Why is the Ringworld unstable?
James Kuyper
...
> But Gauss's law can be easily modified since it's the area enclosed by the
> surface. Thus it should be stable in the plane of the ring. But it will
> drift off along the axis of spin. Once that happens, gauss's law doesn't
> hold, as the sun is not "enclosed" by the sphere, and it will drift in.
You're mis-applying Gauss's law, I'm not exactly sure how. What do you
think it says? What surface are you using to apply it?
All that Gauss's law can give you in this situation is an alternative
way of calculating the force due to gravity. Outside the star, that
force is the same as that given by Newton's law of gravity for a point
mass.
That force is always pointed toward the star. Therefore, if you move the
ring away from the star along it's axis of rotation, all the forces on
each part of the Ring will have an axial component. The components
perpendicular to the axis will cancel out from opposite sides of the
Ring, giving a net force back toward the star along the axis. The Ring
is gravitationally stable in the axial direction. It's unstable with
respect to motions in the plane of the Ring.
Erik Max Francis
> > You're mis-applying Gauss's law, I'm not exactly sure how. What do
> > you
> > think it says? What surface are you using to apply it?
>
> From Maxwell's equations,
> Gauss's law:
> intergral (closed surface) B.ds=0
> the ring is essenctially a closed surface.
The ring is a closed line. It is not a closed surface.
What makes the uniform, spherical shell case special is that you can
have a Gaussian surface that completely encloses everything inside the
shell, and then can say special things about the gravitational field
inside the shell (from that shell).
There is no surface that completely encloses a uniform, circular ring,
so that's where the analogy falls apart.
> thus inside the ring, the gravational field =0
No, a particle in a Ring experiences a 1/r force, driving it into the
nearest edge. This is, after all, why Niven wrote about the Ringworld
being unstable in _The Ringworld engineers_.
--
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Darryl Lewis
> You're mis-applying Gauss's law, I'm not exactly sure how. What do you
> think it says? What surface are you using to apply it?
From Maxwell's equations,
Gauss's law:
intergral (closed surface) B.ds=0
the ring is essenctially a closed surface.
thus inside the ring, the gravational field =0
--
Darryl
Australia
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James Kuyper
>
> James Kuyper <kuy...@wizard.net> wrote:
> > You're mis-applying Gauss's law, I'm not exactly sure how. What do you
> > think it says? What surface are you using to apply it?
>
> From Maxwell's equations,
> Gauss's law:
> intergral (closed surface) B.ds=0
> the ring is essenctially a closed surface.
> thus inside the ring, the gravational field =0
Maxwell's equations describe electro-magnetism. 'B' is conventionally
used for the magnetic field. 'ds' is conventionally used for a line
element, not a surface element. The law for magnetism is that
integral(closed curve) B.ds =
(net current surrounded by the curve)*constant
Gauss's law applies to the electric field, and it says that:
integral(closed surface) E.dA =
(net charge enclosed by the surface)*constant
Where 'dA' is an element of surface area. Electrostatics and gravity
both obey an inverse square law, so the same form applies to gravity:
integral(closed surface) a.dA =
(total mass enclosed by the surface)*constant
Where 'a' is the acceleration due to gravity. I say 'net' for
electrostatics, and 'total' for gravity, because there are negative
electrical charges, but not negative masses.
Now that we have the formulas down, the next question is how to apply
them. Since each of these formulas involves an integral, it can give you
information about the field itself, only in special circumstances. For
instance, if you choose a special surface, such that the gravitation
acceleration is always perpendicular to that surface, and constant in
magnitude, then the integral simplifies:
|a| A = (enclosed mass)*constant
where A is the total area of the surface. However, the only surfaces
which have that property in this problem are spherical surfaces centered
on the star. In that case, A=4*pi*r^2, where 'r' is the radius of the
sphere. Then we get that
|a| = (constant/(4*pi)) * M/r^2
Which is simply Newton's law. This is very relevant to the discussion,
and doesn't support your claim that the gravitational field is 0.
Shawn A. Wilson
>
> Darryl Lewis wrote:
(snip)
> Which is simply Newton's law. This is very relevant to the discussion,
> and doesn't support your claim that the gravitational field is 0.
Now redo all that in two dimensions and you'll discover that the net
gravitational attraction between an object in the plane of a circle and
the circle itself is zero. There is stability in the third dimension
(up and down) though.
Erik Max Francis
> Now redo all that in two dimensions and you'll discover that the net
> gravitational attraction between an object in the plane of a circle
> and
> the circle itself is zero. There is stability in the third dimension
> (up and down) though.
Why do you think Niven wrote _The Ringworld engineers_? Niven rings are
not stable in the plane of their orbit.
Shawn A. Wilson
>
> Shawn A. Wilson wrote:
>
> > Now redo all that in two dimensions and you'll discover that the net
> > gravitational attraction between an object in the plane of a circle
> > and
> > the circle itself is zero. There is stability in the third dimension
> > (up and down) though.
>
> Why do you think Niven wrote _The Ringworld engineers_? Niven rings are
> not stable in the plane of their orbit.
Go back and read what I said. I didn't say rings were stable in the
plane of their orbit, I said there's no reason why an object should
remain at the axis of rotation as opposed to any other point. More
specifically, I was refuting the notion that a ring will attract its
star if the star gets off center.
James Kuyper
>
> Erik Max Francis wrote:
> >
> > Shawn A. Wilson wrote:
> >
> > > Now redo all that in two dimensions and you'll discover that the net
> > > gravitational attraction between an object in the plane of a circle
> > > and
> > > the circle itself is zero. There is stability in the third dimension
> > > (up and down) though.
You'll have to show me how that's done. I don't see how you can use
Gauss's law to derive the net force. The net force is given by a
significantly different integral than the one that appears in Gauss's
law.
Also, you can't arbitrarily drop the law down by one dimension. In two
dimensions, Gauss's law implies that gravity obeys a 1/r force law, and
you get entirely different results. For effectively two dimensional
objects embedded in a three dimensional space, you have to use the three
dimensional form of the law to get the right results.
> > Why do you think Niven wrote _The Ringworld engineers_? Niven rings are
> > not stable in the plane of their orbit.
>
> Go back and read what I said. I didn't say rings were stable in the
> plane of their orbit, I said there's no reason why an object should
> remain at the axis of rotation as opposed to any other point. More
> specifically, I was refuting the notion that a ring will attract its
> star if the star gets off center.
I wasn't promoting that notion. I was merely pointing out an incorrect
formulated and irrelevant reference to Gauss's law to support the idea
that the gravitational field was zero.
The net force is a different matter, and I've claimed elsewhere
(correctly, I hope :-) that the net force is repulsive when the Ring
gets off-center (at least until one end gets so close to the star that
the approximation of the ring as a rigid body fails).
Erik Max Francis
> Go back and read what I said. I didn't say rings were stable in the
> plane of their orbit, I said there's no reason why an object should
> remain at the axis of rotation as opposed to any other point. More
> specifically, I was refuting the notion that a ring will attract its
> star if the star gets off center.
The two notions are the same. Newton's third law. If there is a force
on the Ring pushing it toward the star, there is a force on the star
pushing it towards the Ring.
--
Erik Max Francis / email m...@alcyone.com / whois mf303 / icq 16063900
Alcyone Systems / irc maxxon (efnet) / finger m...@sade.alcyone.com
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\
/ Give me chastity, but not yet.
/ St. Augustine
James Kuyper
>
> Shawn A. Wilson wrote:
>
> > Go back and read what I said. I didn't say rings were stable in the
> > plane of their orbit, I said there's no reason why an object should
> > remain at the axis of rotation as opposed to any other point. More
> > specifically, I was refuting the notion that a ring will attract its
> > star if the star gets off center.
>
> The two notions are the same. Newton's third law. If there is a force
> on the Ring pushing it toward the star, there is a force on the star
> pushing it towards the Ring.
If the Ring has moved so that the star is slightly off-center but still
inside the plane of the Ring, the net gravitational force of the star on
the Ring is pointed away from the star. By Newton's third law, the net
gravitational force of the Ring on the star must be equal, and point
away from the Ring.
