Ringworld Torus...

[Johnny1a]

I've been playing with a vague concept, and going back over old
threads looking for information bearing on it, but I have not found
anything that quite fits it.

Imagine a Niven Ring, i.e. a ringworld around a star, but instead of
the flat ribbon Niven suggests, imagine a torus, a cylinder of rock
and soil and water wrapped around the star at roughly 1 AU radius (or
the equivalent distance for the given star). This is just as
dynamically unstable as Niven's version, but that's not what I'm
pondering right now, assume some agency holds it in place with regard
to the star.

The torus would have an 'inner radius' centered on the star of 2 AU.
The torus is specifcally _not_ rotating around the star, instead its
surface gravity derives from its own mass. Here's where the concept
is uncertain:

1. For a torus this size, is it possible to maintain something close
to a 1G surface gravity over the whole surface of the torus based on
mass alone? That is, a 1G pull on a surface poin on the outer rim,
the inner rim, and 'top' and 'bottom' points at 90 degrees from the
plane? Slight variations might be acceptable, but the idea is a
loosely Earth-like biosphere and environment on the surface.

2. Is there any relatively simple forumla(s) to calculate the
relationship between mass, volume, and surface gravity (and escape
velocity) of this thing, or is it inherently complex? That is, how
big does the diameter of the 'doughnut' from inner to outer edge need
to be for a given density to get close to 1G on the surface (if that
can be done evenly).

3. The interior of the torus _may_ be rotating with regard to the
star, one idea I was toying with was that a circulating liquid or the
equvalent intside the torus might be providing some of the support
aganst stellar gravity.

4. Like the classic 'Gunkel tube', I was toying with the idea that
the torus might rotate with regard to its own circular iner axis,
providing a day-night cycle in that way. How big can the torus get
and do that while maintaiing a viable biosphere on the surface?

Like I said, I'm just toying with the concept and trying to figure out
how it would work or not.

[Andrew Plotkin]

Here, Johnny1a <sherm...@hotmail.com> wrote:
>
> Imagine a Niven Ring, i.e. a ringworld around a star, but instead of
> the flat ribbon Niven suggests, imagine a torus, a cylinder of rock
> and soil and water wrapped around the star at roughly 1 AU radius (or
> the equivalent distance for the given star). This is just as
> dynamically unstable as Niven's version, but that's not what I'm
> pondering right now, assume some agency holds it in place with regard
> to the star.
>
> The torus would have an 'inner radius' centered on the star of 2 AU.
> The torus is specifcally _not_ rotating around the star, instead its
> surface gravity derives from its own mass.

If it's not piecewise orbiting the star (like Niven's), it's *more*
dynamically unstable. In fact it's statically unstable, I guess you'd
say. The whole thing will just crumple together under the star's
gravity -- and its own -- and fall into the star.

So your agency will have to be able to hold it up, literally, against
that.

> 1. For a torus this size, is it possible to maintain something close
> to a 1G surface gravity over the whole surface of the torus based on
> mass alone?

I'm sure it is.

For the math, you can probably approximate it as an infinitely long
straight cylinder. g=2Gd/r, where d is the linear density of the thing
(kilograms per meter of length).

--Z

--
"And Aholibamah bare Jeush, and Jaalam, and Korah: these were the borogoves..."
*

[eripe]

On Monday, May 20, 2013 11:52:16 AM UTC+7, Johnny1a wrote:
> I've been playing with a vague concept, and going back over old
>
> threads looking for information bearing on it, but I have not found
>
> anything that quite fits it.
>
>
>
> Imagine a Niven Ring, i.e. a ringworld around a star, but instead of
>
> the flat ribbon Niven suggests, imagine a torus, a cylinder of rock
>
> and soil and water wrapped around the star at roughly 1 AU radius (or
>
> the equivalent distance for the given star). This is just as
>
> dynamically unstable as Niven's version, but that's not what I'm
>
> pondering right now, assume some agency holds it in place with regard
>
> to the star.
>
>
>
> The torus would have an 'inner radius' centered on the star of 2 AU.
>
> The torus is specifcally _not_ rotating around the star, instead its
>
> surface gravity derives from its own mass. Here's where the concept
>
> is uncertain:
>

Interesting concept!
You mention 1 AU and then later 2 AU ?

>
> 1. For a torus this size, is it possible to maintain something close
>
> to a 1G surface gravity over the whole surface of the torus based on
>
> mass alone? That is, a 1G pull on a surface poin on the outer rim,
>
> the inner rim, and 'top' and 'bottom' points at 90 degrees from the
>
> plane? Slight variations might be acceptable, but the idea is a
>
> loosely Earth-like biosphere and environment on the surface.
>
>
>
> 2. Is there any relatively simple forumla(s) to calculate the
>
> relationship between mass, volume, and surface gravity (and escape
>
> velocity) of this thing, or is it inherently complex? That is, how
>
> big does the diameter of the 'doughnut' from inner to outer edge need
>
> to be for a given density to get close to 1G on the surface (if that
>
> can be done evenly).
>
>

On first thought Id agree with Andrew that the gravity of an infinite cylinder is a good guess, (4240 km radius for eath gravity, given earth density), but on second thought im not so sure. There is just so much mass, and Im not sure you can ignore it.

>
> 3. The interior of the torus _may_ be rotating with regard to the
>
> star, one idea I was toying with was that a circulating liquid or the
>
> equvalent intside the torus might be providing some of the support
>
> aganst stellar gravity.
>

A liquid inside could rotate fast enough to counter gravity and provide tension in the ring, preventing it from collapse. What will keep this liquid flowing? (the earth is moving around the sun at 30 km/sec, this liquid must go a bit faster)
Alternatively it could be kept at high pressure to maintain the shape (like a bike wheel). Astronomically high pressure. If the ring is 4240 km radius, half a toroid is 1,46e29 kg. (25000 earths) This must then be supported by two cross sections of the toroid for a pressure of 13e15 Pa. Thats about 5 million times the maximum strength of steel.

>
>
> 4. Like the classic 'Gunkel tube', I was toying with the idea that
>
> the torus might rotate with regard to its own circular iner axis,
>
> providing a day-night cycle in that way. How big can the torus get
>
> and do that while maintaiing a viable biosphere on the surface?

There is no limit when you are using god-strength materials. It can already maintain the shape of an astronomical amount of mass against gravity.
I suppose the limit is derived from the cycle time. If you only want 12 hours on each side, (to avoid overheating/freezing out) the rotational speed is set. If the radius becomes too large you will eventually rotate so fast that matter gets thrown of the surface.
The supermaterial that makes the torus shell could probably easily be elastic enough that the tension/compression from the rotation isnt a problem. Just remember that anyone building anything on the shell will have to deal with this. (the next city is further away in the night time.)
I have no idea what it will do to a body of Water, probably like an earthquake.

[eripe]

Forgot to say it dosent have to be a liquid core. It can also be an iron core, suspended by magnets, and rotating very fast, like proposed in the launch loop or power loop idea.
That would actually be better because you woulnt have to use frictionless liquid.

http://launchloop.com/PowerLoop

[Johnny1a]

On May 21, 9:32 pm, eripe <eripe...@gmail.com> wrote:
> On Monday, May 20, 2013 11:52:16 AM UTC+7, Johnny1a wrote:
> > I've been playing with a vague concept, and going back over old
>
> > threads looking for information bearing on it, but I have not found
>
> > anything that quite fits it.
>
> > Imagine a Niven Ring, i.e. a ringworld around a star, but instead of
>
> > the flat ribbon Niven suggests, imagine a torus, a cylinder of rock
>
> > and soil and water wrapped around the star at roughly 1 AU radius (or
>
> > the equivalent distance for the given star).  This is just as
>
> > dynamically unstable as Niven's version, but that's not what I'm
>
> > pondering right now, assume some agency holds it in place with regard
>
> > to the star.
>
> > The torus would have an 'inner radius' centered on the star of 2 AU.
>
> > The torus is specifcally _not_ rotating around the star, instead its
>
> > surface gravity derives from its own mass.  Here's where the concept
>
> > is uncertain:
>
> Interesting concept!
> You mention 1 AU and then later 2 AU ?

Sorry, I was being imprecise. The inner _radius_ of the doughnut
would be 1 AU (or something like that, depending on the specific
star), the _diameter_ of the inner hole centered on the star would be
roughly 2 AU. I was simply positing a doughnut at about the distance
of Earth's orbit (adjusted for the details of the star).

> > 1.  For a torus this size, is it possible to maintain something close
>
> > to a 1G surface gravity over the whole surface of the torus based on
>
> > mass alone?  That is, a 1G pull on a surface poin on the outer rim,
>
> > the inner rim, and 'top' and 'bottom' points at 90 degrees from the
>
> > plane?  Slight variations might be acceptable, but the idea is a
>
> > loosely Earth-like biosphere and environment on the surface.
>
> > 2.  Is there any relatively simple forumla(s) to calculate the
>
> > relationship between mass, volume, and surface gravity (and escape
>
> > velocity) of this thing, or is it inherently complex?  That is, how
>
> > big does the diameter of the 'doughnut' from inner to outer edge need
>
> > to be for a given density to get close to 1G on the surface (if that
>
> > can be done evenly).
>
> On first thought Id agree with Andrew that the gravity of an infinite cylinder is a good guess, (4240 km radius for eath gravity, given earth density), but on second thought im not so sure. There is just so much mass, and Im not sure you can ignore it.

That's what I was wondering. Intuition can be a dangerous guide on
such things, I remember a couple of years ago somebody did the math
for an Alderson Disk. It had been assumed that an infinite flat plain
would provide a useful guide to the gravitational behavior of a very
finite Alderson Disk, so that surface gravity would be normal to the
plane except near the edges. That had always been the assumption, but
IIRC it turned out that in fact the infinite plane was not accurate as
a model, and the actual 'direction' of gravity on an Alderson Disk
would be notably tilted.

It's true that locally the torus would be very similar to a cylinder,
but sometimes weird things happen with weird shapes.

>
> > 3.  The interior of the torus _may_ be rotating with regard to the
>
> > star, one idea I was toying with was that a circulating liquid or the
>
> > equvalent intside the torus might be providing some of the support
>
> > aganst stellar gravity.
>
>
>
>

> > 4.  Like the classic 'Gunkel tube', I was toying with the idea that
>
> > the torus might rotate with regard to its own circular iner axis,
>
> > providing a day-night cycle in that way.  How big can the torus get
>
> > and do that while maintaiing a viable biosphere on the surface?
>
> There is no limit when you are using god-strength materials. It can already maintain the shape of an astronomical amount of mass against gravity.

Yeah, but in this case, we're by definition _not_ deailing with
supermaterials, at least at the surface. The Earth-like biosphere on
the outer surface of the torus means that we'd be dealing with rock,
soil, sand, ice, water, air, and other such familiar substances.
There may well be supermaterials inside it, but the surface can't be
made of them.

[Jens Kleimann]

On 22.05.2013 04:50, Johnny1a wrote:
> On May 21, 9:32 pm, eripe <eripe...@gmail.com> wrote:
>> On Monday, May 20, 2013 11:52:16 AM UTC+7, Johnny1a wrote:
>>> I've been playing with a vague concept, and going back over old
>>> threads looking for information bearing on it, but I have not found
>>> anything that quite fits it.
>>> Imagine a Niven Ring, i.e. a ringworld around a star, but instead of
>>> the flat ribbon Niven suggests, imagine a torus, a cylinder of rock
>>> and soil and water wrapped around the star at roughly 1 AU radius (or
>>> the equivalent distance for the given star). This is just as
>>> dynamically unstable as Niven's version, but that's not what I'm
>>> pondering right now, assume some agency holds it in place with regard
>>> to the star.
>>> The torus would have an 'inner radius' centered on the star of 2 AU.
>>> The torus is specifcally _not_ rotating around the star, instead its
>>> surface gravity derives from its own mass. Here's where the concept
>>> is uncertain:

I note in passing that there are _two_ reasons why one might want such a structure to rotate: First to use centrifugal acceleration as a replacement for gravitational acceleration (=> angular frequency sqrt(1gee/1AU) => one rotation every 8.5 days), second to counteract solar gravity in order to reduce mechanical stress (=> angular frequency sqrt[GMsun/(1AU)^3] => one rotation per year, ignoring self-gravity). In your case, you do not need the former, but could well use the latter.

>>> 1. For a torus this size, is it possible to maintain something close
>>> to a 1G surface gravity over the whole surface of the torus based on
>>> mass alone? That is, a 1G pull on a surface poin on the outer rim,
>>> the inner rim, and 'top' and 'bottom' points at 90 degrees from the
>>> plane? Slight variations might be acceptable, but the idea is a
>>> loosely Earth-like biosphere and environment on the surface.

In the general (and still more interesting) case of comparable major and minor radii, this is not possible. On the "outer equator", all the mass pulls inward, on the "inner equator" (where the other side of the torus is up ahead in the sky), a large chunk of mass tries to pull you away from the ground (albeit unsuccessfully), and at 90 degrees, there is a remaining force component towards the center of mass, pulling stuff inwards.
However, the radii which you picture here make the structure (locally) so close to a linear cylinder that these differences won't matter much (see below).

>>> 2. Is there any relatively simple forumla(s) to calculate the
>>> relationship between mass, volume, and surface gravity (and escape
>>> velocity) of this thing, or is it inherently complex? That is, how
>>> big does the diameter of the 'doughnut' from inner to outer edge need
>>> to be for a given density to get close to 1G on the surface (if that
>>> can be done evenly).

