> I wonder about the gravity field on the planet itself, just disregarding
> the speed of rotation. Seems to me that on the outer radius, the gravity
> is strong. On the inner radius, to avoid getting attracted to the sky,
> it is weaker and push some constraints between the major & minor radius
> (so that the ground is stronger than the sky part).
> But on the upper/bottom side(circle) of the torus, it seems that, if the
> ground is just along the torus, the direction of a free water surface
> would not be parallel to the ground. Wouldn't there be a kind of
> desert/cliff making the transition on the small circle between both
> region ? would it be some desert or waterfall ?
>
> What about the clouds ? Isn't the atmosphere somehow more extended
> inside than outside of the torus ?
> What about the difference on the wildlife & flora due to the various
> strength of gravity ? (and the cubic/square rule)
> Is the daily rotation around the main axis (which might means a 6-month
> day if the rotation axis is not aligned with the plane of revolution, or
> an ever dim inside-band if they are (well, maybe the shadow cast by the
> other side is not large enough to hide the sun, so: umbra, penumbra or
> just a bit less light, according to the relative apparent radius of the
> sun/minor radius of the planet)

The torus is actually "in orbit around itself," with gravity perpendicular to
the surface...though it might be distorted from a torus.  It should spin in
about 12 hours or 24 hours or so.

Below is another picture, with some description:

http://www.orionsarm.com/eg-article/49142c044cba7

Below is a further discussion, and also a discussion of how it is not in stable
equilibrium.

http://cosmoquest.org/forum/archive/index.php/t-27790.html

For this picture, I assumed the minor diameter is 4000 km, and the major
diameter is 100,000 km.

It would be built artificially...though heaven only knows who would have the
technology to build something like this, and why anyone would try since it's not
really stable...

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>
> Below is another picture, with some description:
>
> http://www.orionsarm.com/eg-article/49142c044cba7
>

As soon as I saw this picture (I think by Steve Bowers), and remembered reading
J. P. Boyd's Moonbow story (Analog, 1980 or so)...decided that it would not be
that hard to model in POVRAY...

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Am 12.11.2012 19:50, schrieb Le_Forgeron:

> But on the upper/bottom side(circle) of the torus, it seems that, if the
> ground is just along the torus, the direction of a free water surface
> would not be parallel to the ground. Wouldn't there be a kind of
> desert/cliff making the transition on the small circle between both
> region ? would it be some desert or waterfall ?

Of course the gound itself, being subject to the same gravitational 
effcts, would settle in a non-perfect toroidal shape. (Similar to how 
the earth's shape is not spherical, due to the gravitational forces at 
the equator being partially offset by centrifugal forces.)

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On 13/11/2012 4:04 AM, clipka wrote:
> Am 12.11.2012 19:50, schrieb Le_Forgeron:
>
>> But on the upper/bottom side(circle) of the torus, it seems that, if the
>> ground is just along the torus, the direction of a free water surface
>> would not be parallel to the ground. Wouldn't there be a kind of
>> desert/cliff making the transition on the small circle between both
>> region ? would it be some desert or waterfall ?
>
> Of course the gound itself, being subject to the same gravitational
> effcts, would settle in a non-perfect toroidal shape. (Similar to how
> the earth's shape is not spherical, due to the gravitational forces at
> the equator being partially offset by centrifugal forces.)
>

I did some quick calculations and knowing that the centripetal force is 
equal to minus the angular velocity squared times the radius times the 
mass (F = -W^2*r*m).
If the torus was revolving around its centre once in 24 hours. On the 
inner surface the force would be about 0.508g and on the outside surface 
0.529g. If the period was 12 hours the forces would be 2.03g and 2.116g 
respectively. Note the sleight of hand going from force to acceleration ;-)

This is not a stable configuration. If there was a star in the centre of 
the torus. Any slight movement of the torus to the centre would be 
magnified by the closer part being attracted to the star more than the 
part that is further away. Starting a wobble that would end up looking 
like a hula hoop.

Never the less a nice concept and image.

-- 
Regards
     Stephen

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Stephen <mca### [at] aolcom> wrote:
> This is not a stable configuration. If there was a star in the centre of
> the torus. Any slight movement of the torus to the centre would be
> magnified by the closer part being attracted to the star more than the
> part that is further away. Starting a wobble that would end up looking
> like a hula hoop.

