a massive slab of magically-contained antimatter that constantly reacts with matter at a controlled rate, and feeds all of that energy into thrust.

In order to keep up the acceleration, the discworld would use up around ten thousand tons of reacting matter/antimatter. Per. Second.

The good news is that comes up to "merely" some 30 quadrillion tons of it per year. Which, with the size of the discworld, would only amount to around 1% of its total mass... in around 100 millenia. :P

Unless my math is off by a few orders of magnitude, which wouldn't surprise me in the least. :)
(if you factor in conversion losses, and somewhat more "realistic" thrusters, you would probably see around 1% of mass lost per a millenium at best, which would limit the effective "burn time" to maybe 10 millenia before the amount of stored antimatter would be completely improbable)

But wouldn't it be that the energy costs keep increasing? Even purely Newtonian a 1kg object moving at 1m/s has a movement energy of 0.5J, at 2m/s it's 2J and at 3m/s it's 4.5J. Acceleration means paying the difference between these values and thus it keeps getting more expensive. Which is one of the main reasons (the other being air drag) that a car accelerates from 0 to 100 much more quickly than from 100 to 200. (If it does that last one at all, but that's on air drag.) So it would seem to me that a constant pseudo gravity would require a constant acceleration which would require an ever increasing amount of energy. And those amounts get ridiculous pretty fast. I did some quick calculations with ships powered by an internal nuclear fusion drive ones, I don't think you could realistically get near light speed and back with one of those even ignoring all of relativity.

But say you can accelerate at a constant +-10m/s^2 u to the billion km/h or 300 million m/s that's the speed of light, in a Newtonian universe. That would take you 30 million seconds, about one year. By the end of which the energy used for constant acceleration at 1g is positively absurd. Relativity is going to lower the speed towards the end, but I don't think it lowers the energy requirements, does it?

[Sean Mirrsen]

But wouldn't it be that the energy costs keep increasing? Even purely Newtonian a 1kg object moving at 1m/s has a movement energy of 0.5J, at 2m/s it's 2J and at 3m/s it's 4.5J. Acceleration means paying the difference between these values and thus it keeps getting more expensive. Which is one of the main reasons (the other being air drag) that a car accelerates from 0 to 100 much more quickly than from 100 to 200. (If it does that last one at all, but that's on air drag.) So it would seem to me that a constant pseudo gravity would require a constant acceleration which would require an ever increasing amount of energy. And those amounts get ridiculous pretty fast. I did some quick calculations with ships powered by an internal nuclear fusion drive ones, I don't think you could realistically get near light speed and back with one of those even ignoring all of relativity.

But say you can accelerate at a constant +-10m/s^2 u to the billion km/h or 300 million m/s that's the speed of light, in a Newtonian universe. That would take you 30 million seconds, about one year. By the end of which the energy used for constant acceleration at 1g is positively absurd. Relativity is going to lower the speed towards the end, but I don't think it lowers the energy requirements, does it?

A rocket in freefall, at any one point, can be said to be at rest. It is in its own reference frame.

A rocket, therefore, will take the same amount of energy to generate the same amount of apparent acceleration, regardless of how fast it is traveling. The "actual" change in velocity is irrelevant to the matter at hand, since we're not concerned with the velocity relative to any point other than the rocket itself, which is always zero.

That being said, there is always a significant probability of me being horribly wrong, especially on the whole joules-to-newtons thing. :P

Also, the hypothetical, already-magical emDrive, had been reported to produce a whopping 0.2N of thrust, from 850W of power. Before the magnetron burned out. A watt being a joule per second, we can pretty directly plug that into my earlier estimate and get the hypothetical burn time reduced fivethousandfold. Which still puts the best-case-scenario at a couple centuries. Antimatter is a hell of a drug. :P

[factotum]

A rocket in freefall, at any one point, can be said to be at rest. It is in its own reference frame.

A rocket, therefore, will take the same amount of energy to generate the same amount of apparent acceleration, regardless of how fast it is traveling.