Mass and volume: M = rho V = rho 2pi^2 R r^2.
Interestingly, this is the same volume as for an unbent cylinder of the same length, so bending a cylinder into a torus does not change its total volume.

Surface gravity: Complicated in the general case, but not here, see below.

Escape speed: now this is different. For an infinitely long cylinder, the potential does not stay finite at infinity, so the escape speed is infinite; the analogy breaks down here. We have to distinguish what place you want to escape to:

a) To reach a destination "height" hD which is small compared to 1AU, it takes
v_esc = 2 sqrt[G d log(hD/h0)] starting from h0 (e.g. 4240 km). Going to orbit is thus much more expensive.
b) Interplanetary distances: This depends a lot on your directon of departure. Inwards, gravity partially cancels, outwards you need to balance the pull from the entire torus.
c) Leaving the solar system: Think of the entire torus mass (~0.15 Msun) being added to that of the Sun. Escape speed is proportional to sqrt(Msun), hence it goes up by a few percent.

>> On first thought Id agree with Andrew that the gravity of an infinite cylinder is a good guess, (4240 km radius for eath gravity, given earth density), but on second thought im not so sure. There is just so much mass, and Im not sure you can ignore it.
>
> That's what I was wondering. Intuition can be a dangerous guide on
> such things, I remember a couple of years ago somebody did the math
> for an Alderson Disk. It had been assumed that an infinite flat plain
> would provide a useful guide to the gravitational behavior of a very
> finite Alderson Disk, so that surface gravity would be normal to the
> plane except near the edges. That had always been the assumption, but
> IIRC it turned out that in fact the infinite plane was not accurate as
> a model, and the actual 'direction' of gravity on an Alderson Disk
> would be notably tilted.
>
> It's true that locally the torus would be very similar to a cylinder,
> but sometimes weird things happen with weird shapes.

The math for the Alderson gravitational potential had been worked out by Erik and myself a few years back. The conclusions were that
1. the infinite plane is a good approximation as long as you stay away from any of the two edges,
2. noticeable deviations occur as you leave the central part,
3. spinning the disk helps to reduce variations of local g; in particular, it can be adjusted such that either gravity or potential (but usually not both) are the same at two distinct radii that one can pick freely, and
4. having surface density vary with radius can give a reasonably, though not perfectly, constant surface field.
5. Unlike rotation, the latter method cannot be used to counteract the gravitational pull of a central star.
The details are still at [http://www.tp4.rub.de/~jk/science/gravity/chapt_alderson.html, by the way.

The effect of substituting "infinite" for "large but finite" is a reasonable concern. However, using the formula for the potential of a "thin" torus" -- effectively an thin ring of zero minor and finite major radius R (see second page of [http://www.tp4.rub.de/~jk/science/gravity/gravpot-disk.pdf], then differentiating to get the force and noting that for a torus, m = 2pi R d) --, one can evaluate the force at a distance dr from the ring at different positions (inside, on "top", and outside). With a major radius of R=1AU, dr=4240km is very small indeed, and the relative deviations from F=2Gd/dr can be demonstrated to be entirely unnoticeable for all practical purposes.

>>> 3. The interior of the torus _may_ be rotating with regard to the
>>> star, one idea I was toying with was that a circulating liquid or the
>>> equvalent intside the torus might be providing some of the support
>>> aganst stellar gravity.

Is there a specific reason why you do not want your torus to rotate? Wouldn't that be the simplest and most effective way to counteract stellar gravity? The way I see it, it could well be that well-balanced rotation can create an equilibrium even without exoctic super-stiff materials. (The caveat being that this equilibrium would be unstable not only against displacement just like the Niven ring, but also against deformation towards an 8-shaped configuration. But you said you did not want to consider these effects here...)

>>> 4. Like the classic 'Gunkel tube', I was toying with the idea that
>>> the torus might rotate with regard to its own circular iner axis,
>>> providing a day-night cycle in that way. How big can the torus get
>>> and do that while maintaiing a viable biosphere on the surface?
>> There is no limit when you are using god-strength materials. It can already maintain the shape of an astronomical amount of mass against gravity.
>
> Yeah, but in this case, we're by definition _not_ deailing with
> supermaterials, at least at the surface. The Earth-like biosphere on
> the outer surface of the torus means that we'd be dealing with rock,
> soil, sand, ice, water, air, and other such familiar substances.
> There may well be supermaterials inside it, but the surface can't be
> made of them.

If you have an inner rigid "skeleton" to keep it in shape (and that is massive enough to be the main source of local gravity), everything that you place on the outer "skin" will stick to it. No problem with a user-friendly coating here.

Jens.

--
Remove '_nospam' for actual email address.

[Andrew Plotkin]

Here, Jens Kleimann <yatterin...@web.de> wrote:
>
> With a
> major radius of R=1AU, dr=4240km is very small indeed, and the
> relative deviations from F=2Gd/dr can be demonstrated to be entirely
> unnoticeable for all practical purposes.

Happy to hear it, as I did no math whatsoever when I posted earlier.
:)

[Johnny1a]

On May 22, 5:59 am, Jens Kleimann <yattering_nos...@web.de> wrote:
>
>
> >>> 1.  For a torus this size, is it possible to maintain something close
> >>> to a 1G surface gravity over the whole surface of the torus based on
> >>> mass alone?  That is, a 1G pull on a surface poin on the outer rim,
> >>> the inner rim, and 'top' and 'bottom' points at 90 degrees from the
> >>> plane?  Slight variations might be acceptable, but the idea is a
> >>> loosely Earth-like biosphere and environment on the surface.
>
> In the general (and still more interesting) case of comparable major and minor radii, this is not possible. On the "outer equator", all the mass pulls inward, on the "inner equator" (where the other side of the torus is up ahead in the sky), a large chunk of mass tries to pull you away from the ground (albeit unsuccessfully), and at 90 degrees, there is a remaining force component towards the center of mass, pulling stuff inwards.
> However, the radii which you picture here make the structure (locally) so close to a linear cylinder that these differences won't matter much (see below).

That was my concern, I knew that a 'general torus' would produce that
effect, but I didn't know if it would carry over at this scale.

>
> > It's true that locally the torus would be very similar to a cylinder,
> > but sometimes weird things happen with weird shapes.

> The effect of substituting "infinite" for "large but finite" is a reasonable concern. However, using the formula for the potential of a "thin" torus" -- effectively an thin ring of zero minor and finite major radius R (see second page of [http://www.tp4.rub.de/~jk/science/gravity/gravpot-disk.pdf], then differentiating to get the force and noting that for a torus, m = 2pi R d) --, one can evaluate the force at a distance dr from the ring at different positions (inside, on "top", and outside). With a major radius of R=1AU, dr=4240km is very small indeed, and the relative deviations from F=2Gd/dr can be demonstrated to be entirely unnoticeable for all practical purposes.
>
> >>> 3.  The interior of the torus _may_ be rotating with regard to the
> >>> star, one idea I was toying with was that a circulating liquid or the
> >>> equvalent intside the torus might be providing some of the support
> >>> aganst stellar gravity.
>
> Is there a specific reason why you do not want your torus to rotate? Wouldn't that be the simplest and most effective way to counteract stellar gravity? The way I see it, it could well be that well-balanced rotation can create an equilibrium even without exoctic super-stiff materials.

When I commented about rotation, I was mainly thinking in terms of
Ringworld's use of rotation to substitute for gravity, I specifically
didn't want this thing spinning at over 700 miles/sec, for a number of
reasons. Spinning it more slowly to counteract the strain of stellar
gravity, though, is acceptable, and the solution I'll probably go with
when I'm done.

(The caveat being that this equilibrium would be unstable not only
against displacement just like the Niven ring, but also against
deformation towards an 8-shaped configuration. But you said you did
not want to consider these effects here...)

Well, not _yet_. I was mainly concerned with whether the mass-gravity
torus idea was even viable at all before I considered the issue of
displacement.

>
> >>> 4.  Like the classic 'Gunkel tube', I was toying with the idea that
> >>> the torus might rotate with regard to its own circular iner axis,
> >>> providing a day-night cycle in that way.  How big can the torus get
> >>> and do that while maintaiing a viable biosphere on the surface?
> >> There is no limit when you are using god-strength materials. It can already maintain the shape of an astronomical amount of mass against gravity.
>
> > Yeah, but in this case, we're by definition _not_ deailing with
> > supermaterials, at least at the surface.  The Earth-like biosphere on
> > the outer surface of the torus means that we'd be dealing with rock,
> > soil, sand, ice, water, air, and other such familiar substances.
> > There may well be supermaterials inside it, but the surface can't be
> > made of them.
>
> If you have an inner rigid "skeleton" to keep it in shape (and that is massive enough to be the main source of local gravity), everything that you place on the outer "skin" will stick to it. No problem with a user-friendly coating here.
>
> Jens.

Thanks. This is very useful, and very helpful!

[Jens Kleimann]

On 22.05.2013 04:32, eripe wrote:
> On Monday, May 20, 2013 11:52:16 AM UTC+7, Johnny1a wrote:
>> 4. Like the classic 'Gunkel tube', I was toying with the idea that
>> the torus might rotate with regard to its own circular iner axis,
>> providing a day-night cycle in that way. How big can the torus get
>> and do that while maintaiing a viable biosphere on the surface?

> There is no limit when you are using god-strength materials. It can already maintain the shape of an astronomical amount of mass against gravity.
> I suppose the limit is derived from the cycle time. If you only want 12 hours on each side, (to avoid overheating/freezing out) the rotational speed is set. If the radius becomes too large you will eventually rotate so fast that matter gets thrown of the surface.

At the (by now) somewhat canonical radius of 4240 km, centrifugal acceleration for a 24h rotation period is just 0.002g. This is even smaller than the variation on Earth from pole to equator; so no need to worry here. Things will start to fall apart if the spin rate exceeds about one rotation per hour. Or, in answer to the original question, for a 24h rotation period this will happen at a radius of about 4240km/0.002=2.12Mm. Note that if you still want 1g at the surface, density would need to go down by a (probably undesirably low) factor of 0.002!

> The supermaterial that makes the torus shell could probably easily be elastic enough that the tension/compression from the rotation isnt a problem. Just remember that anyone building anything on the shell will have to deal with this. (the next city is further away in the night time.)
> I have no idea what it will do to a body of Water, probably like an earthquake.

Hm, let's see. The total length or a 'grand tour' along the torus is 2pi(R-r) on the inside (dayside) and 2pi(R+r) on the outside (nightside). This difference of 4pi r is uniformly distributed over the entire length of 2piR. The _relative_ length change from dayside to nightside is thus
2r / R = 8480km / 1AU = 0.00005, which seems rather small.
IIRC, the reason why a Gunkel tube could keep rotating in the first place is because the defomation-induced stresses are so very low due to negligible ring curvature. If they were larger, rotation would slow down pretty soon.

[eripe]

The total length or a 'grand tour' along the torus is 2pi(R-r) on the inside (dayside) and 2pi(R+r) on the outside (nightside). This difference of 4pi r is uniformly distributed over the entire length of 2piR. The _relative_ length change from dayside to nightside is thus
>
> 2r / R = 8480km / 1AU = 0.00005, which seems rather small.
>
> IIRC, the reason why a Gunkel tube could keep rotating in the first place is because the defomation-induced stresses are so very low due to negligible ring curvature. If they were larger, rotation would slow down pretty soon.
>
>

Good Work on actually knowing instead of guessing!
The 0,00005 would be the strain on the materials. For steel, it would correspond to the thermal expansion from a 2,2 degree difference in temperature. Clearly, the Railway need not be concerned.

For concrete, the breaking tensile strain is about 0,00012, still bigger but not comfortably so.
However, the breaking compressive strain is 10 times higher, so make sure you do your casting in the nighttime.

For a mountain, im sure there would be some cracking, and I guess that would limit the slope they could stand with.

How would a mountain form? Carefully lowered into position by the builder? or first make the superring, and then throw some dirt at it, to see what happens.

[Johnny1a]

On May 23, 4:20 am, Jens Kleimann <yattering_nos...@web.de> wrote:
>
> Hm, let's see. The total length or a 'grand tour' along the torus is 2pi(R-r) on the inside (dayside) and 2pi(R+r) on the outside (nightside). This difference of 4pi r is uniformly distributed over the entire length of 2piR. The _relative_ length change from dayside to nightside is thus
> 2r / R = 8480km / 1AU = 0.00005, which seems rather small.
> IIRC, the reason why a Gunkel tube could keep rotating in the first place is because the defomation-induced stresses are so very low due to negligible ring curvature. If they were larger, rotation would slow down pretty soon.
>
> Jens.

Excellent. :)

I don't consider that 4240 km radius to be written in stone (well, in
a way it is, given the subject matter), but it's a good starting
default. I might want to increase it somewhat, and compensate for the
lower density in some other way, but like I said, I'm just starting to
flesh out the concept.

Assuming Earth-density, I make the 4240 radius torus as having a mass
of about .15 Sol (assuming I didn't slip a digit when I did the math,
I am half-asleep as I post). I also get a surface area of ~50,000
Earths. From an mass-to-surface area efficiency POV, that's pretty
rotten, compared to (say) a Niven ring, but I'm assuming that the
creators of this thing had other priorities than said efficiency.

[Johnny1a]

On May 24, 4:00 am, eripe <eripe...@gmail.com> wrote:
>
> How would a mountain form? Carefully lowered into position by the builder? or first make the > superring, and then throw some dirt at it, to see what happens.