If the Ring has moved so that the star is off-center along the rotation
axis of the Ring, the net gravitational force of the star on the Ring is
toward the star. By Newton's third law, the net gravitational force of
the Ring on the star must be equal, and point toward the Ring.
Shawn A. Wilson
>
> Erik Max Francis wrote:
> >
> > Shawn A. Wilson wrote:
> >
> > > Go back and read what I said. I didn't say rings were stable in the
> > > plane of their orbit, I said there's no reason why an object should
> > > remain at the axis of rotation as opposed to any other point. More
> > > specifically, I was refuting the notion that a ring will attract its
> > > star if the star gets off center.
> >
> > The two notions are the same. Newton's third law. If there is a force
> > on the Ring pushing it toward the star, there is a force on the star
> > pushing it towards the Ring.
>
> If the Ring has moved so that the star is slightly off-center but still
> inside the plane of the Ring, the net gravitational force of the star on
> the Ring is pointed away from the star. By Newton's third law, the net
> gravitational force of the Ring on the star must be equal, and point
> away from the Ring.
No, but my vector calculus is too rusty to prove it. Give me a few more
days.
Bill Lazar
Ok the numbers prove RW is unstable, is every onewho is crunching the
numbers taking into effect the solar wind from the primary impacting
on the inside surface. It is a large surface area. Another overlooked
property of scrith is the ability to hold a charge, like magnetic
charges repell of coarse perhaps the RW could be slighty charged to
repell the primaries magnetic field..
bill
James Kuyper <kuy...@wizard.net> wrote:
>Michael W. Ruger wrote:
>>
>> Ringworld is unstable because of the Fist of God asteroid. All that kinetic
>> energy smashing into the ringworld literally knocked it for a loop. (It made
>> its orbit unstable).
>
>When you say that something is unstable, that means that if you disturb
>it slightly from its equilibrium point, it will continue moving away
>from that point, rather than returning to it. The Fist of God asteroid
>was an example of a disturbance, it has nothing to do with the
>instability itself.
David Lesher
>Another overlooked
>property of scrith is the ability to hold a charge, like magnetic
>charges repell of coarse perhaps the RW could be slighty charged to
>repell the primaries magnetic field..
See R_E; Louis and friends looked into this to no avail...
--
A host is a host from coast to coast.................wb8foz@nrk.com
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Unless the host (that isn't close).........................pob 1433
is busy, hung or dead....................................20915-1433
James Kuyper
>
> James Kuyper wrote:
> >
> > Erik Max Francis wrote:
> > >
> > > Shawn A. Wilson wrote:
> > >
> > > > Go back and read what I said. I didn't say rings were stable in the
> > > > plane of their orbit, I said there's no reason why an object should
> > > > remain at the axis of rotation as opposed to any other point. More
> > > > specifically, I was refuting the notion that a ring will attract its
> > > > star if the star gets off center.
> > >
> > > The two notions are the same. Newton's third law. If there is a force
> > > on the Ring pushing it toward the star, there is a force on the star
> > > pushing it towards the Ring.
> >
> > If the Ring has moved so that the star is slightly off-center but still
> > inside the plane of the Ring, the net gravitational force of the star on
> > the Ring is pointed away from the star. By Newton's third law, the net
> > gravitational force of the Ring on the star must be equal, and point
> > away from the Ring.
>
> No, but my vector calculus is too rusty to prove it. Give me a few more
> days.
OK - my calculus is fairly rusty too, and so is my physics, but I'll
take the risk of doing it in public.
Assumption: the Ring is rotating so fast that it is essentially rigid,
at least compared with the star's gravity. The ring is rotating fast
enough to require an acceleration of 1 earth gravity to hold it
together; the gravitational acceleration of the Sun at the Earth's orbit
is tiny by comparison. If the ring moves far off center while keeping
the star inside the plane of it's rotation, eventually the part nearest
the sun will get significantly bent. However, this approximation is
sufficient for any small deviation, which is all you need to explore the
stability.
Let the mass per unit length of the Ring be 'rho'. Then the total mass
of the Ring, m = 2*pi*R*rho. Let 'M' be the mass of the star, and 'G' is
the gravitational constant.
Let's handle the simple case first. The ring has been moved off center
in the axial direction. Then the position of a given point at an angle
'theta' along the Ring is:
r = <R cos(theta), R sin(theta), z>
The force of the star's gravity on each line element 'R d theta' of the
Ring is therefore given by:
- <R cos(theta), R sin(theta), z> G M rho R d theta
d F = ---------------------------------------------------
(R^2+z^2)^(3/2)
When you integrate this around the entire Ring, the first two components
vanish by symmetry, and you get a net force along the z-axis of
F_z = - G M m z * (R^2+z^2)^(-3/2)
In other words, the force on the Ring is toward the star, which will
cause z to get smaller, so the system is stable with respect to z-axis
displacements.
Now, let's consider the case where the Ring has moved off center, but is
still co-planar with the star. Chose the x-axis to coincide with the
direction of that displacement. Then the position of a point on the Ring
at an angle of 'theta' with respect to the x-axis is given by:
r = < R cos(theta) + x, R sin(theta), 0 >
And the integrand then becomes:
- <R cos(theta) + x, R sin(theta), 0> G M rho R d theta
d F = -------------------------------------------------------
((R cos(theta) + x)^2 + (R sin(theta))^2)^(3/2)
In this case, the third component of the integral is obviously zero, and
the second component is zero by symmetry. The first element is given by
a more complicated integral than before. It can be simplified by
defining:
delta = x/R
And re-writing the x component integrand as:
- ( cos(theta) + delta ) G M rho R^2 d theta
d F_x = ---------------------------------------------
R^3 ( 1 + 2 delta cos(theta) + delta^2)^(3/2)
Now, when calculating stability, we're only concerned with small
displacements. For small 'delta', we can ignore terms involving delta^2:
(1 + 2 delta cos(theta) + delta^2)^(-3/2)
= 1 - 3 delta cos(theta) + O(delta^2)
This allows us to approximate the integrand by:
d F_x = - ( cos(theta) + delta )*( 1 - 3 delta cos(theta) )
* G M rho/R d theta
= - ( cos(theta) + delta - 3 delta cos^2(theta) )
* G M rho/R d theta
Integrating around the entire circle, this gives:
F_x = - ( 0 + delta - 3/2 delta ) 2 pi G M rho/R
3 G M m x
= ---------
2 R^3
Thus the net force on the Ring is pointed away from the star, making x
larger, so the system is unstable with respect to displacements in the
Ring plane.
Tom Lane
> numbers taking into effect the solar wind from the primary impacting
> on the inside surface. It is a large surface area.
Won't help. The solar wind has a negligible effect on orbits in
the solar system; so it won't be a material effect on RW either.
(Sure, RW has more surface area than the Earth, but it also has
more mass.) Solar wind would only help if it were concentrated
to the point of lethality ... which, come to think of it,
is sort of the plot of _RWE_ ...
> Another overlooked
> property of scrith is the ability to hold a charge, like magnetic
> charges repell of coarse perhaps the RW could be slighty charged to
> repell the primaries magnetic field..
This has more promise, but as David points out, Niven already
considered it and decided it wouldn't work. (Seems to me it
possibly *could* be made to work, given all those superconducting
lines in the RW's floor. But ultimately it would have the same
problem as the attitude jet solution: no mechanical system is
foolproof against sufficiently determined fools.)
regards, tom lane
Darryl Lewis
> Shawn A. Wilson wrote:
>>
>> Erik Max Francis wrote:
>> >
>> > Shawn A. Wilson wrote:
>> >
>> > > gravitational attraction between an object in the plane of a circle
>> > > and
>> > > the circle itself is zero. There is stability in the third dimension
>> > > (up and down) though.
> You'll have to show me how that's done. I don't see how you can use
> Gauss's law to derive the net force. The net force is given by a
> significantly different integral than the one that appears in Gauss's
> law.
OK, but does that mean that Gauss's law shows that a Dyson sphere is
gravationally stable around it's sun?
Erik Max Francis
> OK, but does that mean that Gauss's law shows that a Dyson sphere is
> gravationally stable around it's sun?
