What would living on a toroid planet be like?

[dotchan]

Because I've been playing way too many Square-Enix games that feature the double-wrap* map and have been wondering.

- What would gravity be like?
- What would the day/night cycle be like? (Obviously would depend on how the thing rotated, but I'm not very good at visualizing in 3-D space.)
- Standing on the inner diameter, would you be able to see the other part of the planet?

...of course, realistically, a toroidal planet probably wouldn't be able to survive long enough for anybody to live on it, but play along for the sake of this thread, would ya?

*One that wraps North-South as well as East-West. Our spherical Earth only wraps East-West

[awldune]

Our spherical Earth only wraps East-West

:confused:

What exactly do you mean by "wrap"?

[Amp]

I think dotchan means a planet shaped like a donut.

[Amp]

Something like this (http://www.geocities.com/SiliconValley/Program/9231/pictures/toroidwd.gif)

[Manduck]

Everybody would have to live on the equator (the outer equator I guess), because everywhere else gravity doesn't point toward the ground.

[dotchan]

:confused:

What exactly do you mean by "wrap"?

On a 2-D map of the Earth, if you head east (or west) in one direction long enough you'll "disappear" off one edge of the map and "appear" on the other.

Nearly all of Squeenix' Final Fantasy titles have maps that not only do this for East-West directions, but for North-South (and yet, on games with a quasi-3D view, it shows the world below as round!).

ERAU QSSI DRLO WEHT :D

[Sunspace]

I keep imagining that the oceans would all flow into the hole, so that you'd end up with a dry donut encircling a blob of water and confused fish. The air would follow the water.

[Q.E.D.]

Everybody would have to live on the equator (the outer equator I guess), because everywhere else gravity doesn't point toward the ground.
While you're correct about the gravitational situation - the outer and inner equators will have the highest and the lowest surface gravity, respectively, and the radius that corresponds roughly analogously to the North Pole, at 90 degrees between the equators, it would feel as though the ground was slanted somewhat, with downward being toward the outer equator. However, it does not follow that therefore everyone would live at the equators. It is perfectly possible to live on a hillside, and this occurs in many place on earth, such as these places (http://www.nrsp.co.uk/Nrspweb/highlights/hillside.htm):
There is no doubt that hillside farming can be practised safely when appropriate land use and conservation techniques are used. In Sri Lanka, the Kandy home gardens are renowned for their multi-storey cropping and intensive production, sustained over many centuries. In Bolivia, at over 3000 m above sea level, traditional native American potato and cereal production methods still rely on stonewalls to retain precious topsoil and produce reasonable crops. So the doomsday predictions of bare, eroded hillsides and poverty-stricken peasants seeking a meagre living there need not be a reality.
I've not worked out the numbers yet, but my gut tells me the apparent "slant" would not be very steep, perhaps similar to a hill with a 15-20 degree slope.

[Sage Rat]

I've not worked out the numbers yet, but my gut tells me the apparent "slant" would not be very steep, perhaps similar to a hill with a 15-20 degree slope.
Wouldn't that depend on the two radii* of the doughnut?

* Radius from the middle of the hole to the center of the dirt on the loop, and the radius from the center of the dirt to the surface

[Q.E.D.]

Wouldn't that depend on the two radii* of the doughnut?

* Radius from the middle of the hole to the center of the dirt on the loop, and the radius from the center of the dirt to the surface
Pretty much, hence the range.

Oh and I want to correct myself. Thinking further, I realize that at the "north pole", the ground would seem to slant down towards the inner diameter, not the outer. If you placed a ball on the ground there, it would roll towards the inner equator, with a relatively small acceleration, because the center of gravity would lie in that direction.

[Khan]

Could you stand at the inner equator? My guess would be that you could. I'm also betting that the gravity from the other side of the donut hole would create some pretty wicked tidal forces.

[Beware of Doug]

There would be six points on the compass: East, West, North, South, Up, and Down.

Creation myths would involve an unimaginably vast cauldron of boiling fat.

3/4 of the planet's surface would be covered by Maple Glaze.

[Triskadecamus]

Since magic is the only force that could create, or maintain such a planet, it obviously would be the ruling force of the entire region of space. Given that explanation, down can be arbitrary for any point on the surface, and the weather would be as the spell caster desired.