Interesting question, leading to one reason why the Torus is very
different than the Ringworld.

Assuming the Torus is 4240km in radius (interior to the cylinder), and
made of rock and soil and other Earth-like materials, that means that
unlike the Ringworld, the Torus will have a real active 'live'
geology. The Ringworld doesn't really _have_ a geology as such,
everything is pre-sculpted and constant maintenance is needed to keep
the mountains from eroding into the oceans (among other things). The
Ringworld is in essence a gigantic spacecraft, the Torus, OTOH, is
more like a gigantic planet with a weird shape.

If the materials that went into the Torus include a reasonable
fraction of stuff like potassiumn-40, uranium, and thorium, then it
will have a significant internal heat source. That heat will drive
geological processes, though the details are going to be odd by Terran
standards. If the Torus was extremely hot at some stage during its
creation, that heat too will have to leak away, analogous to the 'iron
catastrophe' many geologists think provided some of Earth's internal
heat.

This will be true even if the 'core' is something weird, as long as
the surrounding layers are familiar materials that go down hundreds or
thousands of kilometers. I don't pretend to have any idea how the
details would shake out, but the Torus would likely have its own
mountains and valleys and other features, that would change on their
own over time.

[alie...@gmail.com]

On May 24, 8:41 pm, Johnny1a <shermanl...@hotmail.com> wrote:
> On May 24, 4:00 am, eripe <eripe...@gmail.com> wrote:
>
> > How would a mountain form? Carefully lowered into position by the builder?
> > or first make the superring, and then throw some dirt at it, to see what
> > happens.
>
> Interesting question, leading to one reason why the Torus is very
> different than the Ringworld.
>
> Assuming the Torus is 4240km in radius (interior to the cylinder), and
> made of rock and soil and other Earth-like materials, that means that
> unlike the Ringworld, the Torus will have a real active 'live'
> geology.  The Ringworld doesn't really _have_ a geology as such,
> everything is pre-sculpted and constant maintenance is needed to keep
> the mountains from eroding into the oceans (among other things).  The
> Ringworld is in essence a gigantic spacecraft, the Torus, OTOH, is
> more like a gigantic planet with a weird shape.

If it's built exactly like a planet, I can't see why it wouldn't
exhibit tectonic activity; volcanoes, mountain building, continental
drift and everything. Well, no ice caps.

> If the materials that went into the Torus include a reasonable
> fraction of stuff like potassiumn-40, uranium, and thorium, then it
> will have a significant internal heat source.  That heat will drive
> geological processes, though the details are going to be odd by Terran
> standards.  If the Torus was extremely hot at some stage during its
> creation, that heat too will have to leak away, analogous to the 'iron
> catastrophe' many geologists think provided some of Earth's internal
> heat.

If there's significant iron in the core the, um, bagelworld will
have a fairly weird magnetic field, won't it? A perfect "smoke ring"
rotation of the core is equivalent to a toroid coil meaning no B field
but you can't make the A field go away (which might make a useful
story point). OTOH perfect smoke ring rotation in the core is unlikely
so there will probably be local N and S poles scattered all over the
thing, no?

> This will be true even if the 'core' is something weird, as long as
> the surrounding layers are familiar materials that go down hundreds or
> thousands of kilometers.  I don't pretend to have any idea how the
> details would shake out, but the Torus would likely have its own
> mountains and valleys and other features, that would change on their
> own over time.

AIUI in Earth's case, mountain building and such happens due to the
interface between the mantle and the crust. If the interior is a
hollow toroidal shell of suoerscrith (full of gravity generators and
whatnot) then there need be no mantle but there will still be cyclic
compression-relaxation stresses in the crust as the thing rotates,
(assuming the shell is capable of the required deformation) allowing
for at least minimal tectonics etc., I'd think, but I don't see that
generating Alps or Himalayas.

How would you get seasons, or say ice ages (assuming you wanted
them); change the coupling between the shell and the crust with a
bigger-than-worlds clutch? That's the only way I can think of to
change the insolation other than changing the major radius somehow,
but wouldn't that crack the hell out of the crust?

I'm pretty sure the Ringworld solution for mountains and seas would
work but would have to be fairly obvious. No way to get a Fist-Of-God,
though.

Also, what's the atmospheric circulation going to be like, more or
less entrained by the ring rotation? The weather will be pretty weird
in any case.

Could a moon stably orbit the thing by threading the hole? I read
Jens' analysis through three times (and I recall his and Erik Max
Francis' Alderson disk analysis) but I just can't quite make up my
mind.


Mark L. Fergerson

[eripe]

>
>
> Could a moon stably orbit the thing by threading the hole?

Sadly I dont have the math, but the moon must rotate around the sun as well as around the torus body, so it will be spiraling along.

The moon only feels gravity towards the center of the torus cross section, so that the orbit will be similar to a polar orbit around a planet.
That Means the plane of the orbit will not turn, and so the moon will crash after a few months.

http://www.phy6.org/Education/wlopolar.html " If the orbital plane of the polar satellite points at the Sun now, in three months' time the Sun's motion across the sky would make that plane perpendicular to the Sun's direction."

[Greg Goss]

"Must rotate around the sun"

Nit: "revolve".

Perhaps not. You are thinking that you need to orbit the sun in order
to prevent falling INTO the sun. But you could provide the necessary
lift by setting the "inside" portion of the moon's orbit a bit closer
to the torus. The gravity of the torus at that point would "lift" the
moon back up from the sun.

So now you have an unbalanced force pulling the torus towards the sun.
You can either install the moons in opposing pairs, or set the
moonside portion of the torus a touch further from the sun.
--
We are geeks. Resistance is voltage over current.

[Johnny1a]

On May 25, 4:47 am, "n...@bid.nes" <alien8...@gmail.com> wrote:
> On May 24, 8:41 pm, Johnny1a <shermanl...@hotmail.com> wrote:
>

> > On May 24, 4:00 am, eripe <eripe...@gmail.com> wrote:
>
>
> > If the materials that went into the Torus include a reasonable
> > fraction of stuff like potassiumn-40, uranium, and thorium, then it
> > will have a significant internal heat source.  That heat will drive
> > geological processes, though the details are going to be odd by Terran
> > standards.  If the Torus was extremely hot at some stage during its
> > creation, that heat too will have to leak away, analogous to the 'iron
> > catastrophe' many geologists think provided some of Earth's internal
> > heat.
>
>     If there's significant iron in the core the, um, bagelworld will
> have a fairly weird magnetic field, won't it? A perfect "smoke ring"
> rotation of the core is equivalent to a toroid coil meaning no B field
> but you can't make the A field go away (which might make a useful
> story point). OTOH perfect smoke ring rotation in the core is unlikely
> so there will probably be local N and S poles scattered all over the
> thing, no?

Excellent question, I hadn't even considered the magnetic effects yet.

>
> > This will be true even if the 'core' is something weird, as long as
> > the surrounding layers are familiar materials that go down hundreds or
> > thousands of kilometers.  I don't pretend to have any idea how the
> > details would shake out, but the Torus would likely have its own
> > mountains and valleys and other features, that would change on their
> > own over time.
>
>   AIUI in Earth's case, mountain building and such happens due to the
> interface between the mantle and the crust. If the interior is a
> hollow toroidal shell of suoerscrith (full of gravity generators and
> whatnot) then there need be no mantle but there will still be cyclic
> compression-relaxation stresses in the crust as the thing rotates,
> (assuming the shell is capable of the required deformation) allowing
> for at least minimal tectonics etc., I'd think, but I don't see that
> generating Alps or Himalayas.

No, but this thing _will_ have a mantle of some sort, or the
equivalent. I don't know yet if it's rock-and-metal all the way to
the center of the cylinder or not, but even if there's an inner core
of weird, there will be _at least_ some _hundreds_ of miles of rock
and other 'conventional' meterials below the outer surface, including
a substantial percentage of heat-producing radioactives. (I don't
know yet if the percentage of radioactives will be higher than that of
Earth or not.)

Now, what form that geology will take is a fantastic good question.

>
>   How would you get seasons, or say ice ages (assuming you wanted
> them); change the coupling between the shell and the crust with a
> bigger-than-worlds clutch? That's the only way I can think of to
> change the insolation other than changing the major radius somehow,
> but wouldn't that crack the hell out of the crust?

One way to get seasons on the Torus would be to use a trick Niven
suggested for a Ringworld, let the object 'rise and fall' along the
'vertical' axis of the central star (vertical relative to the plane of
the Torus/Ringworld). As the object bobs up and down, the star would
be at an angle and you'd get seasons. This would have some potential
side effects, though.

Another way might be to let whatever agency is holding the object in
place against its natural dynamic instability move it back and forth a
bit, so the star is held a bit off-center. That seems inelegant,
though, and would also produce side-effects.

>
>   I'm pretty sure the Ringworld solution for mountains and seas would
> work but would have to be fairly obvious. No way to get a Fist-Of-God,
> though.

Which is one advantage a mass-gravity Torus has for its inhabitants
over a Ringworld. The enormous rotational velocity of a Ringworld
means that anything that hits it hits at the equivalent of over 700
miles per second, with a kinetic energy of gyahh! (More precisely, at
770 miles/sec, every kilogram of impactor strikes with an energy of
about 180 metric tons of TNT, varying a bit depending on the direction
of impact. A 100 kilogram human being striking the ground at that
velocity would have an impact energy greater than the Hiroshima bomb.

The Torus experiences impactors at about the same general energy level
as Earth. Granted, it will also experience more of them, everything
else being equal, because its gravity draws them in in a way the
Ringworld does not, but on balance I'd say the Torus is safer on that
count than the Ringworld. It can also soak up more energy than the
Ringworld can without catastrophe.

>   Also, what's the atmospheric circulation going to be like, more or
> less entrained by the ring rotation? The weather will be pretty weird
> in any case.

That question I have pondered, but I don't have any clear idea yet.
The thing is that on Earth (or similar world), you have a warm equator
and colder poles, and heat flows from equator to poles, generally
speaking. That drives the large-scale climate and ocean movements.

The Torus has a warm and cold zone, the inner and outer rims of the
Torus. But in the simplest conception of the thing, every point on
the surface passes through both every 24 hours. Likewise, there are
zones equivalent to the poles, where the radiation from the star comes
in parallel to the surface, at the 'top' and 'bottom' of the Torus,
but again, every point on the Torus rotates through both the
perpendicular and parallel zones every 24 hours.

At first glance, that ought to make heat distribution very even on the
large scale, like a planet with no axial tilt, only more so. The
differences in albedo between different kinds of large-scale terrain
will have some effect on that, of course, as will the different heat
transfer capacities of various solids and liquids. But it still looks
like a very even distribution at first glance.

The day-night rotation is weird in another way: it's everywhere. On
Earth, you have the highest rate of rotation at the equator, falling
away to zero at the poles. That drives several weather effects. On
the Torus, there's no 'zero point' on the surface, everyone is
rotating once in 24 hours. What would this do to the weather?
Anybody got any thoughts?

Also, you've got potential;y 2 rotations to think about, the 24 hour
'fast' rotation around the axis of the cylinder, and the once-a-year
rotation around the star. The latter is very slow and acts on a big
scale, but it might matter.
>
>   Mark L. Fergerson- Hide quoted text -
>
> - Show quoted text -

[Des]

I would think that the only part of such a torus where "up was up, and
down was down", would be on the inside surface, opposite to the star
and immediately normal to the star. An enormous torus would give a
decent "Non-dizzy" zone. Most of the area would not be very usable.

It is actually quite simple to have a dynamically stable Ringworld, if
one accepts that Scrith exists. A thin scrith disk on the underside of
the ring, concentric with it, extending in the direction of the
primary. 3 or more masses (LARGE) attached symmetrically to the inner
diameter of the disk. Neutronium in stasis, normal matter covered in
scrith for protection, whatever.Needs a bit of calculation, but it is
just Newtonian stuff, nothing hard.

[alie...@gmail.com]

On May 26, 7:47 am, Greg Goss <go...@gossg.org> wrote:

No, he's talking about the angular momentum vector of the moon's
orbit pointing consistently in the same direction WRT the "fixed
stars".

That can't happen with the donut world. Dragging the orbital plane
around would force it to precess, eventually crashing the moon....
unless the orbit "slides" along the donut to maintain the orbital
plane's orientation WRT the stars. ISTM that'd have to be artificially
maintained.


Mark L. Fergerson

[alie...@gmail.com]

On May 26, 2:11 pm, Des <desmondkavan...@gmail.com> wrote:
> I would think that the only part of such a torus where "up was up, and
> down was down", would be on the inside surface, opposite to the star
> and immediately normal to the star. An enormous torus would give a
> decent "Non-dizzy" zone. Most of the area would not be very usable.

Why? Are you thinking solar gravity adding to the planet's gravity?
That's basically solar tides which don't AFAIK make anybody dizzy.
Remember this thing will be at 1 AU from the presumably Sol-type star.

> It is actually quite simple to have a dynamically stable Ringworld, if
> one accepts that Scrith exists. A thin scrith disk on the underside of
> the ring, concentric with it, extending in the direction of the
> primary. 3 or more masses (LARGE) attached symmetrically to the inner
> diameter of the disk. Neutronium in stasis, normal matter covered in
> scrith for protection, whatever.Needs a bit of calculation, but it is
> just Newtonian stuff, nothing hard.