Not a wobble, if it encircled a star there would be no orbital motion - an
outright crash! This is the scenario overlooked by Niven in Ringworld, which he
later retconned with the rim stabilising thrusters.

However, I do not believe the present artifact is supposed to encircle a star,
or spin like a ringworld (at least not enough to generate significant
centrifugal forces). I like the idea that it is planet-scaled, generating
gravity by virtue of its own mass. It is difficult to see how it could form
naturally of course...

Bill

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Le 13/11/2012 07:04, Stephen a écrit :
> This is not a stable configuration. If there was a star in the centre of
> the torus. 

I do not expect a star at the center. Rather far far away.
(a star at the center gives us back to a Dyson sphere, or belt in such
case)

But remains the question of coincidence of planes for rotation &
revolution, and the impact on day-light on some part of the surface.


Any slight movement of the torus to the centre would be
> magnified by the closer part being attracted to the star more than the
> part that is further away. Starting a wobble that would end up looking
> like a hula hoop.

If the star has any significant difference of influence on the near &
far part of the torus, it will crumble the torus fast.

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Le 13/11/2012 07:04, Stephen a écrit :
> 
> I did some quick calculations and knowing that the centripetal force is
> equal to minus the angular velocity squared times the radius times the
> mass (F = -W^2*r*m).
> If the torus was revolving around its centre once in 24 hours. On the
> inner surface the force would be about 0.508g and on the outside surface
> 0.529g. If the period was 12 hours the forces would be 2.03g and 2.116g
> respectively. Note the sleight of hand going from force to acceleration ;-)


There is more than just a delta in the centripetal force. (on the outer
circle, it is opposite direction of gravity (like on earth); on the
inner circle, it should be the same direction as local gravity (but the
local gravity is diminished due to the point being between "two massive
parts"

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On 13-11-2012 9:48, Bill Pragnell wrote:
> However, I do not believe the present artifact is supposed to encircle a star,
> or spin like a ringworld (at least not enough to generate significant
> centrifugal forces). I like the idea that it is planet-scaled, generating
> gravity by virtue of its own mass. It is difficult to see how it could form
> naturally of course...

My idea too. A torus with Earth's diameter at least as cross-section to 
generate the necessary gravity at the surface; the same composition, 
with a molten metallic core (inner torus). The whole structure orbiting 
a star... which would probably tear it apart, or free in the 
interstellar medium, with a need for a light and warmth source...

Interesting musing... ;-)

Thomas

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Le 13/11/2012 13:04, Thomas de Groot a écrit :
> On 13-11-2012 9:48, Bill Pragnell wrote:
>> However, I do not believe the present artifact is supposed to encircle
>> a star,
>> or spin like a ringworld (at least not enough to generate significant
>> centrifugal forces). I like the idea that it is planet-scaled, generating
>> gravity by virtue of its own mass. It is difficult to see how it could
>> form
>> naturally of course...
> 
> My idea too. A torus with Earth's diameter at least as cross-section to
> generate the necessary gravity at the surface; the same composition,
> with a molten metallic core (inner torus). The whole structure orbiting
> a star... which would probably tear it apart, or free in the
> interstellar medium, with a need for a light and warmth source...
> 
> Interesting musing... ;-)

Oh yes, what about the magnetosphere ? (magnetotorus ??)
Is there a north pole too ?
(probably, assuming the inner torus has its own revolution speed)

Would the magnetic field looks like the tokamak helicoidal field ?

And for added fun: could such planet have a moon or more ?

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Le_Forgeron <lef### [at] freefr> wrote:
> Le 13/11/2012 07:04, Stephen a écrit :
> >
> > I did some quick calculations and knowing that the centripetal force is
> > equal to minus the angular velocity squared times the radius times the
> > mass (F = -W^2*r*m).
> > If the torus was revolving around its centre once in 24 hours. On the
> > inner surface the force would be about 0.508g and on the outside surface
> > 0.529g. If the period was 12 hours the forces would be 2.03g and 2.116g
> > respectively. Note the sleight of hand going from force to acceleration ;-)
>
>
> There is more than just a delta in the centripetal force. (on the outer
> circle, it is opposite direction of gravity (like on earth); on the
> inner circle, it should be the same direction as local gravity (but the
> local gravity is diminished due to the point being between "two massive
> parts"

Sorry, I hab a told. :-)
I thought that was implicit when I said centripetal and minus.
It is interesting what happens to the vectors at the edge of the torus.

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