I imagine that day and night would be an "on/off" sort of thing, that being the simplest solution. Or, rotate the torus around the perpendicular axis through the hole. This leaves the center facing surface dark, unless the axis is inclined to the ecliptic enough to allow day night cycles. Given that gravity, and astronomic phenomenon must be magically controlled, I suggest that they be constrained to act in accordance with the book by Newton, except that Up and down be perpendicular to the plane tangent with the circular cross section of the local tubular region, not the body as a whole. (This has the advantage of matching the peculiarities of your mapping convention.)

Tris
------------------------------------
I helped build a world like this, once.

[Myglaren]

Larry Niven built one in the sixties:
[url=http://www.sfsite.com/~silverag/ringworld.html[Ringworld[/url]

[Myglaren]

Ooops, that coding obviously doesn't work here.

[Myglaren]

Ringworld (http://www.sfsite.com/~silverag/ringworld.html)

Looks better

[Jake4]

Ringworld isn't toroidal, it's a ring. There's no gentle curve from the inner surface to the outer surface. It's more like a rectangular prism that's been curved around into a circle. The walls are flat.

[snailboy]

Since magic is the only force that could create, or maintain such a planet, it obviously would be the ruling force of the entire region of space. Given that explanation, down can be arbitrary for any point on the surface, and the weather would be as the spell caster desired.


That's not necessarily true. As long as the interior of the ring was sufficiently rigid to prevent collapsing, it would maintain itself. The water and atmosphere aren't going to migrate into the "donut hole". The gravity for their area of the ring would overrule the gravity of the other side since it's closer. You could have a rigid core covered with dirt, water, and whatever else you wanted and it would maintain its shape.

Creating such a planet would be far beyond our technology and probably will be for hundreds of years at least, but it is technically possible.

[Triskadecamus]

Creating such a planet would be far beyond our technology and probably will be for hundreds of years at least, but it is technically possible.A level of technology sufficiently advanced is indecipherable from magic.

Tris

[Wolfian]

So there would be Day/Night materia?

Good question, dotchan. I never thought of it that way.

: Uses EXIT materia. : MISS

Dangit.

[treis]

I thought there was no gravity on the inside of a ring so the exact middle of the inside face would not have any gravity at all.

[tygerbryght]

Ringworld isn't toroidal, it's a ring. There's no gentle curve from the inner surface to the outer surface. It's more like a rectangular prism that's been curved around into a circle. The walls are flat.
Very true. However, if my memory's not deceiving me, he did have a toroidal ... um, well, planet is an exaggeration. I dunno where my copy of Protector is, but there should be a made toroid (with non-touching sphere in center) somewhere around 2/3 or the way through the book.

[CalMeacham]

Larry Niven did built a toroidal world in the 1960s -- it's in Protector, and the first paperback edition features the toroid world on the cover.


IIRC, the human Pak Brennan who built it used super-science to put it and keep it together. I can't imagine a toroidal planet, even of the size shown on the cover of Protector, being at all stable.

[Emerald Hawk]

I thought there was no gravity on the inside of a ring so the exact middle of the inside face would not have any gravity at all.This is what I learned in physics class as well, but I can't find my textbook for a cite. The basic rule I remember is that for a radially symettric object, if you draw a circle around its center you only need to consider the mass inside the circle when calculating gravitational force on that circle. If we draw a circle along the inside of our toroid, there is nothing inside our circle and therefore no gravity all along the inside edge.

In this case, I would be rather worried about the air and water all leaving after several thousand years because of this. While the atmosphere wouldn't be instantly pulled off the surface, the sun-warmed atoms would start to migrate to the center and form a disk shaped collection inside the ring. If this happened enough, the atmosphere and water could start to have a weak gravitational pull of its own, accelerating the process. Hmm, now I need to download a physics simulation and actually prove this.

[CalMeacham]

This is what I learned in physics class as well, but I can't find my textbook for a cite. The basic rule I remember is that for a radially symettric object, if you draw a circle around its center you only need to consider the mass inside the circle when calculating gravitational force on that circle. If we draw a circle along the inside of our toroid, there is nothing inside our circle and therefore no gravity all along the inside edge.


The problem is that your torus isn't "a radially symmetrical object". In order for that law about ignoring things outside the circle to work, it must be spherically symmetric. In a torus, you'll have conmtributions inside the ring due to gravitational influences outside it.

Heck, the calculation isn't that hard for a simple case -- imagine a point on a circle, and calculate the gravitational forces due to the rest of the circle. You'll find there's a small force pulling the object toward the center.