Nope, still won't work- ring or torus worlds aren't stable because
the center of mass of a ring (or torus) world is not in orbit around
the star. Your dangly bits don't move the center of mass. The first
one that gets closer to the star than the others will drag the whole
thing in.


Mark L. Fergerson

[alie...@gmail.com]

On May 26, 8:34 am, Johnny1a <shermanl...@hotmail.com> wrote:
> On May 25, 4:47 am, "n...@bid.nes" <alien8...@gmail.com> wrote:
>
> > On May 24, 8:41 pm, Johnny1a <shermanl...@hotmail.com> wrote:
>
> > > On May 24, 4:00 am, eripe <eripe...@gmail.com> wrote:
>
> > > If the materials that went into the Torus include a reasonable
> > > fraction of stuff like potassiumn-40, uranium, and thorium, then it
> > > will have a significant internal heat source.  That heat will drive
> > > geological processes, though the details are going to be odd by Terran
> > > standards.  If the Torus was extremely hot at some stage during its
> > > creation, that heat too will have to leak away, analogous to the 'iron
> > > catastrophe' many geologists think provided some of Earth's internal
> > > heat.
>
> >     If there's significant iron in the core the, um, bagelworld will
> > have a fairly weird magnetic field, won't it? A perfect "smoke ring"
> > rotation of the core is equivalent to a toroid coil meaning no B field
> > but you can't make the A field go away (which might make a useful
> > story point). OTOH perfect smoke ring rotation in the core is unlikely
> > so there will probably be local N and S poles scattered all over the
> > thing, no?
>
> Excellent question, I hadn't even considered the magnetic effects yet.

Something to think about depending on the culture(s) living there.

Oh, and the wildlife!

> > > This will be true even if the 'core' is something weird, as long as
> > > the surrounding layers are familiar materials that go down hundreds or
> > > thousands of kilometers.  I don't pretend to have any idea how the
> > > details would shake out, but the Torus would likely have its own
> > > mountains and valleys and other features, that would change on their
> > > own over time.
>
> >   AIUI in Earth's case, mountain building and such happens due to the
> > interface between the mantle and the crust. If the interior is a
> > hollow toroidal shell of suoerscrith (full of gravity generators and
> > whatnot) then there need be no mantle but there will still be cyclic
> > compression-relaxation stresses in the crust as the thing rotates,
> > (assuming the shell is capable of the required deformation) allowing
> > for at least minimal tectonics etc., I'd think, but I don't see that
> > generating Alps or Himalayas.
>
> No, but this thing _will_ have a mantle of some sort, or the
> equivalent.  I don't know yet if it's rock-and-metal all the way to
> the center of the cylinder or not, but even if there's an inner core
> of weird, there will be _at least_ some _hundreds_ of miles of rock
> and other 'conventional' meterials below the outer surface, including
> a substantial percentage of heat-producing radioactives.  (I don't
> know yet if the percentage of radioactives will be higher than that of
> Earth or not.)
>
> Now, what form that geology will take is a fantastic good question.

According to this:

http://blogs.scientificamerican.com/observations/2011/07/18/nuclear-fission-confirmed-as-source-of-more-than-half-of-earths-heat/

nuclear fission of uranium and thorium alone produces more than half
of Earth's internal heat to the tune of 20 terawatts! Scale that up to
your torus world's much greater cylindrical mantle volume and I think
there's a problem. I'm guessing the proportion of fissionables per
unit volume will have to be much lower than Earth's to keep the planet
from staying molten.

> >   How would you get seasons, or say ice ages (assuming you wanted
> > them); change the coupling between the shell and the crust with a
> > bigger-than-worlds clutch? That's the only way I can think of to
> > change the insolation other than changing the major radius somehow,
> > but wouldn't that crack the hell out of the crust?
>
> One way to get seasons on the Torus would be to use a trick Niven
> suggested for a Ringworld, let the object 'rise and fall' along the
> 'vertical' axis of the central star (vertical relative to the plane of
> the Torus/Ringworld).  As the object bobs up and down, the star would
> be at an angle and you'd get seasons.  This would have some potential
> side effects, though.

Yeah, I forgot the bobbing trick. That would change the distance to
the star and hence the amount of solar heat deposited in the
atmosphere but not the number of hours of daylight per day the way
"real" seasons do. Should have the same effect temperature wise but
plants would not get their seasonal cues the same as on Earth.

> Another way might be to let whatever agency is holding the object in
> place against its natural dynamic instability move it back and forth a
> bit, so the star is held a bit off-center.  That seems inelegant,
> though, and would also produce side-effects.

As long as it can prevent the figure eight thing, maintaining an
eccentric orbit might be the best way to go. That way the whole torus
will have predictable pseudoseasons.

> >   I'm pretty sure the Ringworld solution for mountains and seas would
> > work but would have to be fairly obvious. No way to get a Fist-Of-God,
> > though.
>
> Which is one advantage a mass-gravity Torus has for its inhabitants
> over a Ringworld.  The enormous rotational velocity of a Ringworld
> means that anything that hits it hits at the equivalent of over 700
> miles per second, with a kinetic energy of gyahh!  (More precisely, at
> 770 miles/sec, every kilogram of impactor strikes with an energy of
> about 180 metric tons of TNT, varying a bit depending on the direction
> of impact.  A 100 kilogram human being striking the ground at that
> velocity would have an impact energy greater than the Hiroshima bomb.

Gyahh indeed.

> The Torus experiences impactors at about the same general energy level
> as Earth.  Granted, it will also experience more of them, everything
> else being equal, because its gravity draws them in in a way the
> Ringworld does not, but on balance I'd say the Torus is safer on that
> count than the Ringworld.  It can also soak up more energy than the
> Ringworld can without catastrophe.

OTOH if you can't manage a moon the "lunar shield" effect will be
absent.

> >   Also, what's the atmospheric circulation going to be like, more or
> > less entrained by the ring rotation? The weather will be pretty weird
> > in any case.
>
> That question I have pondered, but I don't have any clear idea yet.
> The thing is that on Earth (or similar world), you have a warm equator
> and colder poles, and heat flows from equator to poles, generally
> speaking.  That drives the large-scale climate and ocean movements.

There are also large roughly static cells (Hadley, Ferrell, and
polar) in Earth's atmosphere that maintain position between particular
latitudes; that might transfer to the torus neatly if this:

http://en.wikipedia.org/wiki/File:AtmosphCirc2.png

works as a cross-section of the torus, but that only holds if
there's no (or little) entrainment with rotation. i think.

> The Torus has a warm and cold zone, the inner and outer rims of the
> Torus.  But in the simplest conception of the thing, every point on
> the surface passes through both every 24 hours.  Likewise, there are
> zones equivalent to the poles, where the radiation from the star comes
> in parallel to the surface, at the 'top' and 'bottom' of the Torus,
> but again, every point on the Torus rotates through both the
> perpendicular and parallel zones every 24 hours.
>
> At first glance, that ought to make heat distribution very even on the
> large scale, like a planet with no axial tilt, only more so.  The
> differences in albedo between different kinds of large-scale terrain
> will have some effect on that, of course, as will the different heat
> transfer capacities of various solids and liquids.  But it still looks
> like a very even distribution at first glance.

I oversimplified it in my head to an infinite rotating cylinder with
a linear light/heat source and came to the same conclusion, but there
are those cells to deal with IF they can remain stable. If they can it
will do weird things to the heat transfer between the atmosphere and
the cyclic heating and cooling of the surface by sunlight.

> The day-night rotation is weird in another way:  it's everywhere.  On
> Earth, you have the highest rate of rotation at the equator, falling
> away to zero at the poles.  That drives several weather effects.  On
> the Torus, there's no 'zero point' on the surface, everyone is
> rotating once in 24 hours.  What would this do to the weather?
> Anybody got any thoughts?

If the large cells are stable you'll have very predictably changing
wind direction during the day/night cycle, probably driving equally
predictable rain etc. depending on the locations of seas, lakes,
mountains, and like that.

If the cells are stable their heat internal heat and water vapor
distribution should remain fairly constant as well, adding to the
predictability of the weather.

> Also, you've got potential;y 2 rotations to think about, the 24 hour
> 'fast' rotation around the axis of the cylinder, and the once-a-year
> rotation around the star.  The latter is very slow and acts on a big
> scale, but it might matter.

Oh, it will; there's the entrainment factor.

And we thought climate science on Earth was hard. ;>)


Mark L. Fergerson

[Greg Goss]

Why does the orbital plane need to "drag around"? If the moon
revolves around the same point on the bagel WRT the fixed stars
(regardless of whether the torus is revolving under it), then the
plane of the orbit does not need to change. If the moon does not
revolve around the sun, then you need to provide additional lift to
keep it out of the sun, and that's not difficult.

[Greg Goss]

>"nu...@bid.nes" <alie...@gmail.com> wrote:

>>unless the orbit "slides" along the donut to maintain the orbital
>>plane's orientation WRT the stars. ISTM that'd have to be artificially
>>maintained.

I missed this point in my initial answer. The orbit wouldn't "slide"
along the donut; rather the donut would slide under the moon's orbit.
This was the circumstance I was describing.

It would not be difficult to make it statically stable -- the orbit's
position around the donut could be adjusted to provide enough lift to
keep it out of the sun.

Like the orbit of the donut itself, it's probably dynamically unstable
- I would expect it to be vulnerable to small perturbations, but don't
have the mathematical intuition to describe these.

[Johnny1a]

>   Mark L. Fergerson- Hide quoted text -
>

> - Show quoted text -- Hide quoted text -

>
> - Show quoted text -

Let's consider a simplified case: a Torus motionless with regard to
the star. (Never mind the issues of material strength and stability,
we're just considering the atmosphere and hydrosphere.)

If the Torus did not rotate on its 'inner' axis, and did not rotate
around the star, then the
'hot band' would always be the same part of the Torus, ditto the 'cold
band' on the outside.

By analogue with Earth, the star would heat the ground/water on the
hot strip, via radiation at wavelengths that penetrate an Earth-like
atmosphere. The ground/water would absorb the energy, and reradiate
it at wavelengths the air could absorb, heating it. The hot air would
rise, and more air would rush in to take its place, and a circulation
cell would form driven by the updraft over the 'hot zone'.

The warm air would radiate heat at altitude and fall again, so the
question is whether you'd get a single Torus-wide circulation cell
between the inner and out rims, or a chain of them carrying heat
around the cylinder.

Now if we set the cylinder to spinning on a 24 hour cycle, the thing
is that the spin is in the same direction as the overall circulation,
whereas on Earth the east-to-west spin is perpendicular, more-or-less,
to the equator-to-pole flow of heat. So what happens to our initial
circulation pattern in that case?

At first quick blush one might think that it would accelerate the heat
flow in the direction of spin, while slowing it antispinward. That
is, circulation patterns in the direction of spin would be given an
extra push, while circultion in the opposite direction would be
against the direction of motion, at least for the 'warm' flow. For
the 'cold' return flow the opposite would be the case, assuming our
simplified first assumptions were good.

[Johnny1a]

On May 27, 12:46 am, Johnny1a <shermanl...@hotmail.com> wrote:
> On May 26, 7:50 pm, "n...@bid.nes" <alien8...@gmail.com> wrote:
>
>
>
>
>
> Now if we set the cylinder to spinning on a 24 hour cycle, the thing
> is that the spin is in the same direction as the overall circulation,
> whereas on Earth the east-to-west spin is perpendicular, more-or-less,
> to the equator-to-pole flow of heat.  So what happens to our initial
> circulation pattern in that case?
>

> - Hide quoted text -
>
> - Show quoted text -

Sorry, my error, I meant 'west-to-east', obviously.

[Jens Kleimann]

On 27.05.2013 04:55, Greg Goss wrote:
>> "nu...@bid.nes" <alie...@gmail.com> wrote:
>
>>> unless the orbit "slides" along the donut to maintain the orbital
>>> plane's orientation WRT the stars. ISTM that'd have to be artificially
>>> maintained.
>
> I missed this point in my initial answer. The orbit wouldn't "slide"
> along the donut; rather the donut would slide under the moon's orbit.
> This was the circumstance I was describing.
>
> It would not be difficult to make it statically stable -- the orbit's
> position around the donut could be adjusted to provide enough lift to
> keep it out of the sun.

What has to be kept in mind here is that the local gravity field (with "local" being still large enough to encompass the prospective moon's orbit) is entirely dominated by the Torus; the Sun is way too distant to be anything but a minor correction. As we convinced ourselves upthread, the relevant potential is proportional to log(r/R), and orbits in this form of potential have been studied earlier, for instance at [http://arxiv.org/abs/1009.0422]. They are usually rosette-shaped (see Fig. 5 on page 14), but may be circular in special cases. The important point to note is that there will usually be a smallest and largest distance whose values are fixed by conservation of energy and angular momentum. This finding should not depend on whether the Torus revolves below the moon or not. So these two extreme radii span a region which the moon cannot leave (outbound because its energy is too low, Torus-bound because its angular momentum won't permit it to get any closer).

I'm not entirely sure if this reasoning still applies if there is a noticeable velocity component in the toroidal direction, but in any case the moon will be safe from the Sun because its energy is much too low to climb far enough out of the Torus's steep potential well to enter the Sun's.

[alie...@gmail.com]

On May 27, 12:33 am, Jens Kleimann <yattering_nos...@web.de> wrote:
> On 27.05.2013 04:55, Greg Goss wrote:
>

> >> "n...@bid.nes" <alien8...@gmail.com> wrote:
>
> >>> unless the orbit "slides" along the donut to maintain the orbital
> >>> plane's orientation WRT the stars. ISTM that'd have to be artificially
> >>> maintained.
>
> > I missed this point in my initial answer.  The orbit wouldn't "slide"
> > along the donut; rather the donut would slide under the moon's orbit.
> > This was the circumstance I was describing.