It is not stable, but it is not dynamically unstable either. Dyson
shells (solid Dyson spheres) feel (nor affect) any force on their
central star. Perturbations that knock the Dyson shell (or its star)
off center will not be corrected, however; there is no restoring force.
--
Erik Max Francis / email m...@alcyone.com / whois mf303 / icq 16063900
Alcyone Systems / irc maxxon (efnet) / finger m...@sade.alcyone.com
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James Kuyper
>
> James Kuyper <kuy...@wizard.net> wrote:
> > Shawn A. Wilson wrote:
> >>
> >> Erik Max Francis wrote:
> >> >
> >> > Shawn A. Wilson wrote:
> >> >
> >> > > Now redo all that in two dimensions and you'll discover that the net
> >> > > gravitational attraction between an object in the plane of a circle
> >> > > and
> >> > > the circle itself is zero. There is stability in the third dimension
> >> > > (up and down) though.
>
> > You'll have to show me how that's done. I don't see how you can use
> > Gauss's law to derive the net force. The net force is given by a
> > significantly different integral than the one that appears in Gauss's
> > law.
>
> gravationally stable around it's sun?
No, Gauss's law cannot be used to show that. As I said, the integrals
related to Gauss's law and to stability considerations are very
different. A Dyson Sphere at least has the right kind of symmetry, but
it loses that symmetry as soon as it moves off-center, which renders
Gauss's law useless (not inapplicable, just useless.)
Don Carter
these constructs can ever be practical, since they would seem to have all the
stability problems of a ringworld, only in every direction.
Even if there is no rotation of the shell, and the sphere relies on compression
forces alone for stiffness, what would it keep its central sun from eventually
punching through the shell? Seems like it would require an unbelievably complex
control system, with stellar jets or something like tractor-beam "spokes", to
keep everything centered. Is this a fair assessment or am I missing something?
Has anyone done a stability analysis of a Dyson sphere?
Darryl Lewis wrote:
> James Kuyper <kuy...@wizard.net> wrote:
> > Shawn A. Wilson wrote:
> >>
> >> Erik Max Francis wrote:
> >> >
> >> > Shawn A. Wilson wrote:
> >> >
> >> > > Now redo all that in two dimensions and you'll discover that the net
> >> > > gravitational attraction between an object in the plane of a circle
> >> > > and
> >> > > the circle itself is zero. There is stability in the third dimension
> >> > > (up and down) though.
>
> > You'll have to show me how that's done. I don't see how you can use
> > Gauss's law to derive the net force. The net force is given by a
> > significantly different integral than the one that appears in Gauss's
> > law.
>
> OK, but does that mean that Gauss's law shows that a Dyson sphere is
> gravationally stable around it's sun?
>
Erik Max Francis
> Since the discussion below brings in Dyson spheres, I have long been
> curious how
> these constructs can ever be practical, since they would seem to have
> all the
> stability problems of a ringworld, only in every direction.
They _are_ impractical, because the original form of a Dyson sphere was
only intended to collect all (or at least most) of its star's sunlight,
not necessarily be a solid, habitable surface.
> Even if there is no rotation of the shell, and the sphere relies on
> compression
> forces alone for stiffness, what would it keep its central sun from
> eventually
> punching through the shell? Seems like it would require an
> unbelievably complex
> control system, with stellar jets or something like tractor-beam
> "spokes", to
> keep everything centered. Is this a fair assessment or am I missing
> something?
> Has anyone done a stability analysis of a Dyson sphere?
There are three states of stability:
A system that is *dynamically stable* will experience a restoring force
returning it to its base state. Take, for instance, a ball sitting at
the bottom of a dip. Move the ball, and it experiences a force pushing
it back to the bottom.
A system that is *dynamically unstable* is precisely the reverse; move
it from its base state and it experiences forces moving it even further
away from that base state. Take a ball sitting on top of a hill. Touch
the ball, in any direction, and it rolls off the hill.
There's a third condition, which is *dynamically neutral*; as it
suggests, a deviation from the base state experiences no forces either
toward or away. Take a ball on a flat plane. Push it in any direction.
It moves away from its point of origin, but no net force acts on it
(neglecting friction with the ground, of course).
Niven rings are _dynamically unstable_ -- knock the Ringworld
off-center, and it rushes headlong into its star.
Dyson shells are _dynamically neutral_ -- they are neither stable nor
unstable. Push a Dyson shell off-center, and it drifts linearly to its
own destruction (but does not hurry along its own destruction).
Both need active attitude control systems, but a Niven ring's control
systems must be more proactive.
Both Niven rings and Dyson shells are fantasy; they require fantastic
materials.
--
Erik Max Francis / email m...@alcyone.com / whois mf303 / icq 16063900
Alcyone Systems / irc maxxon (efnet) / finger m...@sade.alcyone.com
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\
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/ George Bernard Shaw
Erik Max Francis
> Not so. A nonrotating Dyson Shell could be supported by outward
> centrifugal force from masses rotating inside it (maybe streams
> of iron dust moving at > orbital velocity inside evacuated tubes).
Sounds pretty fantastic to me.
Lance Purple
[ good stuff about orbital stability, followed by: ]
> Both Niven rings and Dyson shells are fantasy; they require
> fantastic materials.
Not so. A nonrotating Dyson Shell could be supported by outward
centrifugal force from masses rotating inside it (maybe streams
of iron dust moving at > orbital velocity inside evacuated tubes).
.----------------------------.
| lpurple at netcom dot com |
'----------------------------'
Don Carter
dynamically neutral, how can a Ringworld be any *less* stable than this,
when it is essentially a cross-section of a Dyson sphere?
From prior discussions, I gather the Ringworld is stable enough along the
axis of the ring - the central star and the ring will tend to remain in the
same plane, and I can pretty much see why this is true. So much is clear.
But what makes the ring less stable than a sphere within the plane? All
other forces being symmetrical, I would expect their instabilities to be
equal (or maybe differ by a constant). So, where does this reasoning crash?
Erik Max Francis wrote:
> They _are_ impractical, because the original form of a Dyson sphere was
> only intended to collect all (or at least most) of its star's sunlight,
> not necessarily be a solid, habitable surface.
>
> > Has anyone done a stability analysis of a Dyson sphere?
>
> There are three states of stability:
>
> A system that is *dynamically stable* will experience a restoring force
> returning it to its base state. Take, for instance, a ball sitting at
> the bottom of a dip. Move the ball, and it experiences a force pushing
> it back to the bottom.
>
> A system that is *dynamically unstable* is precisely the reverse; move
> it from its base state and it experiences forces moving it even further
> away from that base state. Take a ball sitting on top of a hill. Touch
> the ball, in any direction, and it rolls off the hill.
>
> There's a third condition, which is *dynamically neutral*; as it
> suggests, a deviation from the base state experiences no forces either
> toward or away. Take a ball on a flat plane. Push it in any direction.
> It moves away from its point of origin, but no net force acts on it
> (neglecting friction with the ground, of course).
>
> Niven rings are _dynamically unstable_ -- knock the Ringworld
> off-center, and it rushes headlong into its star.
>
> Dyson shells are _dynamically neutral_ -- they are neither stable nor
> unstable. Push a Dyson shell off-center, and it drifts linearly to its
> own destruction (but does not hurry along its own destruction).
>
> Both need active attitude control systems, but a Niven ring's control
> systems must be more proactive.
>
> Both Niven rings and Dyson shells are fantasy; they require fantastic
> materials.
>
Erik Max Francis
> So far so good, but I still have some confusion. If a Dyson sphere is
> dynamically neutral, how can a Ringworld be any *less* stable than
> this,
> when it is essentially a cross-section of a Dyson sphere?
Because a Niven ring has a different geometry.
> From prior discussions, I gather the Ringworld is stable enough along
> the
> axis of the ring - the central star and the ring will tend to remain
> in the
> same plane, and I can pretty much see why this is true.
Correct. Bump the Ring out of alignment normal to its plane, and there
is a restoring force by the Sun pushing it back into place.
> But what makes the ring less stable than a sphere within the plane?
> All
> other forces being symmetrical, I would expect their instabilities to
> be
> equal (or maybe differ by a constant). So, where does this reasoning
> crash?
Because the geometry is different.
