I’ve recently done the math for the Ringworld case, by the way (I gave a talk about it last week). The doubling time for a slight displacement of the Ring is about 60 days - so after a year, any displacement has grown by 64 times, and after about 5 years, even if the initial displacement is only a meter or so, you’ll be scrapping against the Sun.
By the way, the Ring is stable for displacements vertically - if the ring is slightly “above” the sun, then it will oscillate with a period of about 375 days or
so.
So you do think that a good analogy going can be a valid aid to understanding.
Since Subway Prophet asked in his post “does this analogy make sense”–a question just about the same as asking “What if anything is wrong with this illustration” as fa as I can tell–there’s no call to accuse him of grave evils such as “reasoning by analogy.” There’s a difference between “reasoning by analogy” and “attempting to understand by finding the right analogy.”
I didn’t realize that there was a minimum bar to pass before asking questions on GQ. My bad.
Even though I haven’t taken any college-level calculus or physics classes that stayed with me, I’ve read the Wikipedia article and I do understand that everyone agrees that the math works. I’m not questioning that.
What I’m looking for is a way to visualize the model so that it makes sense past a purely abstract equation.
But this analogy only works if the pressure inside never changes. If you increase the pressure (i.e. the shell’s mass) dramatically inside the balloon - and remember that we’re in a Gedankenexperiment realm where scrith is possible, so the balloon can handle it - then the density of the medium increases, and soon atmospheric drag starts to have a measurable effect.
Come on, smart people. Give me a model that works.
I think of gravity working more like a vacuum cleaner than a rope. Put a ball between two vacuum producers of equal strength, and it won’t be pulled in either direction–but neither will it be “stabilized” into position in any sense either.
Of course, it’s just an illustration. There are obviously many ways in which gravity is not like a vacuum producer. For example, gravity works in a vacuum. But that’s irrelevant to the analogy.
Your rope example doesn’t work because:
a) ropes don’t have any flex in them
b) you don’t have an infinite number of ropes in all directions
c) the ropes don’t pull harder when you get closer to the other end
When an object inside the sphere moves, the forces of gravity from all parts of the sphere continue to balance, e.g. cancel each other out. The “ball on a table” analogy is the best we can give you, I think. When the ball gets a push, it moves, but obeys the normal laws of motion–if there’s friction, it slows down (if there is air inside the sphere a moving object will slow down) and if there’s no friction it continues to move until some other force acts on it.
And this doesn’t work because gravity is not air. Gravity doesn’t have any friction to it. There’s no equivalent to atmospheric drag when talking about gravity (that I know about).
What part of the concept are you having trouble with? An object inside a sphere behaves like the sphere is not there, gravitationally speaking, because the force of gravity from all parts of the sphere is a net zero.
“Intuitively” we expect to be pulled to the ground, because that’s what happens to us every day, because we live on the outside of a sphere.
I can’t think of any situation roughly analogous to a Dyson sphere which is stable. They do show up in other contexts in physics, though. The closest one that comes to mind is the fourth and fifth Lagrange points (also known as Trojan points): If you have three objects of significantly different mass, M1 >> M2 >> M3 (such as the Sun, a planet, and an asteroid), and the planet is orbiting the Sun, then there are a couple of points leading and trailing the planet in its orbit by 60 degrees, such that if you put an asteroid there, it’ll stay in the same position relative to the planet and the Sun. If you take an asteroid that’s there and nudge it slightly, it’ll just wobble around in that general vicinity, like the marble in the bowl.
Ok. First I’ll try to explain better the air analogy. Imagine you are standing outside on a breezy day. There is air all around you, but because the air is moving, you can actually feel it. In fact, if the wind is strong enough it will move you around. Blowing you this way and that. (If you were smaller and lighter, the amount of wind it would take to move you would be less.)
Now, if you move to a different place the forces of the air will be different. For instance, if you walk into your house (which has storm doors and weatherstripped windows) you no longer feel the wind. In fact, there aren’t any drafts, either. But does that mean that the air isn’t exerting any force on you? No. There is air pressing in all around you, but those forces cancel each other out and so you don’t move at all. If you move closer to the wall, the forces pulling you one way or the other cancel each other out there, too.