Same same; I was trying to look at things from the moon's FOR
keeping its orbital angular momentum in mind.

> > It would not be difficult to make it statically stable -- the orbit's
> > position around the donut could be adjusted to provide enough lift to
> > keep it out of the sun.
>
> What has to be kept in mind here is that the local gravity field (with "local" being still large enough to encompass the prospective moon's orbit) is entirely dominated by the Torus; the Sun is way too distant to be anything but a minor correction. As we convinced ourselves upthread, the relevant potential is proportional to log(r/R), and orbits in this form of potential have been studied earlier, for instance at [http://arxiv.org/abs/1009.0422]. They are usually rosette-shaped (see Fig. 5 on page 14), but may be circular in special cases. The important point to note is that there will usually be a smallest and largest distance whose values are fixed by conservation of energy and angular momentum. This finding should not depend on whether the Torus revolves below the moon or not. So these two extreme radii span a region which the moon cannot leave (outbound because its energy is too low, Torus-bound because its angular momentum won't permit it to get any closer).

Thank you very much for the nice reference; Johnny can have a moon
without artificially maintaining its orbit. Glad that's settled.

> I'm not entirely sure if this reasoning still applies if there is a noticeable velocity component in the toroidal direction, but in any case the moon will be safe from the Sun because its energy is much too low to climb far enough out of the Torus's steep potential well to enter the Sun's.

Rotation fast enough to generate frame dragging is ruled out already
and I don't see anything slower causing trouble.

Wait, how about atmospheric friction? What does the Torus' peculiar
gravitational potential do to the atmosphere's scale height? I looked
at the math describing scale height but it seems to assume spherical
symmetry- I can see there might be a problem here but I have no clue
how to calculate it.


Mark L. Fergerson

[Jens Kleimann]

On 27.05.2013 02:50, nu...@bid.nes wrote:
> On May 26, 8:34 am, Johnny1a <shermanl...@hotmail.com> wrote:
>> No, but this thing _will_ have a mantle of some sort, or the
>> equivalent. I don't know yet if it's rock-and-metal all the way to
>> the center of the cylinder or not, but even if there's an inner core
>> of weird, there will be _at least_ some _hundreds_ of miles of rock
>> and other 'conventional' meterials below the outer surface, including
>> a substantial percentage of heat-producing radioactives. (I don't
>> know yet if the percentage of radioactives will be higher than that of
>> Earth or not.)
>>
>> Now, what form that geology will take is a fantastic good question.
>
> According to this:
>
> http://blogs.scientificamerican.com/observations/2011/07/18/nuclear-fission-confirmed-as-source-of-more-than-half-of-earths-heat/
>
> nuclear fission of uranium and thorium alone produces more than half
> of Earth's internal heat to the tune of 20 terawatts! Scale that up to
> your torus world's much greater cylindrical mantle volume and I think
> there's a problem. I'm guessing the proportion of fissionables per
> unit volume will have to be much lower than Earth's to keep the planet
> from staying molten.

With terrestrial composition, the absolute rate of heating input by fission will indeed be staggering. However, equilibrium temperature stems from the balance between thermal energy production and the surface's ability to radiate it away into space. Energy generation by fission scales (roughly) with volume, but radiation losses scale with surface area. The Torus has 50,000 times the volume of Earth, but its surface area is also larger by _exactly_ the same factor. (This surprising result turns out to follow from the requirement that the surface gravity be exactly that of Earth, leading to the known relation
R_torus = (2/3) R_earth = 4,240 km.) So at least in this respect, similar composition should lead to a similar thermal energy balance.

>> One way to get seasons on the Torus would be to use a trick Niven
>> suggested for a Ringworld, let the object 'rise and fall' along the
>> 'vertical' axis of the central star (vertical relative to the plane of
>> the Torus/Ringworld). As the object bobs up and down, the star would
>> be at an angle and you'd get seasons. This would have some potential
>> side effects, though.
>
> Yeah, I forgot the bobbing trick. That would change the distance to
> the star and hence the amount of solar heat deposited in the
> atmosphere but not the number of hours of daylight per day the way
> "real" seasons do. Should have the same effect temperature wise but
> plants would not get their seasonal cues the same as on Earth.
>
>> Another way might be to let whatever agency is holding the object in
>> place against its natural dynamic instability move it back and forth a
>> bit, so the star is held a bit off-center. That seems inelegant,
>> though, and would also produce side-effects.

Two more thoughts on this:

1. Keeping the Torus positioned in an unstable equilibrium requires constant but small (infinitesimal, in the mathematical idealization) action. Moving it out of equilibrium far enough to make changes of solar irradiation become noticeable and then back in again and to the other side requires a literally astronomical expenditure of energy by whatever agent does these adjustments. The same holds true if the sun does not do radially linear oscillations but move in a small circle relative to the Torus.

2. As opposed to this, having the Sun wobble up and down will occur all by itself as soon as an initial out-of-plane displacement has occurred, so this seems more natural and convenient. If the sun moves out sufficiently far, it may even help to stabilize the Torus' position, because at maximum elongation, the sun will be pulled towards the Torus' center of mass (i.e. exactly where you want it to be) even if it is slightly off-set already, rather than to the part of the ring that it happens to be closest to.

To determine how far you can move the sun and the torus with respect to each other before the climatic effects thus induced become fatal, the fact that absolute surface temperature (in K) scales approximately with distance r to a heat source as T~1/sqrt(r) may provide some guidance to fix numbers.

Another noteworthy point on the second possibility is that the length of the 'illumination cycle' (what the inhabitants might be tempted to call 'one year') will be of order sqrt[1AU/(GM)] and thus be somewhat larger than an Earth year by a factor that one could in principle determine exactly.

>> The enormous rotational velocity of a Ringworld
>> means that anything that hits it hits at the equivalent of over 700
>> miles per second, with a kinetic energy of gyahh! (More precisely, at
>> 770 miles/sec, every kilogram of impactor strikes with an energy of
>> about 180 metric tons of TNT, varying a bit depending on the direction
>> of impact. A 100 kilogram human being striking the ground at that
>> velocity would have an impact energy greater than the Hiroshima bomb.
>
> Gyahh indeed.
>
>> The Torus experiences impactors at about the same general energy level
>> as Earth. Granted, it will also experience more of them, everything
>> else being equal, because its gravity draws them in in a way the
>> Ringworld does not, but on balance I'd say the Torus is safer on that
>> count than the Ringworld. It can also soak up more energy than the
>> Ringworld can without catastrophe.

I've tried to put in some numbers, and what I find is this:
It is widely known that an object which starts to fall towards Earth from infinity with negligible initial velocity will impact the planet with slightly more than 11 km/s. For a ring geometry of the proportions discussed here, I get about 2.4 times that value upon impact, or 5.6 times the kinetic energy. What matters in addition is that a large impact can potentially influence a much larger area: Even if every spot on the surface is as likely to receive a direct hit as its terrestrial analogue, impacts on torus sections several 10,000 km away can still be devastating, whereas everything that misses a planetary observer by more than the planet's diameter cannot do any harm. But then as you say, the energy is also distributed on larger areas. There will be safe distances even from impactors that otherwise would have wiped out a planetary biosphere completely.

[Jens Kleimann]

On 27.05.2013 09:56, nu...@bid.nes wrote:
>
> Wait, how about atmospheric friction? What does the Torus' peculiar
> gravitational potential do to the atmosphere's scale height? I looked
> at the math describing scale height but it seems to assume spherical
> symmetry- I can see there might be a problem here but I have no clue
> how to calculate it.

Good point! When we discussed the Alderson disk back then, Tim Little noted that an isothermal atmosphere with a surface pressure of one bar would outmass both disk and star, and thus spontaneously collapse to form a star of its own!

For a given dependence of gravity on radius g(r), the density profile of an isothermal atmosphere can be computed from
rho(r)/rho(R) = exp[Int(g(x)/c^2,x=R..r)], c being the speed of sound, as in c=sqrt(dp/drho). With g(r)=2Gd/r as in our case, I arrive at
rho(r)/rho(R) = (r/R)^[-g(R) R/c^2]. The exponent is equal to about -350. Relative to density at the surface (100%), at 1km height (i.e. r=(4240+1)km) we thus have 91%, at 8.3km we are down to 50%, and at the "height" of the terrestrial moon, it has become completely irrelevant as far as friction is concerned (though I would be glad about someone checking this).

[eripe]

Regarding the internal heating, there is another source besides fission, namely that of the strain cycle as the torus rotates about itself.

As Jens said the surface strain is 0,00005, so one meter will change length by that many meters. At the same time our cubic meter will excert a counter force. It works like a spring, storing energy. This force is elastic modulus x strain = best guess for rock 50 GPa x 0,00005 = 2,5 MPa. The energy stored is then 0,5 x 0,00005 x 2,5e6 = 62,5 J/m3. if the hysteresis loss is just 1 % your still getting 7,2 kW pr cubic kilometer. I have no idea how that compares to radioactive decay.

[Johnny1a]

On May 27, 7:00 am, Jens Kleimann <yattering_nos...@web.de> wrote:

> On 27.05.2013 02:50, n...@bid.nes wrote:
>
>
>
>
>
> > On May 26, 8:34 am, Johnny1a <shermanl...@hotmail.com> wrote:
> >> No, but this thing _will_ have a mantle of some sort, or the
> >> equivalent.  I don't know yet if it's rock-and-metal all the way to
> >> the center of the cylinder or not, but even if there's an inner core
> >> of weird, there will be _at least_ some _hundreds_ of miles of rock
> >> and other 'conventional' meterials below the outer surface, including
> >> a substantial percentage of heat-producing radioactives.  (I don't
> >> know yet if the percentage of radioactives will be higher than that of
> >> Earth or not.)
>
> >> Now, what form that geology will take is a fantastic good question.
>
> >    According to this:
>

> >http://blogs.scientificamerican.com/observations/2011/07/18/nuclear-f...

>
> >    nuclear fission of uranium and thorium alone produces more than half
> > of Earth's internal heat to the tune of 20 terawatts! Scale that up to
> > your torus world's much greater cylindrical mantle volume and I think
> > there's a problem. I'm guessing the proportion of fissionables per
> > unit volume will have to be much lower than Earth's to keep the planet
> > from staying molten.
>
> With terrestrial composition, the absolute rate of heating input by fission will indeed be staggering. However, equilibrium temperature stems from the balance between thermal energy production and the surface's ability to radiate it away into space. Energy generation by fission scales (roughly) with volume, but radiation losses scale with surface area. The Torus has 50,000 times the volume of Earth, but its surface area is also larger by _exactly_ the same factor. (This surprising result turns out to follow from the requirement that the surface gravity be exactly that of Earth, leading to the known relation
> R_torus = (2/3) R_earth = 4,240 km.) So at least in this respect, similar composition should lead to a similar thermal energy balance.

That was my thinking, and it has the interesting property of giving
the Torus the likely potential for volcanoes, earthquakes in the
terrestrial sense, and the rest of the panoply of geology. That's
something that simply doesn't exist for the 'classic' Ringworld, Dyson
Sphere, etc. It also means that the Torus could, conceivably, operate
unmaintained over vastly larger time scales than the Ringworld or its
cousins, at least as far as the surface environment goes.

>
> >> One way to get seasons on the Torus would be to use a trick Niven
> >> suggested for a Ringworld, let the object 'rise and fall' along the
> >> 'vertical' axis of the central star (vertical relative to the plane of
> >> the Torus/Ringworld).  As the object bobs up and down, the star would
> >> be at an angle and you'd get seasons.  This would have some potential
> >> side effects, though.
>
>

> 2. As opposed to this, having the Sun wobble up and down will occur all by itself as soon as > an initial out-of-plane displacement has occurred, so this seems more natural and
> convenient. If the sun moves out sufficiently far, it may even help to stabilize the Torus' > position, because at maximum elongation, the sun will be pulled towards the Torus' center of > mass (i.e. exactly where you want it to be) even if it is slightly off-set already, rather
> than to the part of the ring that it happens to be closest to.

OK, now that is interesting, I hadn't considered that.

>
> To determine how far you can move the sun and the torus with respect to each other before
> the climatic effects thus induced become fatal, the fact that absolute surface temperature
>(in K) scales approximately with distance r to a heat source as T~1/sqrt(r) may provide some > guidance to fix numbers.
>

> >> The enormous rotational velocity of a Ringworld
> >> means that anything that hits it hits at the equivalent of over 700
> >> miles per second, with a kinetic energy of gyahh!  (More precisely, at
> >> 770 miles/sec, every kilogram of impactor strikes with an energy of
> >> about 180 metric tons of TNT, varying a bit depending on the direction
> >> of impact.  A 100 kilogram human being striking the ground at that
> >> velocity would have an impact energy greater than the Hiroshima bomb.
>
> >    Gyahh indeed.
>
> >> The Torus experiences impactors at about the same general energy level
> >> as Earth.  Granted, it will also experience more of them, everything
> >> else being equal, because its gravity draws them in in a way the
> >> Ringworld does not, but on balance I'd say the Torus is safer on that
> >> count than the Ringworld.  It can also soak up more energy than the
> >> Ringworld can without catastrophe.
>
> I've tried to put in some numbers, and what I find is this:
> It is widely known that an object which starts to fall towards Earth from infinity with
> negligible initial velocity will impact the planet with slightly more than 11 km/s. For a
> ring geometry of the proportions discussed here, I get about 2.4 times that value upon
> impact, or 5.6 times the kinetic energy.