I have a short non-mathematical (well, mostly) essay on this at
http://mirror/alcyone/max/writing/essays/niven-rings.html
Dyson shells are dynamically neutral because any point inside is being
attracted by a close-by section of the shell and a far-away, much larger
section of the shell. The size of the intersected shell varies as r^2,
and the gravitational force (naturally) varies as r^-2, which when
combined together cancel each other out. That is, the near part of the
shell is closer, but the far part of the shell is proportionately larger
so that the forces balance and you feel no net force (and so neither
does the shell).
This isn't true for Niven rings. Gravity still varies as r^-2, but
since you now have a circular ring, rather than an encompassing shell,
the amount of ring intersected only varies at by most r. This means
that you have an unbalanced r^-1 force acting on you, and it pushes you
into the Ring. Or, if looking at it the other way, if a Niven ring is
off-center, it feels a force pushing it even further off-center.
Whereas, a Dyson shell will feel no force either pushing it back
on-center or further off-center.
Niven rings are dynamically unstable; Dyson shells are dynamically
neutral. Both are unstable (meaning just "not dynamically stable"), but
Niven rings are more so.
--
Erik Max Francis / email m...@alcyone.com / whois mf303 / icq 16063900
Alcyone Systems / irc maxxon (efnet) / finger m...@sade.alcyone.com
San Jose, CA / languages En, Eo / web http://www.alcyone.com/max/
USA / icbm 37 20 07 N 121 53 38 W / &tSftDotIotE
\
/ There are no dull subjects. There are only dull writers.
/ H.L. Mencken
James Kuyper
>
> So far so good, but I still have some confusion. If a Dyson sphere is
> dynamically neutral, how can a Ringworld be any *less* stable than this,
> when it is essentially a cross-section of a Dyson sphere?
The fact that it's a cross-section isn't relevant, as you can check by
examining the math.
The Ring has a different symmetry then a Dyson sphere. Move it off
center in the axial direction, and there's a restoring force. Move it
off center in the plane of the ring, and the net force pulls it farther
off center. In a sense, that averages out to the neutral stability of
the Dyson sphere.
Lance Purple
>> centrifugal force from masses rotating inside it (maybe streams
>> of iron dust moving at > orbital velocity inside evacuated tubes).
>
Let's design a Dyson Shell at the 1 gee radius around Neptune, so
a radius of 26 000 000 meters. Figure that the support tubes are
average 1 km apart, and that a square km of shell masses 10^14 kg.
(10 m. deep lake plus an equal mass of diamond structural plates)
Let this be supported by centrifugal force from a 10^10 kg. mass
moving below (perhaps a 1km by 20m by 20m stream of iron dust).
How fast must the mass move to support the shell?
g(m + M) = mV^2/R or V = sqrt(Rg(m+M)/m)
So V = 1600 km/sec. This would take some -serious- engineering,
but it isn't utterly impossible; it's not even relativistic.
Don Carter
appreciated. Let me try pushing my luck and ask about another bothersome
aspect of a Dyson sphere.
If a Dyson shell is not solid, or at least a solid framework, then what
keeps it from collapsing? Having material orbiting in different planes
(polar, equatorial, and all inclinations in between) does not sound viable
or stable, even if the planes are located at different distances from the
center star. Random collisions will still tend to clear out the material
pretty quickly. And the material does have to be thick enough to block just
about all visible light from the star, to produce the kind of
absorption-emission spectrum characteristic of a Dyson sphere.
Worst of all, I find the whole Dyson concept stretches credibility for me,
to accept that any civilization which can enclose a star and keep the shell
stable, would have failed to discover much better energy sources: more
portable ones of higher output. Put another way, by the time a civilization
has the resources to pulverize its planetary system and position it
carefully around a star, one might argue that it would necessarily have
developed energy sources that would make mere stars seem feeble and
cumbersome. [They might build the sphere anyway, as kind of an kids'
erector-set, but as a useful power source?] Well, who knows?
Again, thanks for the analysis and clarifications. DC
David Lesher
>Worst of all, I find the whole Dyson concept stretches credibility for me,
That is, I am sure, BEST of all....
As the job of good science fiction is to do exactly that, stretch
your thinking.
Erik Max Francis
> Let's design a Dyson Shell at the 1 gee radius around Neptune, so
> a radius of 26 000 000 meters.
I don't know why you chose _this_ as a particular example, since nobody
was talking about "outside" shells, and certainly no one mentioned
Neptune . . .
> Figure that the support tubes are
> average 1 km apart, and that a square km of shell masses 10^14 kg.
> (10 m. deep lake plus an equal mass of diamond structural plates)
> Let this be supported by centrifugal force from a 10^10 kg. mass
> moving below (perhaps a 1km by 20m by 20m stream of iron dust).
> How fast must the mass move to support the shell?
>
> g(m + M) = mV^2/R or V = sqrt(Rg(m+M)/m)
>
> So V = 1600 km/sec.
So each km^2 of the surface is supported by a 10^10 kg mass moving at
1600 km/s? That means that each km^2 requires a body with 1.3 x 10^22 J
of kinetic energy to keep it running.
With a 26 Mm radius, you have 8.5 x 10^15 m^2 of surface area to contend
with, or 8.5 x 10^9 km^2. If the energy budget is 1.3 x 10^22 J/km^2,
then that means you're going to require 1.1 x 10^32 J to keep the thing
running.
And since you have to contend with frictional losses, which means
there's going to be a constant power requirement to keep the system
running. Even if you only lose 1% of the kinetic energy as heat per
year, that amounts 3.2 x 10^-10 s^-1, or 3.5 x 10^22 W, which is about
1/10 000 the Sun's total output, or about 20 000 times the total amount
of sunlight that fallson the Earth.
And this heat has to come through the surface, which means that the
amount of heat bubbling up through the shell will be 3.5 x 10^22 W
through 8.5 x 10^15 m^2, or 4.1 MW/m^2. Every square metre of the
surface will be radiating 4.1 MW of heat. Doesn't sound very practical
to me.
And that's with frictional losses of _1% per year_.
And God only help you if you have a breach.
> This would take some -serious- engineering,
> but it isn't utterly impossible; it's not even relativistic.
I never said "impossible." I said "fantastic."
--
Erik Max Francis / email m...@alcyone.com / whois mf303 / icq 16063900
Alcyone Systems / irc maxxon (efnet) / finger m...@sade.alcyone.com
San Jose, CA / languages En, Eo / web http://www.alcyone.com/max/
USA / icbm 37 20 07 N 121 53 38 W / &tSftDotIotE
\
/ Love is the selfishness of two persons.
/ Antoine de la Salle
Don Carter
Certainly I enjoy having my imagination stretched, but I also value and
appreciate credibility - science with a "ring" of plausibility. The
distinction is important, and one of the reasons I especially like Niven's
works.
Let me tickle your imagination a little with a comparison: I think the Dyson
sphere may prove to be kind of a silly thing to build, in much the same way
that an abacus made from silicon computer chips is kind of silly. The
civilization that can accomplish it would likely have little need for one, is
my point. If you already possess technology that can smash and rearrange solar
systems, you probably have better power sources on hand. As I also mentioned,
however, civilizations might decide to build the darn things regardless - for
artistic expression, as neat toys, or to get a really good campfire going,
among hundreds of other possible reasons. It is still a neat thing to
envision, no question.
I remain interested in hearing from the theoreticians wandering this group,
about proposed ways that the sphere can be kept spherical, since most
discussions imply that a Dyson shell is not solid. Niven has his elegant
spinning ring, "a suspension bridge with no endpoints". Maybe that's not
practical, but by Ghawd, it sure would be beautiful to see, and to walk on! As
for the Dyson sphere, gravity generators seem to be about the only recourse.
Which is like saying, "Hey, it's magic!" :)
> Don Carter <tdc...@one.net> wrote:
>
> >Worst of all, I find the whole Dyson concept stretches credibility for me,
>
Lance Purple
> I don't know why you chose _this_ as a particular example, since
> nobody was talking about "outside" shells, and certainly no one
> mentioned Neptune . . .