If that were true, the Oberth effect wouldn't exist:

https://en.wikipedia.org/wiki/Oberth_effect

[Sean Mirrsen]

If that were true, the Oberth effect wouldn't exist:

https://en.wikipedia.org/wiki/Oberth_effect

The Oberth effect is about gaining kinetic energy, not acceleration. It uses a bunch of formulas but to my untrained eye it just goes back to the whole "mass times velocity squared" thing. Same amount of acceleration, when already moving relative to something, gets you more energy the faster you were moving. If it were the thing you're moving relative to that pushes you along, then your acceleration would decrease with velocity. But a rocket accelerates itself, which is why it works.

[halfeye]

The Oberth effect is about gaining kinetic energy, not acceleration. It uses a bunch of formulas but to my untrained eye it just goes back to the whole "mass times velocity squared" thing. Same amount of acceleration, when already moving relative to something, gets you more energy the faster you were moving. If it were the thing you're moving relative to that pushes you along, then your acceleration would decrease with velocity. But a rocket accelerates itself, which is why it works.

Does it actually work?

It would have to be outside any atmosphere, but on the inside of an eliptical orbit. There is no contact with the planet, so there is no collision, elastic or inelastic. Are people sure this isn't simply a mistake?

[Sean Mirrsen]

Does it actually work?

It would have to be outside any atmosphere, but on the inside of an eliptical orbit. There is no contact with the planet, so there is no collision, elastic or inelastic. Are people sure this isn't simply a mistake?

Uh.

Well, it does work, it's kind of one of the most basic things in orbital mechanics. Whether or not it works on the principles we think it does is deemed irrelevant as long as the equations line up with the observations, it's the reason why, i.e., relativity is so hard to dislodge.

I recommend Kerbal Space Program as a handy interactive visual reference. Obligatory xkcd:
https://imgs.xkcd.com/comics/orbital_mechanics.png

[Tirunedeth]

A rocket in freefall, at any one point, can be said to be at rest. It is in its own reference frame.

A rocket, therefore, will take the same amount of energy to generate the same amount of apparent acceleration, regardless of how fast it is traveling. The "actual" change in velocity is irrelevant to the matter at hand, since we're not concerned with the velocity relative to any point other than the rocket itself, which is always zero.

That being said, there is always a significant probability of me being horribly wrong, especially on the whole joules-to-newtons thing. :P

Also, the hypothetical, already-magical emDrive, had been reported to produce a whopping 0.2N of thrust, from 850W of power. Before the magnetron burned out. A watt being a joule per second, we can pretty directly plug that into my earlier estimate and get the hypothetical burn time reduced fivethousandfold. Which still puts the best-case-scenario at a couple centuries. Antimatter is a hell of a drug. :P

The issue here is that we aren't working with a rocket, we're working with a reactionless drive, which stop making sense the minute you try to change reference frames. In it's own reference frame, the power needed to create a given acceleration is always zero, since it's velocity is zero by definition in that reference frame.

The reason this doesn't happen with a rocket, and also incidentally the reason the Oberth effect works, is that a rocket also has the exhaust propellant to account for. Consider a rocket of mass m moving at velocity v carrying propellant of mass Δm which it expels at an average velocity ve (relative to itself). Conservation of momentum indicates that the final velocity of the rocket is v' = v + Δm/m ve. The kinetic energy of the propellant after being expelled is
1/2 Δm (v - ve)2 = 1/2 Δm ve2 - Δmvve + 1/2 Δmve2
Similarly, the kinetic energy of the rocket is
1/2 m (v + Δm/m ve)2 = 1/2 m v2 + Δmvve + 1/2 Δm2/m ve2
Combining the two, we can see that the 1/2 Δm ve2 and 1/2 m v2 terms simply constitute the initial kinetic energy of the rocket, the Δmvve terms cancel out, and the 1/2 Δm ve2 and 1/2 Δm2/m ve2 terms are the energy added to the propellant to make it move.
Everything checks out conservation of energy wise, regardless of frame of reference, but lets return to those Δmvve terms. Note that this term subtracts from the kinetic energy of the propellant, but adds to that of the rocket. In other words, some of the initial kinetic energy of the propellant winds up with the rocket instead of the propellant, and the quantity increases the faster the rocket is moving. This is where the Oberth effect comes from.
Another way of looking at the Oberth effect is to consider that we are leaving some portion of our propellant deeper in the gravity well of the planet, and then using the liberated potential energy to accelerate the rocket.