Same order of magnitude as Earth, whereas the Ringworld, when it gets
hit at all, usually gets it at 770 miles/sec, four orders of magnitude
worse in terms of impact energy. Niven hints at this with a scene in
_The Ringworld Engineers_ where Louis Wu, examining the underside of
the Ring, notices that on their previous visit, the actually managed
to bend the scrith underside of the Ringworld when their previous
spacecraft crashed at hundreds of miles a second.

If we assume that the previous ship massed (Niven never specified, but
the scale would be about right) as much as a big jet, say a 747, that
would be about 400-500 tons. If that hits at 770 miles/sec, you have
an impact energy of 70-90 megatons, bigger than the biggest nuke ever
detonated. But that's just the equivalent of a rock _35 feet across_.

(Which is also another reason the Torus is different from a
storytelling POV than the Ringworld, it's possible to land safely and
leave with a _much_ more manageable expenditure of delta-vee.)


>
> Jens.
> --
> Remove '_nospam' for actual email address.- Hide quoted text -
>
> - Show quoted text -- Hide quoted text -
>
> - Show quoted text -- Hide quoted text -

[Johnny1a]

On May 27, 9:20 am, eripe <eripe...@gmail.com> wrote:
> Regarding the internal heating, there is another source besides fission, namely that of the strain cycle as the torus rotates about itself.
>
> As Jens said the surface strain is 0,00005, so one meter will change length by that many meters. At the same time our cubic meter will excert a counter force. It works like a spring, storing energy. This force is elastic modulus x strain = best guess for rock 50 GPa x 0,00005 = 2,5 MPa. The energy stored is then 0,5 x 0,00005 x 2,5e6 = 62,5 J/m3. if the hysteresis loss is just 1 % your still getting 7,2 kW pr cubic kilometer.  I have no idea how that compares to radioactive decay.

Umm...it looks to be greater by a factor of ~200 or so, at first
glance, assuming the Torus has the same radioactive heat production
per cubic kilometer as Earth. But the strain would be greater at the
surface, I would think, and fall away with depth, so it might not be
that bad. Still, that's a lot of energy. It would drive an
_extremely_ active geology, and it would tend to bleed off the angular
momentum of the Torus, too, over time.

This might be a problem.

[Johnny1a]

On May 19, 11:52 pm, Johnny1a <shermanl...@hotmail.com> wrote:
>
> Like I said, I'm just toying with the concept and trying to figure out
> how it would work or not.

Here's another question about the Torus, assuming it existed: how
would be to detectable over interstellar distances?

If the Torus 'bobs' up and down on the vertical axis (relative to the
plane of the Torus) for seasons, then that would probably produce some
kind of motion in the star that could be detected, but what if the
Torus stays in the equatorial plane? Would the tiny adjustments
necessary to keep position show up in the star enough to detect?
Would there by anything else what would make the Torus noticeable over
interstellar ranges?

[Jens Kleimann]

On 31.05.2013 03:28, Johnny1a wrote:>
> Here's another question about the Torus, assuming it existed: how
> would be to detectable over interstellar distances?
>
> If the Torus 'bobs' up and down on the vertical axis (relative to the
> plane of the Torus) for seasons, then that would probably produce some
> kind of motion in the star that could be detected,

These near-sinusoidal motions could in principle be detected using Doppler-shifted spectral features of the stellar light (in the direction to/from the observer) or in the star's proper motion in the sky (perpendicular to the line of sight). Each of these alone could easily be mistaken as being the result of a high-mass planetary (or low-mass stellar) companion that forces the primary star into an ellipsoidal orbit around the common center of mass. If the star's maximum elongation is of the order of, or even larger than, the Torus size, careful observers might be puzzled by deviations in the predicted curves. When both methods can be combined, it could become evident that they point towards linear, rather than ellipsoidal oscillations, and it may even be possible to constrain the mass and geometry of the object that causes these motions, provided the observer would actually be inclined to consider the possibility of artificially created astronomical objects.

> but what if the Torus stays in the equatorial plane? Would the tiny adjustments
> necessary to keep position show up in the star enough to detect?

Probably not, else they would not be tiny any more. To be efficient, these adjustments need to be frequent but small, and their very objective is to keep everything static.

> Would there by anything else what would make the Torus noticeable over
> interstellar ranges?

Both night and dayside would be a source of infrared radiation peaking near room temperature, with an effective emitting area comparable to that of the Sun. It might get mistaken for a protoplanetary disk at first glance, but this would probably soon be ruled out by arguments about stellar evolution. This temperature would probably also be too low to suggest a brown dwarf. If the structure cannot be optically resolved, the IR output would likely be interpreted as a compact object of the corresponding temperature very close to a star of comparable size (as inferred from absolute flux). The lack (or inconsistency) of detectable motions (see above) might then strike an observer as unusual.

[Percival]

Planets are now easily detected by how much they make their stars
wobble as they orbit them. Bobbing could be considered as a sort of
linear orbit (harmonic motion, anyway); granted the motion involved
won't be as great as an ordinary planet's motion but I think the bobbing
should be as easily detectable as ordinary wobble is since AFAIK no
known planets are anywhere near 0.15 times their star's mass. Certainly
it would be plainly different from ordinary wobble since it would be
perpendicular to the star's rotation, assuming that could be nailed down.

Speaking of that, if the Torus + star system had any ordinary planets
that induced ordinary wobble, the wobble and bobbing would add to a sort
of spiraling motion of the star. If the other planet's mass and relative
orbital distance were just right (so as not to destabilize the Torus'
orbit) it would do weird things to the surface insolation; you'd get two
types of seasons- one due to the bobbing, the other due to the changing
radial distance from a given part of the Torus to the star. That could
be a fun plot point or an unnecessary complication depending on whether
you're thinking short story or full blown novel.


Mark L. Fergerson

[eripe]

What do you think of a slightly less ambitious project, where the torus major radius is 50x the minor radius, spinning head over heals, and orbiting a star at 1 AU. If it turns over in 24 hours you would get 0,1 g acceleration, which is a lot, but it drops off with radius so I don't think all the material would slide out to the tip.

That would give some interesting day-night, season cycles.

[Johnny1a]

On Jun 1, 7:13 am, eripe <eripe...@gmail.com> wrote:
> What do you think of a slightly less ambitious project, where the torus major radius is 50x the minor radius, spinning head over heals, and orbiting a star at 1 AU. If it turns over in 24 hours you would get 0,1 g acceleration, which is a lot, but it drops off with radius so I don't think all the material would slide out to the tip.
>
> That would give some interesting day-night, season cycles.

The Torodial equivalent of a Banksian Orbital?

From the POV of humans building such structures, they would make more
sense than the Grand Torus, for the same reason Orbitals make more
sense than the Ringworld: more living space per unit mass. Or at
least, they would make more sense from the standpoint of living space
efficiency. Other motives produce other definitions of 'efficient'.

From the POV of my personal concept right now, such a structurew would
be too small. But...I might well imagine that the entities that
created the Torus might create smaller but similar structures, the
same star encircled by the Grand Torus might also have smaller
structures like the above in not-intersecting orbits. The more I
think about that, the more I like it.

[Johnny1a]

On May 27, 12:46 am, Johnny1a <shermanl...@hotmail.com> wrote:

> simplified first assumptions were good.- Hide quoted text -

>
> - Show quoted text -

Another element to consider is the hydrosphere (or hydrotorus) of the
Torus. If the surface ocean of the Torus is single interconnected
body, as on Earth, heat will circulate throughout the ocean mass. On
the other hand, if the land is so distributed that there is more than
one ocean, that too will shape heat flow.

There could be 'rings' of land wrapped around the Torus that would
divide the ocean, such could be part of the design or they might come
(and go) naturally with continental change.

[Jens Kleimann]

On 27.05.2013 14:00, Jens Kleimann wrote:
> On 27.05.2013 02:50, nu...@bid.nes wrote:
>> On May 26, 8:34 am, Johnny1a <shermanl...@hotmail.com> wrote:

>>> One way to get seasons on the Torus would be to use a trick Niven
>>> suggested for a Ringworld, let the object 'rise and fall' along the
>>> 'vertical' axis of the central star (vertical relative to the plane of
>>> the Torus/Ringworld). As the object bobs up and down, the star would
>>> be at an angle and you'd get seasons. This would have some potential
>>> side effects, though.
>>
>> Yeah, I forgot the bobbing trick. That would change the distance to
>> the star and hence the amount of solar heat deposited in the
>> atmosphere but not the number of hours of daylight per day the way
>> "real" seasons do. Should have the same effect temperature wise but
>> plants would not get their seasonal cues the same as on Earth.
>>
>>> Another way might be to let whatever agency is holding the object in
>>> place against its natural dynamic instability move it back and forth a
>>> bit, so the star is held a bit off-center. That seems inelegant,
>>> though, and would also produce side-effects.
>
> Two more thoughts on this:
>
> 1. Keeping the Torus positioned in an unstable equilibrium requires constant but small (infinitesimal, in the mathematical idealization) action. Moving it out of equilibrium far enough to make changes of solar irradiation become noticeable and then back in again and to the other side requires a literally astronomical expenditure of energy by whatever agent does these adjustments. The same holds true if the sun does not do radially linear oscillations but move in a small circle relative to the Torus.
>
> 2. As opposed to this, having the Sun wobble up and down will occur all by itself as soon as an initial out-of-plane displacement has occurred, so this seems more natural and convenient. If the sun moves out sufficiently far, it may even help to stabilize the Torus' position, because at maximum elongation, the sun will be pulled towards the Torus' center of mass (i.e. exactly where you want it to be) even if it is slightly off-set already, rather than to the part of the ring that it happens to be closest to.

In an attempt to be more specific about this conjecture, I have set up a simulation to model the dynamics of the star and its torus (effectively a ring of 40 equidistant point masses) for maximum bobbing elongations of 1, 2, and 3 AU. From these, it looks as if these configurations tend to become unstable after a while as well, after which the behavior turns chaotic, with obviously fatal consequences for habitability. I was hoping that the star would at least continue to pass near the torus' center of mass in quasi-regular intervals, but apparently the torque that the torus gets from the net effect of gravity acting on its constituent masses is too erratic for this. Movies of these studies can be found at

[http://www.tp4.rub.de/~jk/science/gravity/torus_thin/torus_breather-1AU.mpg]
[http://www.tp4.rub.de/~jk/science/gravity/torus_thin/torus_breather-2AU.mpg]
[http://www.tp4.rub.de/~jk/science/gravity/torus_thin/torus_breather-3AU.mpg]
[http://www.tp4.rub.de/~jk/science/gravity/torus_thin/torus_moon-figure8.mpg]

where the last one shows the trajectory of a "moon" (a massless test particle) orbiting the torus in something like an 8-shaped figure. ('*' is the star, '+' is the common center of mass, and the diamonds mark the point masses that form the ring/torus.) It starts out fairly regular, but still crashes after a while even with the torus remaining totally static.

It would be nice if similar stable paths could be achieved for the much more massive star, but my impression from various attempts is that such regular motions do not persist for more than a few cycles, if at all.
(For those interested in the details, the integrator employs a standard Leapfrog scheme with a step size of 0.0005 years, and motion is confined to the plane of symmetry, which includes the star and the torus' axis of symmetry.)
So the preliminary conclusion at this point seems to be that one cannot avoid the need to apply forcing at regular intervals to keep a constant distance from the star, irrespective of whether a massive torus or the traditional Ringworld is under consideration. A moderately bobbing sun is nice to get seasons (the duration of which depends on elongation, as can be seen from the above movies), but does not aid stability in any way, though I'd be pleased to be shown wrong on this point.

[alie...@gmail.com]

On Jun 6, 5:30 am, Jens Kleimann <yattering_nos...@web.de> wrote:
> On 27.05.2013 14:00, Jens Kleimann wrote:
>
>
>
>
>
>
>
>
>
> > On 27.05.2013 02:50, n...@bid.nes wrote:
> >> On May 26, 8:34 am, Johnny1a <shermanl...@hotmail.com> wrote:
> >>> One way to get seasons on the Torus would be to use a trick Niven
> >>> suggested for a Ringworld, let the object 'rise and fall' along the
> >>> 'vertical' axis of the central star (vertical relative to the plane of
> >>> the Torus/Ringworld).  As the object bobs up and down, the star would
> >>> be at an angle and you'd get seasons.  This would have some potential
> >>> side effects, though.
>
> >>    Yeah, I forgot the bobbing trick. That would change the distance to
> >> the star and hence the amount of solar heat deposited in the
> >> atmosphere but not the number of hours of daylight per day the way
> >> "real" seasons do. Should have the same effect temperature wise but
> >> plants would not get their seasonal cues the same as on Earth.
>
> >>> Another way might be to let whatever agency is holding the object in
> >>> place against its natural dynamic instability move it back and forth a
> >>> bit, so the star is held a bit off-center.  That seems inelegant,
> >>> though, and would also produce side-effects.
>
> > Two more thoughts on this:
>
> > 1. Keeping the Torus positioned in an unstable equilibrium requires constant but small (infinitesimal, in the mathematical idealization) action. Moving it out of equilibrium far enough to make changes of solar irradiation become noticeable and then back in again and to the other side requires a literally astronomical expenditure of energy by whatever agent does these adjustments. The same holds true if the sun does not do radially linear oscillations but move in a small circle relative to the Torus.
>
> > 2. As opposed to this, having the Sun wobble up and down will occur all by itself as soon as an initial out-of-plane displacement has occurred, so this seems more natural and convenient. If the sun moves out sufficiently far, it may even help to stabilize the Torus' position, because at maximum elongation, the sun will be pulled towards the Torus' center of mass (i.e. exactly where you want it to be) even if it is slightly off-set already, rather than to the part of the ring that it happens to be closest to.
>
> In an attempt to be more specific about this conjecture, I have set up a simulation to model the dynamics of the star and its torus (effectively a ring of 40 equidistant point masses) for maximum bobbing elongations of 1, 2, and 3 AU. From these, it looks as if these configurations tend to become unstable after a while as well, after which the behavior turns chaotic, with obviously fatal consequences for habitability. I was hoping that the star would at least continue to pass near the torus' center of mass in quasi-regular intervals, but apparently the torque that the torus gets from the net effect of gravity acting on its constituent masses is too erratic for this. Movies of these studies can be found at
>

> [http://www.tp4.rub.de/~jk/science/gravity/torus_thin/torus_breather-1...]
> [http://www.tp4.rub.de/~jk/science/gravity/torus_thin/torus_breather-2...]
> [http://www.tp4.rub.de/~jk/science/gravity/torus_thin/torus_breather-3...]
> [http://www.tp4.rub.de/~jk/science/gravity/torus_thin/torus_moon-figur...]