I'd like to design the largest possible 1 gee living space, without
requiring imaginary materials like scrith. One possibility is your
"outside" shell idea, built around a smaller gas-giant (since stars
or even Jupiter-size planets have their 1 gee altitude right in the
middle of unlivable radiation belts)
> [...] Even if you only lose 1% of the kinetic energy as heat per
> year, that amounts 3.2 x 10^-10 s^-1, or 3.5 x 10^22 W, which is
> about 1/10 000 the Sun's total output, or about 20 000 times the
> total amount of sunlight that fallson the Earth.
>
> [...] which means that the amount of heat bubbling up through the
> shell will be 3.5 x 10^22 W through 8.5 x 10^15 m^2, or 4.1 MW/m^2.
> Every square metre of the surface will be radiating 4.1 MW of heat.
Damn! Didn't think of frictional losses. Scratch that idea...
(And it would've looked -so- cool to go down into the basement,
onto the lowest catwalk hanging under one of the support tubes,
switch on the floodlamps and see a banded gas-giant planet below...)
Alan
Don Carter <tdc...@one.net> writes:
>Worst of all, I find the whole Dyson concept stretches credibility for me,
Remember, Dyson never talked about a solid shell around a star, but a
dense cloud of orbiting structures that would appear as such from a
distance. So all this discussion about the stability of and the
gravitational force on a solid shell is actually beside the point.
Dyson spheres in the original sense should be almost as common as
intelligence, and thus he suggested searching for them.
Shawn A. Wilson
>
> Erik Max Francis <m...@alcyone.com> wrote:
>
> > I don't know why you chose _this_ as a particular example, since
> > nobody was talking about "outside" shells, and certainly no one
> > mentioned Neptune . . .
>
> I'd like to design the largest possible 1 gee living space, without
> requiring imaginary materials like scrith. One possibility is your
> "outside" shell idea, built around a smaller gas-giant (since stars
> or even Jupiter-size planets have their 1 gee altitude right in the
> middle of unlivable radiation belts)
Hmmm, what's the 1G altitude for the Sun? Makes the Dyson Sphere
smaller and live on the outside.
Lance Purple
>> Lance Purple wrote:
>> I'd like to design the largest possible 1 gee living space, without
>> requiring imaginary materials like scrith. One possibility is your
>> "outside" shell idea, built around a smaller gas-giant (since stars
>> or even Jupiter-size planets have their 1 gee altitude right in the
>> middle of unlivable radiation belts)
>
> Hmmm, what's the 1G altitude for the Sun? Makes the Dyson Sphere
> smaller and live on the outside.
It's easy to calculate: r = sqrt(gm/a)
g = 7x10^-11 Nm^2/kg^2 Newton's constant
m = 2x10^30 kg mass of the sun
a = 10 m/s^2 1 gee acceleration
so r is about 1.2x10^10 m, or 12 million kilometers
So this is in fact way -bigger- than the Neptune shell, and probably
can't be built at all. Even worse, the inhabitants would be exposed
to unlivable heat and radiation because they are 5x closer to the Sun
than the planet Mercury.
Any other ideas for the biggest 1 gee mega-habitat?
Erik Max Francis
> So this is in fact way -bigger- than the Neptune shell, and probably
> can't be built at all.
Naturally; the size of the shell is proportional to the mass of the body
it's around.
> Any other ideas for the biggest 1 gee mega-habitat?
You probably know about this, but there's my "outside Dyson spheres"
essay:
http://www.alcyone.com/max/writing/essays/outside-dyson.html
If you want to choose a star to build an externally-habitable Dyson
shell (I wasn't calling them Dyson shells back then) such that the
temperature and gravity are around that of Earth, then you can choose
stars at the very (red) end of the main sequence -- the smallest red
dwarfs should suffice. This also has the advantage that red dwarfs are
the longest-lived main sequence stars in the Universe -- they last
hundreds of billions to trillions of years.
--
Erik Max Francis / email m...@alcyone.com / whois mf303 / icq 16063900
Alcyone Systems / irc maxxon (efnet) / finger m...@sade.alcyone.com
San Jose, CA / languages En, Eo / web http://www.alcyone.com/max/
USA / icbm 37 20 07 N 121 53 38 W / &tSftDotIotE
\
/ So little time, so little to do.
/ Oscar Levant
Lance Purple
>> Any other ideas for the biggest 1 gee mega-habitat?
>
> You probably know about this, but there's my "outside Dyson spheres"
> essay: <http://www.alcyone.com/max/writing/essays/outside-dyson.html>
Yes, but since my kinetic-support idea doesn't work, wouldn't
these need unobtanium? The equations for minimum thickness vs
mass would be something like:
Tmin = (pressure * radius)/(2 * compression_strength)
pressure = (Tmin * rho * a) + (misc_loads * a)
Which, if I did the math correctly, simplifies out to:
(misc_loads * a * radius)
Tmin = -------------------------------
(2 * Scmp) - (rho * a * radius)
Even before we guess at the misc_load for an earthlike biosphere,
we have a problem. Look at the bottom term; for the thickness to
be nonnegative, we need:
2 * Scmp > rho * a * radius
If the shell is made of diamond (Scmp = 20 GPa, rho = 3500 kg/m^2)
and is built around a 1 gee isogravity surface, then radius can't
be more than 10^6 meters. This makes sense; a diamond tower on
Earth couldn't reasonably exceed 1000 km tall, but it makes the
shell utterly useless; you'd get more habitable surface from an
ordinary planet.
Erik Max Francis
> Yes, but since my kinetic-support idea doesn't work, wouldn't
> these need unobtanium?
Yes. The point is, if you're talking about Niven rings or Dyson shells,
you're already at the point of fantastic materials and unbelievable
stresses. You're already well beyond the point of plausibility.
RX7drivr
something equally inane, to a sufficient thickness that 1g is maintained at the
surface. Omit the star or planet in the center. Live on the outside of the
shell. How big?
James
Don Carter
"dense cloud" of structures has stability problems of its own, solid or not,
and stability is far from irrelevant. Also, size really matters. If the cloud
is too small, things get really hot. Too large, there is not enough material
in several solar systems to build it.
If you digested the early popular accounts that I did about the Dyson sphere,
it came from FD's projection of our energy growth demands, extended a few
hundred years into the future. Somewhere along this exponential curve the
value intersects the total energy output of a star. Voila, build a shell out
of the planetary system and collect all this energy. I don't recall Dyson
talking about any particular kind of structures, just somehow trapping the
energy. The one consideration I do recall (but not sure if it was from Dyson)
was whether there was enough material in the solar system to accomplish this.
With a few breezy postulates and calculations, it turns out there is probably
enough, but only if it's spread damn thin.
I recall at the time, there was some mention that the calculated appearance of
the Dyson shell (its modeled spectrum) roughly matched that of a few anomalous
stars already observed and catalogued by astronomers. The match was poor, but
evidently close enough to raise the speculation that these objects might be
Dyson spheres.
[What I don't find in the more recent articles is any mention of this rough
match. Maybe it was dropped as explainable by natural phenomena. Maybe it was
just a few science writers going overboard. Whatever - it was a long time
ago.]
Anyway, the sphere originally came from a projection of our continued,
exponential energy growth. Exponential growth rates, however, are dangerous
things to work with. See Mark Twain's observations on the Mississippi River
delta, for instance. Or the calculations that indicate our entire galaxy
should have filled with bacteria by now. In every case, limits are reached:
Something Else Happens. Jules Verne projected that a bigger cannon was the
answer to space travel. The list goes on.
Dyson has stimulated intense interest and awareness with his theoretical
construct, even helped inspire the Ringworld. If the concept just turns out to
be a mathmatical toy, it will still have been extremely worthwhile.
DC
P.S. Sometimes I wonder what he thinks about it after all this time. Does
anyone have a recommendation for recent interviews or articles by Dyson?
Bill Woods
> Lance Purple wrote:
> >
> > Erik Max Francis <m...@alcyone.com> wrote:
> >
> > > I don't know why you chose _this_ as a particular example, since
> > > nobody was talking about "outside" shells, and certainly no one
> > > mentioned Neptune . . .