[CalMeacham]

This is what I learned in physics class as well, but I can't find my textbook for a cite. The basic rule I remember is that for a radially symettric object, if you draw a circle around its center you only need to consider the mass inside the circle when calculating gravitational force on that circle. If we draw a circle along the inside of our toroid, there is nothing inside our circle and therefore no gravity all along the inside edge.


The problem is that your torus isn't "a radially symmetrical object". In order for that law about ignoring things outside the circle to work, it must be spherically symmetric. In a torus, you'll have conmtributions inside the ring due to gravitational influences outside it.

Heck, the calculation isn't that hard for a simple case -- imagine a point on a circle, and calculate the gravitational forces due to the rest of the circle. You'll find there's a small force pulling the object toward the center.

[David Simmons]

I've not worked out the numbers yet, but my gut tells me the apparent "slant" would not be very steep, perhaps similar to a hill with a 15-20 degree slope.That works out to a 26-36% grade. That's a pretty steep slope for loose soil. It seems to me that whenever the wind picks up some dust it would fall toward the inner part of the torus so the world would wind up lopsided over time.

[Mac Guffin]

If the planet was spinning around an imaginary axis at the center of the hole, would not the centrifugal forces on the inner edge of the torus counteract any gravitational effects?

[CalMeacham]

If the planet was spinning around an imaginary axis at the center of the hole, would not the centrifugal forces on the inner edge of the torus counteract any gravitational effects?


That, I think, was largely the point of Niven's Ringworld. But the gravitational force is still there, even if centrifugal force gives a fictitious force in the other direction (It's there in Ringworld, too). But the original premise said nothing about spinning. In fact, why assume spinning about that axis , or only that axis. Spinning about an axis that passed through the torus itself would give more interesting, if less useful, results.

[Emerald Hawk]

Blah, I've been out of physics class too long to add anything useful. I was thinking of a spherically symmetric object, and that doesn't apply in this situation.

However, This link (http://www.mathpages.com/home/kmath402.htm), suggests that the torus would hold together, and the inside of the ring would feel attracted out toward the ring. Ask a scientist (http://www.ccmr.cornell.edu/education/ask/?quid=378) agrees, points inside the torus would be pulled outward. I guess this could work after all, even without having to spin it.

[rpinrd]

*One that wraps North-South as well as East-West. Our spherical Earth only wraps East-West
What exactly do you mean by "wrap"?
On a 2-D map of the Earth, if you head east (or west) in one direction long enough you'll "disappear" off one edge of the map and "appear" on the other.
I'm sorry, maybe I'm being dense (not to mention 3 days late), but I don't think that awldune's question has been answered yet. I still don't understand what is meant by "Our spherical Earth only wraps East-West." On a sphere, what difference does it make what direction you travel? If you travel long enough, you eventually come back to where you started (or "'appear' on the the other" side).

If the Earth were a cylinder I could understand this, but it isn't, ergo, I can't.

[Manduck]

If you walk off the west edge of a map of the earth, you reappear on the eastern edge of that map. But, if you walk off the north edge, you don't reappear on the south.

[KP]

That's entirely an artifact of how we draw maps, not a property of a sphere.

If we use essentially *any* other rectangular coordinate system, then walking due North would eventually have you reappearing on the other side of the map. We just happen to use unique distorted mapping, where the entire northern edge is really a single point, which we deem "as far north as you can get".

It's not an entirely arbitrary choice --it has much to recommend it-- but still, it's a cartographic property, not a geometric one. Cartographic properties don't affect physics in the slightest; they're social choices.

In fact, the whole issue of "the opposite edge" presumes a rectangular map (which has little merit for drawing the surface of a globe). As individuals, we may carry this prejudice over to, say a Mercator projection, because we're accustomed to seeing them drawn on rectangular sheets, but all we should really say about a Mercator or any other projection is "if you keep walking in any direction, you will hit some edge, and reappear on some other edge. THAT would be the only appropriate and generally meaningful geometric interpretation of a "wrap".

[HPL]

If you walk off the west edge of a map of the earth, you reappear on the eastern edge of that map. But, if you walk off the north edge, you don't reappear on the south.

Unless you live in a Square RPG.

[Manduck]

That's entirely an artifact of how we draw maps, not a property of a sphere.