>
> where the last one shows the trajectory of a "moon" (a massless test particle) orbiting the torus in something like an 8-shaped figure. ('*' is the star, '+' is the common center of mass, and the diamonds mark the point masses that form the ring/torus.) It starts out fairly regular, but still crashes after a while even with the torus remaining totally static.
>
> It would be nice if similar stable paths could be achieved for the much more massive star, but my impression from various attempts is that such regular motions do not persist for more than a few cycles, if at all.
> (For those interested in the details, the integrator employs a standard Leapfrog scheme with a step size of 0.0005 years, and motion is confined to the plane of symmetry, which includes the star and the torus' axis of symmetry.)
> So the preliminary conclusion at this point seems to be that one cannot avoid the need to apply forcing at regular intervals to keep a constant distance from the star, irrespective of whether a massive torus or the traditional Ringworld is under consideration. A moderately bobbing sun is nice to get seasons (the duration of which depends on elongation, as can be seen from the above movies), but does not aid stability in any way, though I'd be pleased to be shown wrong on this point.

Well, darn. Would adding a Jupiter-scale planet to the system work
as a counterweight?


Mark L. Fergerson

[Jens Kleimann]

Not sure were you would want to place it. My guess is that adding more masses would tend to make it more unstable still, as in those cases where you add a third body to an otherwise stable Kepler problem. Since one starts from an unstable equilibrium (but an equilibrium nevertheless), by definition one cannot predict where the first correction needs to occur. Jupiter may well be a couple of AU away from the place where you need it right now.

But what might help is to spin the Torus head over heels around an axis perpendicular to its own symmetry axis. If the spin rate is high enough, the star would perceive the Torus' gravity as being smeared out over a hollow sphere with itself at the center. By virtue of Newton's Theorem, the effective gravitational acceleration will effectively be zero not only there, but also within a larger region around it. Effectively it would have to be a combined rotation around two perpendicular axes, since otherwise there will always be mass along the rotational axis, which breaks the desired spherical symmetry.

I have set up a sequence of simulations with the star displaced from the center by 0.1 AU within the Torus' plane, and then varied the spin frequency from zero (the instable 'Niven case') to 1.0 and 1.2 full rotations per year, to be seen again at

[http://www.tp4.rub.de/~jk/science/gravity/torus_thin/torus_spin-00.mpg]
[http://www.tp4.rub.de/~jk/science/gravity/torus_thin/torus_spin-10.mpg]
[http://www.tp4.rub.de/~jk/science/gravity/torus_thin/torus_spin-12.mpg]

(One rotation axis is enough here because everything is confined to a plane by construction.)
While the first two fail pretty soon, the third seems to survive much longer, despite the asymmetric initial setting. The spin frequency oscillates with low amplitude around about 1.28 rotations/year for about 300 years (with a slightly increasing mean trend), but then it also crashes. Spinning twice every year, the torus survives for 500 years. Five rotations per year result in a lifetime of 670 years, although the star's off-center displacement attains dangerously high values earlier (e.g. 0.5 AU after ~520 years, see [http://www.tp4.rub.de/~jk/science/gravity/torus_thin/dist_osc050.pdf]).

There seems to be a clear trend here, although spinning much faster still will result in non-negligible centrifugal forces. Whether any of this harbors the potential for eternal stability I cannot say.

[Johnny1a]

On Jun 6, 7:30 am, Jens Kleimann <yattering_nos...@web.de> wrote:
> On 27.05.2013 14:00, Jens Kleimann wrote:
>
>
>
>
>
> > On 27.05.2013 02:50, n...@bid.nes wrote:
> >> On May 26, 8:34 am, Johnny1a <shermanl...@hotmail.com> wrote:
> >>> One way to get seasons on the Torus would be to use a trick Niven
> >>> suggested for a Ringworld, let the object 'rise and fall' along the
> >>> 'vertical' axis of the central star (vertical relative to the plane of
> >>> the Torus/Ringworld).  As the object bobs up and down, the star would
> >>> be at an angle and you'd get seasons.  This would have some potential
> >>> side effects, though.
>
> >>    Yeah, I forgot the bobbing trick. That would change the distance to
> >> the star and hence the amount of solar heat deposited in the
> >> atmosphere but not the number of hours of daylight per day the way
> >> "real" seasons do. Should have the same effect temperature wise but
> >> plants would not get their seasonal cues the same as on Earth.
>
> >>> Another way might be to let whatever agency is holding the object in
> >>> place against its natural dynamic instability move it back and forth a
> >>> bit, so the star is held a bit off-center.  That seems inelegant,
> >>> though, and would also produce side-effects.
>
> > Two more thoughts on this:
>
> > 1. Keeping the Torus positioned in an unstable equilibrium requires constant but small (infinitesimal, in the mathematical idealization) action. Moving it out of equilibrium far enough to make changes of solar irradiation become noticeable and then back in again and to the other side requires a literally astronomical expenditure of energy by whatever agent does these adjustments. The same holds true if the sun does not do radially linear oscillations but move in a small circle relative to the Torus.
>
> > 2. As opposed to this, having the Sun wobble up and down will occur all by itself as soon as an initial out-of-plane displacement has occurred, so this seems more natural and convenient. If the sun moves out sufficiently far, it may even help to stabilize the Torus' position, because at maximum elongation, the sun will be pulled towards the Torus' center of mass (i.e. exactly where you want it to be) even if it is slightly off-set already, rather than to the part of the ring that it happens to be closest to.
>
> In an attempt to be more specific about this conjecture, I have set up a simulation to model the dynamics of the star and its torus (effectively a ring of 40 equidistant point masses) for maximum bobbing elongations of 1, 2, and 3 AU. From these, it looks as if these configurations tend to become unstable after a while as well, after which the behavior turns chaotic, with obviously fatal consequences for habitability. I was hoping that the star would at least continue to pass near the torus' center of mass in quasi-regular intervals, but apparently the torque that the torus gets from the net effect of gravity acting on its constituent masses is too erratic for this. Movies of these studies can be found at
>

> [http://www.tp4.rub.de/~jk/science/gravity/torus_thin/torus_breather-1...]
> [http://www.tp4.rub.de/~jk/science/gravity/torus_thin/torus_breather-2...]
> [http://www.tp4.rub.de/~jk/science/gravity/torus_thin/torus_breather-3...]
> [http://www.tp4.rub.de/~jk/science/gravity/torus_thin/torus_moon-figur...]
>

> where the last one shows the trajectory of a "moon" (a massless test particle) orbiting the torus in something like an 8-shaped figure. ('*' is the star, '+' is the common center of mass, and the diamonds mark the point masses that form the ring/torus.) It starts out fairly regular, but still crashes after a while even with the torus remaining totally static.
>
> It would be nice if similar stable paths could be achieved for the much more massive star, but my impression from various attempts is that such regular motions do not persist for more than a few cycles, if at all.
> (For those interested in the details, the integrator employs a standard Leapfrog scheme with a step size of 0.0005 years, and motion is confined to the plane of symmetry, which includes the star and the torus' axis of symmetry.)
> So the preliminary conclusion at this point seems to be that one cannot avoid the need to apply forcing at regular intervals to keep a constant distance from the star, irrespective of whether a massive torus or the traditional Ringworld is under consideration. A moderately bobbing sun is nice to get seasons (the duration of which depends on elongation, as can be seen from the above movies), but does not aid stability in any way, though I'd be pleased to be shown wrong on this point.
>
> Jens.
> --

> Remove '_nospam' for actual email address.- Hide quoted text -

>
> - Show quoted text -

Sigh.

I can't say I'm 100% surprised, though. I has a hunch it might be too
good to be true. Nature just doesn't seem to like stellar-scale
megastructures.

Another possibility with regard to the seasons, of course, would be to
dispense with the 'axial' rotation of the Torus. That would have the
advantage of removing the 'stress heat' issue, but it would leave one
side of the Torus always facing the star, and one side always facing
away. I'm not sure you could maintain an environment that could
really be called 'earthlike' under such conditions, though a biosphere
might be possible. It would be sort of like what we once believed
Mercury to be, one side always bright and hot and once side always
dark and cool.

An in an atmosphere of Earth-like composition and density and you'd
get some peculiar climate and weather effects, to say the least.

[Jens Kleimann]

On 06.06.2013 23:45, nu...@bid.nes wrote:

After thinking about your suggestion a little more, I occurred to me that there is one way in which this might actually work: Use not a gas giant, but another star as a 'counterweight', i.e. a low-eccentricity binary star system, with stellar components of comparable masses. Then place the torus such that
1. its axis of symmetry contains both stars and
2. it intersects the orbital plane exactly at the L4 and L5 Lagrange points.

Since L4 and L5 each form equilateral triangles with the two stars, this implies that the Torus' major radius has to be equal to 0.87 times the stellar separation. (Suitable distances have to be reworked depending on the stellar properties in question, of course.)
This is an equilibrium (by arguments of symmetry) that should also be stable against any perturbation that tries to move the intersection point away from L4/L5. A static torus will still be unstable against perturbations that try to 'fold' the plane of the Torus onto the orbital plane (in which case both stars will simultaneously be brought into fatal proximity with opposing sides of the Torus), but in this case it would help to spin the Torus around its axis of symmetry! The perturbation would then induce a torque which the Torus would try to evade by turning its axis a little into the perpendicular direction, but then immediately feel a restoring force as it drifts away from L4/L5.
This system is admittedly more complicated than the original approach, but seems more likely to work out in the long run.

From the surface, both suns would keep a constant mutual separation in the sky of 120 degrees.
In addition, the Torus could revolve around its spine axis for a day/night cycle consisting of one third darkness (no suns above the horizon), one third with both suns visible, and one sixth of the time with just one of them. Both suns will rise and set perpendicular to the horizon, and pass through the zenith once per day for every observing location. Torus-wide seasonal effects could be achieved with mild stellar eccentricity.

If this should turn out to work as suspected, the long-term stability without intervention would be ensured. The remaining points that need to be handwaved are then

how to
a) cause rocky matter to condensde into a ring-like, rather than spherical shape
b) warrant the stability against deformations
c) get together sufficient quantities of it (0.15 Msun is clearly way above our solar system's combined non-solar mass), and
d) induce day-night-rotations, if so desired.

One way to go could be to first pick a suitable binary protostellar system, then fabricate a massive ring from some hypothetical ultra-stiff (Scrith-like) material of desired major (but possibly small minor) radius that later forms the Torus' central spine, place it into the system with proper orientation, and wait a very long time until enough matter has condensed around it (and has thus been prevented from falling into either protostar). Maybe one could direct the impactors to selectively impact from a given direction to add angular momentum to the ring. When everything is cooled down, start to bring in settlers, or wait for them to evolve all by themselves.

How does that sound so far?

[Johnny1a]

On Jun 10, 4:12 am, Jens Kleimann <yattering_nos...@web.de> wrote:

> On 06.06.2013 23:45, n...@bid.nes wrote:
>
> > On Jun 6, 5:30 am, Jens Kleimann <yattering_nos...@web.de> wrote:
> >> It would be nice if similar stable paths could be achieved for the much more massive star, but my impression from various attempts is that such regular motions do not persist for more than a few cycles, if at all.
> >> (For those interested in the details, the integrator employs a standard Leapfrog scheme with a step size of 0.0005 years, and motion is confined to the plane of symmetry, which includes the star and the torus' axis of symmetry.)
> >> So the preliminary conclusion at this point seems to be that one cannot avoid the need to apply forcing at regular intervals to keep a constant distance from the star, irrespective of whether a massive torus or the traditional Ringworld is under consideration. A moderately bobbing sun is nice to get seasons (the duration of which depends on elongation, as can be seen from the above movies), but does not aid stability in any way, though I'd be pleased to be shown wrong on this point.
>
> >    Well, darn. Would adding a Jupiter-scale planet to the system work
> > as a counterweight?
>
> After thinking about your suggestion a little more, I occurred to me that there is one way in which this might actually work: Use not a gas giant, but another star as a 'counterweight', i.e. a low-eccentricity binary star system, with stellar components of comparable masses. Then place the torus such that
> 1. its axis of symmetry contains both stars and
> 2. it intersects the orbital plane exactly at the L4 and L5 Lagrange points.
>
> Since L4 and L5 each form equilateral triangles with the two stars, this implies that the Torus' major radius has to be equal to 0.87 times the stellar separation. (Suitable distances have to be reworked depending on the stellar properties in question, of course.)
> This is an equilibrium (by arguments of symmetry) that should also be stable against any perturbation that tries to move the intersection point away from L4/L5. A static torus will still be unstable against perturbations that try to 'fold' the plane of the Torus onto the orbital plane (in which case both stars will simultaneously be brought into fatal proximity with opposing sides of the Torus), but in this case it would help to spin the Torus around its axis of symmetry! The perturbation would then induce a torque which the Torus would try to evade by turning its axis a little into the perpendicular direction, but then immediately feel a restoring force as it drifts away from L4/L5.
> This system is admittedly more complicated than the original approach, but seems more likely to work out in the long run.