> >
> > I'd like to design the largest possible 1 gee living space, without
> > requiring imaginary materials like scrith. One possibility is your
> > "outside" shell idea, built around a smaller gas-giant (since stars
> > or even Jupiter-size planets have their 1 gee altitude right in the
> > middle of unlivable radiation belts)
>
> Hmmm, what's the 1G altitude for the Sun? Makes the Dyson Sphere
> smaller and live on the outside.
Heh.
R = Sqrt{ G Msun / 9.8 m/s^2 }
= 3.68 e9 m = 0.025 AU radius of shell
I = Lsun / 4 pi R^2 = 2.30 MW/m^2 solar energy flux
T = ( I / sigma )^0.25 = 2500 K minimum outside temperature
--
Bill Woods
Minnesota's new slogan:
"Our governor can beat up your governor."
Lance Purple
A shell made of diamond can't span more than 1000 km radius in a 1g field,
regardless of whether it is from a star or from self-gravity (and anyway,
you can't fit a star inside a 1000 km sphere, and it won't produce 1g of
self-gravity even if it were a solid sphere).
If the shell was built around a solid planet, you could maybe get a radius
of R_planet + 1000 km. which won't provide enough extra space to be worth
the trouble of building it.
Here's another idea for the largest 1 gee living space: the YesWorld.
This would be an artificial gas-giant made out of some dense gas mix
(maybe 50% argon/30% nitrogen/20% oxygen) topped with flying islands
built out of some ultralight material (maybe neon-foamed diamond).
This would be nearly as big as an "outside" Dyson Shell, and really
could be built with normal matter. Any problems I am overlooking
with this one?
Shawn A. Wilson
> Heh.
>
> R = Sqrt{ G Msun / 9.8 m/s^2 }
>
> = 3.68 e9 m = 0.025 AU radius of shell
>
> I = Lsun / 4 pi R^2 = 2.30 MW/m^2 solar energy flux
>
> T = ( I / sigma )^0.25 = 2500 K minimum outside temperature
Yes, but remember that the entire purpose of a Dyson Sphere is to
capture all the energy radiated from a star. If it can be captured I
assume it can be redirected.
Erik Max Francis
> What about making the shell out of normal matter, such as cast iron or
> something equally inane, to a sufficient thickness that 1g is
> maintained at the
> surface. Omit the star or planet in the center. Live on the outside
> of the
> shell. How big?
If that's your goal, then there's no reason to have it be a shell in the
first place. Just make it a sphere. There's certainly no way it would
be able to support itself -- this is an even worse case than a Dyson
shell, since the shell _itself_ has to be massive enough to create 1 gee
at its surface.
And if it's a sphere, then all you've done is construct an artificial
planet.
And the surface gravity of a sphere of density rho and radius r is
g = (4/3) pi rho G r.
If rho = 7.8 x 10^3 kg/m^3 and g = 9.81 m/s^2, then radius of the
artificial planet will be 4500 km, which is just what you'd expect,
given the Earth's radius is 6370 km and its density is 5.5 x 10^3
kg/m^3.
--
Erik Max Francis / email m...@alcyone.com / whois mf303 / icq 16063900
Alcyone Systems / irc maxxon (efnet) / finger m...@sade.alcyone.com
San Jose, CA / languages En, Eo / web http://www.alcyone.com/max/
USA / icbm 37 20 07 N 121 53 38 W / &tSftDotIotE
\
/ The pure and simple truth is rarely pure and never simple.
/ Oscar Wilde
Frank Mango
>OK, a Dyson sphere is not necessarily solid. I am only positing that this
>"dense cloud" of structures has stability problems of its own, solid or not,
>and stability is far from irrelevant. Also, size really matters. If the cloud
>is too small, things get really hot. Too large, there is not enough material
>in several solar systems to build it.
>
>If you digested the early popular accounts that I did about the Dyson sphere,
>it came from FD's projection of our energy growth demands, extended a few
>hundred years into the future. Somewhere along this exponential curve the
>value intersects the total energy output of a star. Voila, build a shell out
>of the planetary system and collect all this energy. I don't recall Dyson
>talking about any particular kind of structures, just somehow trapping the
>energy. The one consideration I do recall (but not sure if it was from Dyson)
>was whether there was enough material in the solar system to accomplish this.
>With a few breezy postulates and calculations, it turns out there is probably
>enough, but only if it's spread damn thin.
>
>I recall at the time, there was some mention that the calculated appearance of
>the Dyson shell (its modeled spectrum) roughly matched that of a few anomalous
>stars already observed and catalogued by astronomers. The match was poor, but
>evidently close enough to raise the speculation that these objects might be
>Dyson spheres.
But if *all* of the energy output of a star is collected, what is left
for astronomers many light-years away to detect? Granted, there's no
such thing as 100% efficiency, even for a civilization that could
attempt such a feat. However, if you grab "almost all" (yeah, I know
that's pretty vague) of the energy, what escapes will probably not
exceed the "background noise" level at interstellar distances.
So what *would* we look for, if we're looking for Dyson spheres?
--
Frank Mango
(change "xlii" to "ix" in my address to reply)
Erik Max Francis
> But if *all* of the energy output of a star is collected, what is left
> for astronomers many light-years away to detect? Granted, there's no
> such thing as 100% efficiency, even for a civilization that could
> attempt such a feat. However, if you grab "almost all" (yeah, I know
> that's pretty vague) of the energy, what escapes will probably not
> exceed the "background noise" level at interstellar distances.
Conservation of energy. If you're not releasing the heat to the
environment, then your shell is going to get hotter and hotter without
bound. Even if you're presuming you're somehow converting that energy
into matter, then that process itself will not be very efficient and
will release copious amounts of heat _itself_.
Your sphere has to be in thermal equilibrium, and so will be radiating
_all_ the heat of its central star through its surface.
> So what *would* we look for, if we're looking for Dyson spheres?
If it's a 1-au Dyson shell around a Sun-like star, then you'll look for
a near-blackbody supergiant radiating mostly in the infrared. Searches
_have_ been conducted for Dyson shells; there are no promising
candidates. (Very cool supergiants have very distinct spectra, which
will look very different from the outside of a warm Dyson shell.)
James Kuyper
>
> Shawn A. Wilson wrote:
>
> > Lance Purple wrote:
> > > I'd like to design the largest possible 1 gee living space, without
> > > requiring imaginary materials like scrith. One possibility is your
> > > "outside" shell idea, built around a smaller gas-giant (since stars
> > > or even Jupiter-size planets have their 1 gee altitude right in the
> > > middle of unlivable radiation belts)
> >
> > Hmmm, what's the 1G altitude for the Sun? Makes the Dyson Sphere
> > smaller and live on the outside.
>
>
> R = Sqrt{ G Msun / 9.8 m/s^2 }
>
> = 3.68 e9 m = 0.025 AU radius of shell
>
> I = Lsun / 4 pi R^2 = 2.30 MW/m^2 solar energy flux
>
> T = ( I / sigma )^0.25 = 2500 K minimum outside temperature
That's not the minimum; its the fourth root of the average value of T^4.
If you can make some parts (radiators) much hotter, the rest of the
surface can be much cooler.
James Kuyper
...
> But if *all* of the energy output of a star is collected, what is left
> for astronomers many light-years away to detect? Granted, there's no
> such thing as 100% efficiency, even for a civilization that could
> attempt such a feat. However, if you grab "almost all" (yeah, I know
> that's pretty vague) of the energy, what escapes will probably not
> exceed the "background noise" level at interstellar distances.
You can grab it, and use it, but if you don't discard exactly the same
amount of energy afterward you'll end up vaporizing whatever you store
it in. Therefore, Dyson shell searches look for objects radiating the
same amount of energy as a normal star, but at a much lower temperature.
RX7drivr
surface area than an artificial planet. I didn't expect that it would collapse
from its own weight
::Tucks his tail and hides in the corner, whimpering::
James
Charles Brabham
Lance Purple wrote in message ...
>snip<
>
>Any other ideas for the biggest 1 gee mega-habitat?
I'd do a bit of bioengineering to bypass the " 1 gee " requirement. Then you
have an infinite habitat. Seems like a lot less trouble in the long run. "Go
solar" or whatever looks most convenient. Maybe surf the Ort cloud instead.
It may even turn out that the best "real estate" is not in or near solar
systems at all, depending on what you decide to get by on.