But the point is, if you had that "wrap" property on both dimensions of the map, the map would be describing a torus.

[David Simmons]

Here's my quick and dirty solution (http://pg.photos.yahoo.com/ph/dwsimm2000/detail?.dir=/8cf7&.dnm=f5ac.jpg&.src=ph) for the case where you are standing on top of the donut.

It looks like you would feel a force of 1.02 times your normal weight inclined at 11.3 deg. when the opposite side's center is 2r away. In other words the case where the donut has no hole. That's worst case.

[David Simmons]

Here's my quick and dirty solution (http://pg.photos.yahoo.com/ph/dwsimm2000/detail?.dir=/8cf7&.dnm=f5ac.jpg&.src=ph) for the case where you are standing on top of the donut.

It looks like you would feel a force of 1.02 times your normal weight inclined at 11.3 deg. when the opposite side's center is 2r away. In other words the case where the donut has no hole. That's worst case.Correction, correction. I went to all the trouble of figuring the angel of the gravitation from the opposite side of the torus and then forgot to use it (hardly anyone is perfect any more).

The corrected worst case is that the total force would be 1.1 inclined at an angle of just over 9.3o.

[CalMeacham]

I went to all the trouble of figuring the angel of the gravitation from the opposite side of the torus and then forgot to use it (hardly anyone is perfect any more).



I know it's just a typo, but I love the idea of "the Angel of Gravitation", and I'd like to see a picture.

[David Simmons]

I know it's just a typo, but I love the idea of "the Angel of Gravitation", and I'd like to see a picture.I'm searching for a picture of something like a giant suction cup with slimy tentacles pulling us down into Great Dismal Swamp.

[David Simmons]

And how many times to you preview to make sure that Gaudere's Law didn't bite you?

[Loopydude]

Another ask the experts (http://www.newton.dep.anl.gov/newton/askasci/1993/physics/PHY42.HTM) sort of link. Corresponds with the others pretty well.

It would be pretty weird, standing on a flat plain (near the circular poles) and feeling like you're being pulled down a hill. Maybe your senses would tell you you were merely on a vast hillside, with "real" hills feeling like terraces.

Seems like a darned impractical sort of world to live on. Everything wants to pool in the inner ring of the torus. Only at the outer equator would things feel "normal" to our experience, and yet that position is likely unstable for anything not firmly rooted down or willing itself to stay there. Everywhere on the inner equator would probably be underwater, if the planet had as much ocean as the Earth does. Living on the shores of this inner-equatorial ocean would give one the bizarre experience of being constantly pulled as if downhill from the shore into the water. How would the water pile up in the middle? Depth would be greatest right at the equator, I guess.

It's really tough to imagine an Earth like environment suddenly transported to Donutworld. Seems like things would go completely wild, with calamatous redistribution of materials according to their viscocity, etc.

[Omphaloskeptic]

It would be pretty weird, standing on a flat plain (near the circular poles) and feeling like you're being pulled down a hill. Maybe your senses would tell you you were merely on a vast hillside, with "real" hills feeling like terraces.

Seems like a darned impractical sort of world to live on. Everything wants to pool in the inner ring of the torus. Only at the outer equator would things feel "normal" to our experience, and yet that position is likely unstable for anything not firmly rooted down or willing itself to stay there. Everywhere on the inner equator would probably be underwater, if the planet had as much ocean as the Earth does. Living on the shores of this inner-equatorial ocean would give one the bizarre experience of being constantly pulled as if downhill from the shore into the water. How would the water pile up in the middle? Depth would be greatest right at the equator, I guess.Why would your senses tell you anything other than that you were standing on a hillside? For a sufficiently large torus you wouldn't be able to discern any curvature, so you would only have gravity to go by.

You could make a more practical (can I use that word when the torus has to be supported by an unobtanium-scrith alloy?) torus by choosing a noncircular cross-section so that the surface is an equipotential (this may require a torus of nonconstant density, I'm not sure). This would avoid the everything-runs-downhill problem and allow outer oceans. On the other hand, a vast low-gravity inner ocean sounds pretty cool too.

[Omphaloskeptic]

It would be pretty weird, standing on a flat plain (near the circular poles) and feeling like you're being pulled down a hill. Maybe your senses would tell you you were merely on a vast hillside, with "real" hills feeling like terraces.Oh, never mind, I think I see what you mean here: the perception of gravity dueling with the human expectation of a horizontal horizon line. OK, I can see that being a little disorienting.