I want to make sure I'm visualizing this right.

In this scenario, the Torus would not be centered on one of the stars
_per se_, it would instead be 'perpendicular' to the plane of their
mutual orbit, with one arc of the rotating Torus passing throught he
LaGrange points 45 degrees off from the line between the stars, do I
have that one right?

[Jens Kleimann]

Essentially yes, except that none of the angles involved amount to 45 degrees.
For clarity (and fun on my side!), I have prepared an animation (~6MB) at [http://www.tp4.rub.de/~jk/science/gravity/torus_thin/lagrange-torus.avi] that may serve to illustrate the idea more vividly. This example uses a mass ratio of 1:2 (of red to yellow star) and circular orbits, as viewed by a stationary observer. The Torus' thickness is obviously not drawn to scale, but has been much increased for visual clarity. Note that the rotation axis (vertical rod) passes through the stars' common barycenter, but not through the Torus.
The Torus' angular spinning frequency around its axis of symmetry happens to be equal to the orbit frequency, but of course that need not be the case; in fact it was just chosen to allow the movie to loop seamlessly. The dark-reddish disk shows selected equipotential (gravity plus centrifugal) contours in the orbital plane, indicating that the Torus indeed intersects this plane at L4/L5 where the potential has a maximum(!). The purple rods form said equilateral triangles (i.e. they join under 60 degrees at the vertices, independently of mass ratio).
In contrast to the case depicted here, eccentric orbits would have the distance between the two stars oscillate in a non-sinusoidal fashion, with 'summers' being short and 'winters' long, like on Aldiss' Helliconia. Since the triangular geometry has to be conserved in the process (all rods changing their length in sync), the Lagrange points will also move inwards and out again, which means additional stress on the rigid structure of the Torus. Besides climate issues, an upper limit for eccentricity would thus also depend on how far away from the exact Lagrange points dynamical stability persists (which could be --and possibly has already been-- determined somewhere, though I did not find anything about it so far).

Now for a disclaimer:
I do not know if spinning the Torus is really a suitable means to ensure dynamic stability, and even if so, I have no idea (yet) how fast it would have to spin. This would also depend on how these equipotential lines change as one shifts the plotting plane up or down parallel to itself.

As a side remark, it could well be that the configurations which feature a single bobbing star (see upthread) could also be stabilized by sufficiently fast spinning, so maybe even there not all hope is lost.
From a storyteller's point of view, I guess one has in any case a much better chance of getting away with these ideas than with the classic Ringwold, the inherent instability of which seems fairly obvious at least in hindsight.

[alie...@gmail.com]

Extremely cool, but spinning the torus in its own plane would cause
it to precess, wouldn't it?

I hate to pick physical nits with such a beautiful solution but
there it is...


Mark L. Fergerson

[eripe]

>Umm...it looks to be greater by a factor of ~200 or so, at first
>glance, assuming the Torus has the same radioactive heat production
>per cubic kilometer as Earth. But the strain would be greater at the
>surface, I would think, and fall away with depth, so it might not be
>that bad. Still, that's a lot of energy. It would drive an
>_extremely_ active geology, and it would tend to bleed off the angular
>momentum of the Torus, too, over time.

>This might be a problem.

It just occured to me that the earth has a lot of "old heat" in its core, that also contributes to keeping the temperature up.
On http://en.wikipedia.org/wiki/Geothermal_gradient its average of 87 kW pr km2, so by picking the correct mantle thinkness you should be able to have the same heat flux out. Id like to remark that having some heat, say 100 miles of 5000 degree hot material is an excellent way of protecting the core from tampering :)

Do you want tectonics as well?

>
> Extremely cool, but spinning the torus in its own plane would cause
>
> it to precess, wouldn't it?
>

I agree; I dont see how you can turn the angular momentum of the spinning torus?


Another thing regarding the stability issue is that you can have active stabilization by shifting matter around inside the core of the ring. Essentially your moving the center of gravity. It would seem like magig until you get close with some pretty sensitive gravitometer.
(though you now need to power it, I dont suppose having Worm Holes as a the Cold point of a heat engine tastes too well, hmmm)


Also I made a simple numerical solution to calculating the gravity at various points in the starsystem. (ok ok its a spreadsheet, but it gives 9,91 at 4240 km and 0,000004 at the center of the sun, so i recon its good enough for fictional work :) )
http://www.eripe.dk/Torusworld.xlsx
Also note the Larange point at 6 million kilometers towards the sun for a stationary satelite, and the nice speedy orbit 1000 km over the surface on the shadow side at 1097 km/s; around the sun in 10 days (You would need a permit, its a little dangerous.).

[Jens Kleimann]

"The tragedy of science: the slaying of a beautiful theory by an ugly fact."
I can't remember who first said this, but it fits this situation quite well...

Yes, it would precess, and unfortunately in such a way that the Torus' angular momentum acquires a component that would spin it around the L4-L5 connection line, causing the Torus' plane to tip over pretty soon.
It is ironic that the very mechanism that I tried to invoke in order to warrant stability now brings about its demise. :-|

So spinning the upright Torus seems to be a bad idea. But I'm not yet ready to give up. The way I see it, at least three lines of inquiry are still open to us:

First, an upright, non-spinning torus is clearly stable at L4/L5. One could check whether this stability near the orbital plane suffices to counteract the (likely, but not yet established) instability of torus sections that are further away from the plane.

Second, spinning a torus that is bobbing up and down around a single star could still work out by exploiting the same effect that is being used to stabilize bullets and satellites.

Finally, I would not yet dismiss the possibility of placing the Torus right _in_ the binaries' orbital plane, rather than perpendicular to it. This would be stable against displacement perpendicular to the line connecting both stars (because both Torus sides would then be moved away from stable L4/L5). The case of displacement along this line is not so clear: unstable with respect to sections near L2 and L3, but such displacement would move the structure away from L4/L5 as well. The question is again which contribution dominates, except we have a 2D situation here that is potentially easier to analyze than option #1.
As for climate effects, the energy flux that is incident at a given location of the Torus goes with the inverse square of distance to the source, and absolute temperature is proportional to to (1/4)-th power of flux. With two equally bright stars, temperature thus turns out to vary by a factor of sqrt(2) over the Torus (or during the year on a spinning torus, but let's start with the simpler case first). If we arrange for the mean temperature to be at, say, -10 degC, the expected range goes from about -45 degC to +45 degC. One could either spin it rather fast to average out these extreme values, or accept (or even exploit!) the fact that this Torus features two antipodal habitable regions separated by two large deserts that are either too hot or too cold for anything but extremophiles to survive.
Or, on second thoughts, how about an elliptic "torus" to keep it habitable throughout (provided the stability issue can be brought to a happy ending)? The required eccentricity for constant temperature would be 0.54 (implying a moderate aspect ratio near 1.2).

[Johnny1a]

On Jun 13, 7:47 am, eripe <eripe...@gmail.com> wrote:
> >Umm...it looks to be greater by a factor of ~200 or so, at first
> >glance, assuming the Torus has the same radioactive heat production
> >per cubic kilometer as Earth.  But the strain would be greater at the
> >surface, I would think, and fall away with depth, so it might not be
> >that bad.  Still, that's a lot of energy.  It would drive an
> >_extremely_ active geology, and it would tend to bleed off the angular
> >momentum of the Torus, too, over time.
> >This might be a problem.
>
> It just occured to me that the earth has a lot of "old heat" in its core, that also contributes to keeping the temperature up.

> Onhttp://en.wikipedia.org/wiki/Geothermal_gradientits average of 87 kW pr km2, so by picking the correct mantle thinkness you should be able to have the same heat flux out. Id like to remark that having some heat, say 100 miles of 5000 degree hot material is an excellent way of protecting the core from tampering :)

>
> Do you want tectonics as well?

Maybe so. I want the Torus to have a 'live' geology, unlike most of
the versions of the Ringworld or the solid Dyson Sphere. The
Ringworld was either 1000 feet or 1000 meters thick, IIRC, a thin
shell of scrith with a layer or rock/soil/water that was too thin for
real geology. The Torus, OTOH, with a minimum of _hundreds of miles_
of rock in its radius, and lots of heat sources, would have a live
geology.

Whether that would take the form of plate tectonics as we know them is
a good question.

The Ringworld, by its very nature, needs constant upkeep. The Torus
(other than stability issues) probably or at least conceivably might
be as self-sustaining as Earth, in terms of its habitability. It
could remain viable over millions or billions of years, because with a
live geology, it can renew itself. This would also mean that a
civilization could fall all the way back to the stone age and rise
again, with the environment intact, which would be difficult on the
Ringworld.

(That the Ringworld could be a trap for a high-tech society that fell
was actually discussed in the first _Ringworld_ novel.)

>
>
>
> >   Extremely cool, but spinning the torus in its own plane would cause
>
> > it to precess, wouldn't it?
>
> I agree; I dont see how you can turn the angular momentum of the spinning torus?
>
> Another thing regarding the stability issue is that you can have active stabilization by >shifting matter around inside the core of the ring. Essentially your moving the center of >gravity. It would seem like magig until you get close with some pretty sensitive gravitometer.

That thought was in my mind when I posited that the interior might be
a hollow tube, with a liquid of some kind circulating inside it. That
requires not only a power source, but also some controlling agency to
monitor the position of the Torus, and adjust the flow to compensate
for deviations from equilibrium. It could be a viable option, though.

[Johnny1a]

On Jun 13, 2:20 am, Jens Kleimann <yattering_nos...@web.de> wrote:
> On 12.06.2013 05:27, Johnny1a wrote:
>
> Essentially yes, except that none of the angles involved amount to 45 degrees.
>

> Jens.
> --

> Remove '_nospam' for actual email address.- Hide quoted text -
>
> - Show quoted text -

I don't know where I came up with that 45 degree angle. I was tired
when I posted, I must not have been thinking very straight. :sigh:


I really like the idea of the two suns in the sky a third of the time,
from the POV of the surface. That arrangement would create an
interesting visual effect from the POV of an observer on the Torus.
Like the classic Niven ring, you'd have an 'arch' effect in the sky
from the rest of the Torus, seeming to rise from one side of the world
and cross the other.

Unlike the Niven ring, though, the Gunkel rotation of the Torus would
cause the arch to seem to 'rise and set', with the two suns
equidistant on either side of the arch. So one sun would rise and
pass overhead, then the arch would rise and pass overhead, then the
other sun.

That would make for some interesting myths...

[Jens Kleimann]

On 17.06.2013 05:33, Johnny1a wrote:
> I really like the idea of the two suns in the sky a third of the time,
> from the POV of the surface. That arrangement would create an
> interesting visual effect from the POV of an observer on the Torus.
> Like the classic Niven ring, you'd have an 'arch' effect in the sky
> from the rest of the Torus, seeming to rise from one side of the world
> and cross the other.

The visual impression on the surface is an interesting point. Given the extreme ratio of major to minor radius, and considering that most of the geometries discussed so far have at least one sun on the 'inner' side, the far-away parts of the Torus will be hidden below the local horizon during the night. So what could one hope to see of it in bright sunlight? Even one degree above the horizon, the Torus section that is visible in this direction would already be 0.017 AU away, so the apparent width of that section is 8480km/0.017AU = 0.003 rad, which is about 0.2 degrees. With an effective atmospheric scale height of, say, 8km, the light ray travels just a tiny fraction of these 0.017 AU, but still about
8km / sin(1deg) ~ 450km, though the atmosphere. (Double this number to see the ground on the other side, rather than just the top of the atmosphere.) But if the atmosphere is of nearly terrestrial composition, there's no way you could see that far even on a very clear day. Further up (away from the horizon), this number goes down, but the target is of course still farther away: For 20 degrees, I get 0.35 AU and less than 35 arc seconds of width. Therefore, my guess is that the visual impression will be less spectacular than initially suspected because the local topography is just too similar to that of a straight cylinder, and the distant topography is, well, too distant.

However, the body's unusual shape could for example become apparent by observing that distant objects cannot vanish below the horizon if they recede from the observer in one of two special directions opposing each other, but regularly do so when receding perpendicularly. Also, when looking along the Torus on the dayside towards the arch footpoint, i.e. along the direction of maximum "upward" curvature, there'd always be a (rather shallow) viewing angle under which the light ray suffers total reflection at the top rim of the atmosphere. I picture a part of the Torus being reflected upside down as a mirage in the low sky. This, however, would again occur quite close to the horizon, and require excellent viewing conditions.