I don't see planets and habitats designed to simulate them as a reasonable
long-term solution. All of that is great for "starters', but in the long run
I believe we'll end up adjusting ourselves to the environment instead of the
other way around, whether it's planned that way or not.
Low gee and zero gee accommodations is space cost less and are easier to
build. Some people will find that they prefer low gee or can't afford the
high-gee ( tourist ) rates, and it is not unlikely that selection and
adaptation would do their thing with the first "permanent" low gee
populations to occur. Those people will tend to adapt, and low or zero gee
habitats for them will always be cheaper and easier to build... And so on.
That's right.. We'll evolve due to economic factors in space.
Same thing goes for air, the need for all those weird trace elements we now
require. If we get into space and hang out long enough, some people will
adapt to the environment and those people are the ones who will have the
most habitat and resources to work with. ( Infinite )
Who knows? Maybe someday the idea of living on a planet or a habitat which
simulates one may be viewed as a sucker bet!
Not trying to be disruptive here. Just a thot!
Charles Brabham, N5PVL
WWWeb: http://www.texoma.net/~n5pvl
jlk1...@gmail.com
> Hi,Could someone explain to me why the Ringworld is unstable the way that Louis first found it? I tried putting a model (on my dining room table) together of it to better understand what physical forces are involved but I can't put all the pieces (in my head) together correctly to see why it is. BTW, does anyone here know that Ringworld is now almost 30 years old?-- Marc Fury, Cybernaut at Delta College Univ Center, Michigan When I surf the net, my wife Brenda rides the board also E-Mail address: mf...@alpha.delta.edu Web Site: http://www.delta.edu/~mfury In CyberSpace, no one can hear you scream....
Think about a ball on the top of a hill
once you nudge it, it will fall faster and faster
same thing with ringworld, if you nudge it one side will be closer to the sun
Des
Erik Max Francis
> Besides the Fist of God, solar winds and the meteor/intruder defense
> system
> were satid to be destablizing forces.
These are nothing compared to the inherent instability of the Ringworld
itself.
The gravitational field inside a uniform, circular ring (_not_ a
uniform, spherical shell), the gravitational field points toward the
near edge. There is a point of unstable equilibrium (which doesn't
help) in the very center (where the Sun would go). Everywhere there is
roughly a 1/r force pushing a particle toward the Ring (where r is the
distance between the particle and the near edge).
Now replace the test particle with the sun, and reverse the sign for the
force of the Sun on the Ring, from Newton's third law. The Ring
dynamically and deliberately destroys itself unless you have very good,
dynamic attitude control. (Niven of course didn't realize this when he
wrong _Ringworld_, which was much of his motive for writing the first
sequel, _The Ringworld Engineers_.)
--
Erik Max Francis / email m...@alcyone.com / whois mf303 / icq 16063900
Alcyone Systems / irc maxxon (efnet) / finger m...@sade.alcyone.com
San Jose, CA / languages En, Eo / web http://www.alcyone.com/max/
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\
/ Virtue has never been as respectable as money.
/ Mark Twain
David Goerndt
Marc Fury wrote in message <71i49g$n...@alpha.delta.edu>...
>Hi,
>
> Could someone explain to me why the Ringworld is unstable the way that
>Louis first found it?
> I tried putting a model (on my dining room table) together of it to
>better understand what physical forces are involved but I can't put all
>the pieces (in my head) together correctly to see why it is.
> BTW, does anyone here know that Ringworld is now almost 30 years old?
>
Several reasons come to mind, Fist of God was caused by an enormous meteor.
Dismounting attitude jets from parts of Ringworld.
Marc Fury
Could someone explain to me why the Ringworld is unstable the way that
Louis first found it?
I tried putting a model (on my dining room table) together of it to
better understand what physical forces are involved but I can't put all
the pieces (in my head) together correctly to see why it is.
BTW, does anyone here know that Ringworld is now almost 30 years old?
--
S. Wilson
> Louis first found it?
Because it's not in orbit. Ignore the spinning for a moment. If the
Ringworld is balanced perfectly, with the sun in the exact center, all the
forces cancel out and the Ringworld stays still. (Never gonna happen.)
Nudge it off by a centimeter, and suddenly the sun is pulling harder on
one side of the Ringworld than the other, pulling it closer and making the
differential even more, increasing the pull...
Hemlock
Anthony Argyriou
> Could someone explain to me why the Ringworld is unstable the way that
>Louis first found it?
> I tried putting a model (on my dining room table) together of it to
>better understand what physical forces are involved but I can't put all
>the pieces (in my head) together correctly to see why it is.
IIRC, the basic reason is that *any* perturbation will generate forces
which will tend to *increase* the perturbation.
For example, a small impact will cause the ring to drift so the star
is off-center, which will increase the attraction of the closer range
of the orbit more than it will decrease the attraction of the further
part of the orbit, pulling the ring closer to the star. Positive
feedback.
Anthony Argyriou
GrapeApe
were satid to be destablizing forces.
An easy table top demonstatation, (if you have the 'antique' technology
available) take a turntable and a vinyl forty five record without an adapter,
centered around the 33rpm spindle. As the turntable is turning, nudge the
inneredge of the hole and see what happens. especially at higher speeds or in a
situation where it might over come friction.
RX7drivr
>centered around the 33rpm spindle. As the turntable is turning, nudge the
>inneredge of the hole and see what happens. especially at higher speeds
Now imagine that the turntable is moving with a rim velocity of 770 miles/sec.
James
Cheers,
James
In accordance with 47 U.S.C.A. section 227, sending Unsolicited Commercial
Communications to the originator's account implies acknowledgment of the
account owner's rights to minimum damages of $500 per violation.
Dr John Stockton
14:50:12 in alt.books.larry-niven, Erik Max Francis <m...@alcyone.com>
wrote:
>These are nothing compared to the inherent instability of the Ringworld
>itself.
>
>The gravitational field inside a uniform, circular ring (_not_ a
>uniform, spherical shell), the gravitational field points toward the
>near edge. There is a point of unstable equilibrium (which doesn't
>help) in the very center (where the Sun would go). Everywhere there is
>roughly a 1/r force pushing a particle toward the Ring (where r is the
>distance between the particle and the near edge).
>
>Now replace the test particle with the sun, and reverse the sign for the
>force of the Sun on the Ring, from Newton's third law. The Ring
>dynamically and deliberately destroys itself unless you have very good,
>dynamic attitude control. (Niven of course didn't realize this when he
>wrong _Ringworld_, which was much of his motive for writing the first
>sequel, _The Ringworld Engineers_.)
It is absolutely clear that a rigid ring of negligible mass, whether or
not spinning, and a massive, central, sun are a case of unstable
equilibrium.
But a set of point objects of negligible mass in a circular orbit around
a massive, central, sun are assuredly in a very stable situation; and
the same must be true of a "dense set" joined into a ring by massless,
strengthless connections (e.g. with frictionless sliding and hingeing
joints).
What happens in the intermediate case of a flexible, inextensible rope
of negligible mass and proper orbital velocity - "Stringworld" ? ISTR
mention of a "suspension bridge without endpoints" - is there a simple
treatment, akin to yours above?
Or, indeed, an elastic rope - which should be more difficult to
understand - RubberBandWorld ?
Or if the sliding, hingeing joints were lossy (but without static
friction) ?
--
John Stockton, Surrey, UK. j...@merlyn.demon.co.uk JR.St...@physics.org
Web <URL: http://www.merlyn.demon.co.uk/> - FAQqish topics, acronyms & links;
some Astro stuff in astro.htm; quotes.htm; puzzles.htm; pascal.htm; &c &c &c.
Don't Mail News. Y2k for beginners http://www.merlyn.demon.co.uk/year2000.txt
Michael W. Ruger
energy smashing into the ringworld literally knocked it for a loop. (It made
its orbit unstable).
Marc Fury wrote:
> Hi,
>
> Could someone explain to me why the Ringworld is unstable the way that
> Louis first found it?
> I tried putting a model (on my dining room table) together of it to
> better understand what physical forces are involved but I can't put all
> the pieces (in my head) together correctly to see why it is.
