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Fortunately Newton's third law takes care of that.Mr_Rose wrote:It's not the gravity of the ring or sphere that's the problem; it's the gravity of the star in the middle.
You are wrong about this assumption. Go through how the fact about spheres is derived and see how it doesn't apply to a ring.Levelheaded wrote:Now, I don't know how Gauss' Law applies to a ring compared to a sphere, but it seems like the net gravitational force at the center of a ring would also be zero. As would the net gravitational force for an object that is off-center. Please correct me if I'm wrong about this assumption, but I don't see why a ring would be different than a sphere / shell.
Jerry Bona wrote:The Axiom of Choice is obviously true; the Well Ordering Principle is obviously false; and who can tell about Zorn's Lemma?
antonfire wrote:You are wrong about this assumption. Go through how the fact about spheres is derived and see how it doesn't apply to a ring.Levelheaded wrote:Now, I don't know how Gauss' Law applies to a ring compared to a sphere, but it seems like the net gravitational force at the center of a ring would also be zero. As would the net gravitational force for an object that is off-center. Please correct me if I'm wrong about this assumption, but I don't see why a ring would be different than a sphere / shell.
Levelheaded wrote:Now, I don't know how Gauss' Law applies to a ring compared to a sphere, but it seems like the net gravitational force at the center of a ring would also be zero.
As would the net gravitational force for an object that is off-center.
Please correct me if I'm wrong about this assumption, but I don't see why a ring would be different than a sphere / shell.
You, sir, name? wrote:SummerGlauFan wrote:How about the entire movie 10,000 BC?
Yeah. I facepalmed at a rate of 30 Hz. It interfered with the TV.
heheXanthir wrote:like they do on the real ringworld.
Treatid basically wrote:widdout elephants deh be no starting points. deh be no ZFC.
whereswalden90 wrote:Only if the force from the sails is exactly equal to the gravitational force. I think it'd be safe to assume that that would not be true in practice.
Sockmonkey wrote:Or you could do the easy thing furling and unfurling the sails as needed.
whereswalden90 wrote:Only if the force from the sails is exactly equal to the gravitational force. I think it'd be safe to assume that that would not be true in practice.
Jerry Bona wrote:The Axiom of Choice is obviously true; the Well Ordering Principle is obviously false; and who can tell about Zorn's Lemma?
Xanthir wrote:If you want to be precise... they're not. In deep time all the planets will be flung out of the solar system.
Jerry Bona wrote:The Axiom of Choice is obviously true; the Well Ordering Principle is obviously false; and who can tell about Zorn's Lemma?
Charlie! wrote:Xanthir wrote:If you want to be precise... they're not. In deep time all the planets will be flung out of the solar system.
Explain? Conservation of energy would seem to disagree. Strongly.
antonfire wrote:Even if that were not the case, according to your definition the orbits would be unstable. And so would the L_{4} and L_{5} Lagrange points, and so on. The word "stable" becomes pretty much useless in reference to orbital mechanics.
But hey I suppose I should just link you to the actual definitions.
Xanthir wrote:True. My original statement wassomewhatincorrect. I was trying to exclude only oscillations with positive feedback, whichcan happen in a system as described if you're not carefulis irrelevant to the situation of a reflective ringworld where the light pressure exceeds gravity.
skeptical scientist wrote:The difference is that gravity is a 1/r^{2} force, while the surface area at distance r of a 2-dimensional object inside a certain solid angle goes as r^{2}. The fact that these exactly cancel is what balances the gravitational forces from a sphere so that they all cancel out in the interior.Levelheaded wrote:Now, I don't know how Gauss' Law applies to a ring compared to a sphere, but it seems like the net gravitational force at the center of a ring would also be zero.
Cave Wizard wrote:The Ringworld is already out there, it was built by SPOILERS millions of years ago
Xanthir wrote:To be fair, even perfectly friendly antimatter wildebeests are pretty deadly.
HopDavid wrote:For the sphere, the two opposing masses look even less similar to one another.
Cyclocross4life wrote:I have no physics background, but wouldn't the doppler effect result in a dampening affect on the solar sales? the energy transpher from the light on the sales would be red-shifted on the side that began moving in towards the star, while the otherside would be blueshifted.
Pseudomammal wrote:Biology is funny. Not "ha-ha" funny, "lowest bidder engineering" funny.
Soralin wrote:The key is, being closer to the smaller side, you feel a stronger attraction towards it (half the distance = 4x the attraction). There's more mass on the far side, but it's further away, and so each amount of mass has a smaller pull. From the inside of a sphere, these two factors balance each other out.
Zamfir wrote:@ HopDavid: suppose you have a hollow sphere of non-negligible thinkness. You can see the gravitation of this sphere as the total gravitation of N thinner spheres exactly surrounding each other. By making N large enough, each of those thinner spheres will resemble the ideal situation of negligible thickness. The inner particle is (neutrally) stable with respect to all of those spheres, and therefore with respect to the larger sphere.
EricH wrote:Cyclocross4life wrote:I have no physics background, but wouldn't the doppler effect result in a dampening affect on the solar sales? the energy transpher from the light on the sales would be red-shifted on the side that began moving in towards the star, while the otherside would be blueshifted.
Except for two things--1) the radial component of motion isn't very large, so the doppler effect would quite small, and 2) the shift is in the opposite direction from what you said--that is, the side approaching the star would see its light (very slightly) blue-shifted, while the receding sail would receive red-shifted light.
Cyclocross4life wrote:If we found an infinitely strong material that could withstand temperatures higher than the core of a star and managed to encicrle a star in a ring of it, would it actually matter if the star pulled it offcenter? seems like it would just have one side going through the middle of a star, while the rest of it stuck out.
Soralin wrote:And if it's not rotating, then there's no centripetal force keeping you, (or other things, for example, air), stuck to the inside surface of the ring.
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