Now, you’re about to say “but if we were in water, which is much thicker than air, then there’s a lot more drag from the water, so if you made the gravity be really strong then you’d start to feel it” or something to that effect. And that’s exactly why this isn’t a very good analogy. With gravity, there is no drag.
I know that’s what you’re about to say because you already did.
Ok, let’s talk about rubber sheets. A rubber sheet is a pretty good model to hold in your head for things like gravity because it’s a way of visualizing two dimensional force fields. Force fields as in “fields of forces” and not “they’ve activated their force field, they’re invulnerable to bullets!” (Force fields are vector fields, for those following along at home, because forces are vectors.)
So we have our rubber sheet, which we stretch out to make a flat surface about the size of a dining room table. What is gravity in this picture? Gravity is the tilt of the surface. If there are no objects on the sheet then the sheet is perfectly flat and there is no force. We could tilt the whole sheet sideways (like putting a book under a table leg) and then there would be a uniform tilt everywhere on the sheet. That’s like having a uniform field everywhere. No matter where you are, you feel a force which pushes you “that way” and the “that way” is always the same direction and the push is always the same amount.
But that’s not how gravity works. The closer you are to something, the more you feel gravity. This is kind of how heavy objects on rubber sheets work. If you drop a bowling ball onto the sheet, it sinks a bit. And if you look at the surface of the sheet, the closer you are to the bowling ball, the steeper the sheet is.
Ok, there are no objects on our sheet, so there is no gravity. Now we put a bowling ball down on the sheet, and it stretches the sheet and makes a depression. That’s the sun.
Now we take a marble and set it down on the sheet. No matter where we set the marble, what will it do? It will start rolling down towards the sun. Even if we put the marble really far away from the bowling ball, the sheet is inclined ever so slightly down toward the bowling ball, so the marble starts to roll. As the marble gets closer to the bowling ball the sheet is curved more and more towards to bowling ball so the marble rolls faster and faster until it eventually rolls into the bowling ball.
Now the force of gravity doesn’t depend on how fast the marble is rolling. The force of gravity is how tilted the sheet is. In this model gravity is the tilt at any given point.
So now let’s talk about the Earth in this model. We have a bowling ball sun in the middle of the sheet. Check. Now take a blue and green marble to represent the Earth. What we’re going to do is roll the Earth marble. As it rolls, it’s constantly falling toward the sun, but because it’s already rolling it sort of just curves around. This is kind of like those coin funnels you see at science centers. Something like this.
Ok, so that’s how gravity works: frictionless rubber sheet which is curved in all kinds of directions.
What about a hollow sphere? Why doesn’t it have gravity inside? Well, of course it does have gravity inside, the forces just cancel each other out.
So take the bowling ball and the marbles off the sheet. Now it’s flat again. At every point on the sheet there is no net force from gravity. (That’s because there are no objects.) Ok, now let’s make a “Tenebras Ring” which is like a Dyson Sphere but one dimension lower. It’s going to be a circle (a one dimensional sphere) instead of a sphere (a two dimensional sphere) because our rubber sheet is two dimensional and space is three dimensional.
We take a bit of scrith and we lay it down on the sheet. It obviously bends the sheet, because scrith is pretty heavy. So we keep laying out pieces of scrith around in a circle until they join up. And now a funny thing happens. Inside the ring of scrith the rubber sheet is flat! Why is it flat? Because the tilt which is caused by any bit of the Tenebras Ring is exactly cancelled out by the tilts caused by the bits on the far side of the ring.
What does it mean if the sheet is flat? Well, it means that you don’t feel any gravity from the ring when you’re on the inside of the ring.
Now we have a smaller flat part of the rubber sheet table inside the Tenebras Ring. it’s big enough to drop a bowling ball into, so we do that. If you’re a marble inside the ring, the ring doesn’t put any tilt on the sheet, but the bowling ball does. Just as if there was no ring there in the first place.
Now there’s a caveat: it doesn’t work out like this in just two dimensions. The forces won’t cancel exactly, but it’s an analogy. You can represent the “tiltiness” of the table mathematically, and then compute the tilt/gravity imparted by the various pieces of matter. Inside a hollow sphere, the gravitational forces cancel each other out exactly, so as far as gravity is concerned, if you’re inside the sphere there’s no sphere. You can’t feel it.
The basic point is that it doesn’t matter why the table is flat. Only that it is flat.