Erik Max Francis
> Ringworld is unstable because of the Fist of God asteroid. All that
> kinetic
> energy smashing into the ringworld literally knocked it for a loop.
> (It made
> its orbit unstable).
No, the Ringworld is unstable because Niven rings are by their very
nature unstable. The Fist of God impact would certainly have made
things more difficult (particularly with respect to shockwaves rippling
through the whole Ring), but it is unstable regardless.
--
Erik Max Francis / email m...@alcyone.com / whois mf303 / icq 16063900
Alcyone Systems / irc maxxon (efnet) / finger m...@sade.alcyone.com
San Jose, CA / languages En, Eo / web http://www.alcyone.com/max/
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\
/ But who shall dwell in these worlds if they be inhabited?
/ Johannes Kepler
Motti
actually said...
>Ringworld is unstable because of the Fist of God asteroid. All that kinetic
>energy smashing into the ringworld literally knocked it for a loop. (It made
>its orbit unstable).
-<Motti>-
Rewriting one law of physics is worse than trying to eat one peanut.
--Lucas Garner UN ARM--
Erik Max Francis
> Could someone explain to me why the Ringworld is unstable the way
> that
> Louis first found it?
See my other post in this thread; it's unstable because a rigid ring
around a central star cannot be dynamically stable; it is dynamically
unstable and will push itself further and further off center until it
crashes into its sun and is destroyed.
There's also a comparison of the stability of Dyson shells (solid Dyson
spheres) and Niven rings at
http://www.alcyone.com/max/writing/essays/niven-rings.html
> I tried putting a model (on my dining room table) together of it to
> better understand what physical forces are involved but I can't put
> all
> the pieces (in my head) together correctly to see why it is.
The reason has to do with the properties of Newtonian gravity and isn't
terribly easy to visualize with a model in front of you.
There is a famous theorem in Newtonian gravity (and an analogous one
exists for electromagnetism as well) which says that the gravitational
field inside a uniform, spherical shell is zero (from that shell). So
if you put a shell around a star, there is no force acting on the shell
from the star or vice versa. This happens because for every part of the
shell that's near you and pulling on you hard, there is a larger part of
the shell that's further away but pulling on you softly. These terms
(it's actually an r^2 times an r^-2) cancel each other out, and the
forces will always balance.
That won't be the case with a Niven ring. Gravity still varies as r^-2,
of course, but the amount of the ring subtended on each side now only
varies as r, leaving you with an unbalanced r^-1 force. This is what
makes the Ringworld unstable.
--
Erik Max Francis / email m...@alcyone.com / whois mf303 / icq 16063900
Alcyone Systems / irc maxxon (efnet) / finger m...@sade.alcyone.com
San Jose, CA / languages En, Eo / web http://www.alcyone.com/max/
USA / icbm 37 20 07 N 121 53 38 W / &tSftDotIotE
\
/ Whoever named it necking was a poor judge of anatomy.
/ Groucho Marx
RX7drivr
>circle-mass on that side of the point, so the sun would attract with more
>strenght the FAR side, and the system becomes stable again.
Nope. The law of gravity works on inverse proportion to distance. Once the
ring loses it's center, it will drift off center _faster and faster_ because of
the sun's attraction to the closer ring material. The system is inherently
unstable... think of balancing a spinning plate on the tip of your (unmoving)
finger.
James
GrapeApe
>of negligible mass and proper orbital velocity - "Stringworld" ? ISTR
>mention of a "suspension bridge without endpoints" - is there a simple
>treatment, akin to yours above?
>Or, indeed, an elastic rope - which should be more difficult to
>understand - RubberBandWorld ?
>Or if the sliding, hingeing joints were lossy (but without static
>friction) ?
What if it were actually oblong ellipseworld? Less Stable/More stable?
Alberto Garcia Briz
In fact, when you have a circle around a point, both having mass, you find
out that if you displace a bit the circle to one side, there is more
circle-mass on that side of the point, so the sun would attract with more
strenght the FAR side, and the system becomes stable again. You can prove
that with Newton愀 Theoremes and Gauss尊aw...
Alberto Garcia
A.Garc...@tu-bs.de
S. Wilson schrieb in Nachricht ...
>> Could someone explain to me why the Ringworld is unstable the way that
>> Louis first found it?
>
Erik Max Francis
> In fact, when you have a circle around a point, both having mass, you
> find
> out that if you displace a bit the circle to one side, there is more
> circle-mass on that side of the point, so the sun would attract with
> more
> strenght the FAR side, and the system becomes stable again. You can
> prove
> that with Newton´s Theoremes and Gauss´Law...
Nope. The theorem exists for _spheres_, but not for rings. There is an
unbalanced 1/r force pushing a Niven ring offcenter, similar to positive
feedback. The Ringworld _actively_ tries to destroy itself if it gets
the chance.
--
Erik Max Francis / email m...@alcyone.com / whois mf303 / icq 16063900
Alcyone Systems / irc maxxon (efnet) / finger m...@sade.alcyone.com
San Jose, CA / languages En, Eo / web http://www.alcyone.com/max/
USA / icbm 37 20 07 N 121 53 38 W / &tSftDotIotE
\
/ Scars are like memories. We do not have them removed.
/ Chmeee
Alberto Garcia Briz
Just suppose you have a stone tied at the end of a rope, and you wing it
over your head. It will turn describing (more or less) circles. You may find
tow different problems there:
1) If you wing very fast, either the stone´s mass or speed will end up by
breaking the rope (at a certain high speed). Then, make any calculations
with the Ring´s mass AND speed, and you will find it needs almost infinite
resistence to strain - which is impossible. That´s why Mr. Niven had to made
up a very light and strong material.
2) And most important: When you are swinging the same rope fast, imagine you
make a slight movement with your hand: The stone will then make a ellipse,
and not a circle. You can correct this, by applying a force with your hand.
But if you where winging a loop - and a rigid one - it just would move its
center. And imagine again a huge loop, maybe a big meteorite banging into it
an so displacing it a little. The effect is not strong, but there is no hand
to correct it, so the Ring moves and is not centered anymore... So you have
Book 2.
Alberto Garcia
A.Garc...@tu-bs.de
Marc Fury schrieb in Nachricht <71i49g$n...@alpha.delta.edu>...
>Hi,
>
> Could someone explain to me why the Ringworld is unstable the way that
>Louis first found it?
> I tried putting a model (on my dining room table) together of it to
>better understand what physical forces are involved but I can't put all
>the pieces (in my head) together correctly to see why it is.
S. Wilson
> In fact, when you have a circle around a point, both having mass, you find
> out that if you displace a bit the circle to one side, there is more
> circle-mass on that side of the point, so the sun would attract with more
> strenght the FAR side, and the system becomes stable again. You can prove
If that were the case, you wouldn't need the attitude jets. You're saying
that the Ringworld is at stable equilibrium in the center. Yes, there is
more mass on the far side, but it's further away, so the net pull is on
the nearest side, pulling it more of center. (I don't _really_ want to
show the math, but I will if you need it, unless someone beats me to it.)
I'm intrigued by the idea someone suggested of a non-rigid Ringworld
(Rubberbandworld). It seems like this idea might have a chance of actually
being able to orbit, since the segments operate indepenedently of each
other. But perhaps I'm overlooking something?
Hemlock
James Kuyper
>
> Ringworld is unstable because of the Fist of God asteroid. All that kinetic
> energy smashing into the ringworld literally knocked it for a loop. (It made
> its orbit unstable).
When you say that something is unstable, that means that if you disturb
it slightly from its equilibrium point, it will continue moving away
from that point, rather than returning to it. The Fist of God asteroid
was an example of a disturbance, it has nothing to do with the
instability itself.
Darryl Lewis
>> prove
> Nope. The theorem exists for _spheres_, but not for rings. There is an
> unbalanced 1/r force pushing a Niven ring offcenter, similar to positive
> feedback. The Ringworld _actively_ tries to destroy itself if it gets
> the chance.
But Gauss's law can be easily modified since it's the area enclosed by the
surface. Thus it should be stable in the plane of the ring. But it will
drift off along the axis of spin. Once that happens, gauss's law doesn't
hold, as the sun is not "enclosed" by the sphere, and it will drift in.
--
Darryl
Australia
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