[Loopydude]

Oh, never mind, I think I see what you mean here: the perception of gravity dueling with the human expectation of a horizontal horizon line. OK, I can see that being a little disorienting.

Yeah, that's basically what I mean. Imagine yourself on a hillside: You look down, and there's level ground somewhere below. You might even see a summit above you. That's simply the way our experience tells us topography is arranged, and we can always point to the center of the Earth. It's down. The hillside is at an angle, the plain roughly perpendicular (given that the curvature of the Earth is difficult to perceive until high altitudes are reached, so a plain looks flat).

So, now you're transported to a place where even a pan-flat plain that stretches off to the horizon in all directions feels exactly like being on a steep hillside. Or maybe there's a hill not far off, and the slope facing away from the inner equator is, to your senses, a terrace on an incredibly vast slope. A landscape photograph level to the horizon would look perfectly normal. A film of the same scene would look bizarre, with people leaning forward (if they're moving away from the inner equator), as if in a steady gale, as they traverse the aforementioned pan-flat plain.

I figure actually being in that scene would be weirder still.

[Pleonast]

You could make a more practical (can I use that word when the torus has to be supported by an unobtanium-scrith alloy?) torus by choosing a noncircular cross-section so that the surface is an equipotential (this may require a torus of nonconstant density, I'm not sure). This would avoid the everything-runs-downhill problem and allow outer oceans. On the other hand, a vast low-gravity inner ocean sounds pretty cool too.This is on the right track. A torus with the correct non-uniform density could have a "level" surface. That is, at least one gravitational equipotential surface could have toroidal symmetry. Rather computationally difficult to determine the necessary density distribution, though.

[iamthewalrus(:3=]

So, now you're transported to a place where even a pan-flat plain that stretches off to the horizon in all directions feels exactly like being on a steep hillside. Or maybe there's a hill not far off, and the slope facing away from the inner equator is, to your senses, a terrace on an incredibly vast slope. A landscape photograph level to the horizon would look perfectly normal. A film of the same scene would look bizarre, with people leaning forward (if they're moving away from the inner equator), as if in a steady gale, as they traverse the aforementioned pan-flat plain.The film would only look strange if you set the camera up in a strange way. If you put it on a normal tripod or had someone carry it normally, it'd just look like people on a hill.

This brings up another observation: Think how easy navigation would be on such a planet! You could look up to see whether you were on the inside or the outside of the torus. If you were on the inside, you could probably determine your location using just a plumb bob and a sight. And you could use a level to determine compass directions.

[Loopydude]

The film would only look strange if you set the camera up in a strange way. If you put it on a normal tripod or had someone carry it normally, it'd just look like people on a hill.


:sigh:

A really big-ass, horizon-spanning, flat-plain-looking hill with hills on it!

[snailboy]

You could make a more practical (can I use that word when the torus has to be supported by an unobtanium-scrith alloy?) torus by choosing a noncircular cross-section so that the surface is an equipotential (this may require a torus of nonconstant density, I'm not sure). This would avoid the everything-runs-downhill problem and allow outer oceans. On the other hand, a vast low-gravity inner ocean sounds pretty cool too.

You could make a more practical torus planet more practically by simply making it spin such that the gravity from non-local areas of the torus are cancelled out by centrifugal force. Not only would you get rid of the massive hill effect, but the planet wouldn't be trying to collapse in on itself either.

[Omphaloskeptic]

You could make a more practical torus planet more practically by simply making it spin such that the gravity from non-local areas of the torus are cancelled out by centrifugal force. Not only would you get rid of the massive hill effect, but the planet wouldn't be trying to collapse in on itself either.True; though then you'd have tidal forces trying to rip it apart instead. And the days might be shorter than you'd like. (Fun times with low gravity and Coriolis forces in the middle, though!)

[Loopydude]

Wheee! Just imagine the tides!

[David Simmons]

(Fun times with ... Coriolis forces in the middle, though!)Wouldn't the Coriolis effect be more pronounced at the poles where the distance from the center of rotation increases most rapidly?

From either equator when you go 100 miles toward the pole you've hardly increased your distance from the center at all and the linear speed of rotation of the surface around the center is nearly the same as at the equator. On the other hand, at the pole when you go 100 miles you have increased or decreased you distance from the center by virtually 100 miles and so have changed the linear speed of the surface accordingly.