28 Feb 07
Originally posted by FabianFnasGuess I missed that, describing orbits around a torus is tricky.
I think I mentioned it a week ago:
"Yes, you are right. In the middle of the torus hole, at the torus mass centre, the gravitation is zero. In the rotational axis the gravitation is pointed towards the mass centre. But off the rotational centre the gravitation is pointed towards the nearest surface. Correct me if I'm wrong."
The "In the rotational a ...[text shortened]... have a back and forth movement.
...and I think others has mentioned the samt thing too.
01 Mar 07
Originally posted by sonhouseI don't think that this 8-shaped orbit is stable in practical sense. If you don't find the exact initial parameters the orbit will detoriate (*).
Interesting. That might make the instabilities cancel out. Fab, what do you think?
But if you find the exact initial parameters it could very well be stable, and then it is so in mathematical sense.
With this definition of practical sense and mathematical sense I think you can find several practical orbits, but I doubt there will be so many mathematical ones, perhaps only the trivial ones.
Analogy:
Is it possible to put a stick to balance on its tip, without falling?
Yes, there is a mathematical solution of this problem. If you find the exact position of the stick, the stick will stand forever.
In practical sense it is not possible to find this very position. It will fall eventually.
But if you do corrections of the sticks position continually, you can bring the stick to stand forever.
You can always find an orbit around a torus, besides the trivial ones, but perhaps you have to corrections to stabilize it continually, or else it will detoriate (*) more or less quickly.
This is a more deeply analyze of the concept of 'stableness'. Perhaps this contradicts what I've said earlier. But I have tuned my opinion during days of reflection of this subject. Orbits around toruses interests me a lot and occupies my thoughts a lot. But I haven't made any mathematical calculations, I use intuition only. I might be wrong.
(*) "detoriate" - Is this word well understood? Do I spell it all right?
What I mean is that the stableness is growing less and less stable over time.
01 Mar 07
Originally posted by FabianFnasWhat I was looking at is the idea that a single loop orbit through the needle so to speak would because of its curved nature only meet the zero gravity point at most in two places so the orbit would be continuously perturbed as it passes through the hole. But a figure 8 shaped orbit would hit the zero point in 4 places and the curves would always be opposite the last transit, so it seems intuitively to me there would be a swapping of perturbances, where they cancel out.
I don't think that this 8-shaped orbit is stable in practical sense. If you don't find the exact initial parameters the orbit will detoriate (*).
But if you find the exact initial parameters it could very well be stable, and then it is so in mathematical sense.
With this definition of practical sense and mathematical sense I think you can find sever ...[text shortened]... l right?
What I mean is that the stableness is growing less and less stable over time.
01 Mar 07
Originally posted by sonhouseThe more i think about the 8-shaped orbit, the more I tend to change view.
What I was looking at is the idea that a single loop orbit through the needle so to speak would because of its curved nature only meet the zero gravity point at most in two places so the orbit would be continuously perturbed as it passes through the hole. But a figure 8 shaped orbit would hit the zero point in 4 places and the curves would always be opposit ...[text shortened]... so it seems intuitively to me there would be a swapping of perturbances, where they cancel out.
Now I'm not so sure anymore... 😕
The 8-shaped orbit is an interesting one.
01 Mar 07
Originally posted by FabianFnasI think it would not be a simple 8 shaped but each half of the 8 very elongated so the entry into the hole would be as vertical as possible still making an orbit. Of course that could extend to a billion Km but which would make each entry near vertical but that would not be much of a usable orbit. There is a relation therefore between the skinnyness of the torous and the height of each lobe of the 8, you can see where a torous one cm in diameter crossection and 10,000 Km in main diameter would have much relaxed orbital restrictions but as the cross sectional diameter gets close to the overall diameter the orbit would be more restricted in terms of stabilitiness.
The more i think about the 8-shaped orbit, the more I tend to change view.
Now I'm not so sure anymore... 😕
The 8-shaped orbit is an interesting one.
01 Mar 07
Let's take it from the start. We have to simplify.
Say we have two same planets in a fix location relative to eachother, but of some strange reason not orbiting around eachother. Is it possible to form a stable 8-shaped orbit then?
It reminds me of the Apollo XVI in a Earth-Lunar trajectory. But was it stable? I don't know. And the planets moves.
But even if there exist this kind of 8-shaped orbit between to point like masses - is it the same situation in a torus shaped body and an 8-shaped orbit? I have no idea. I can guess but my guessing has no value at all.
Therefore I conclude that this problem lies way above my qualifications and mathematical skills.
01 Mar 07
Originally posted by FabianFnasWell I actually worked on the Apollo (Apollo Tracking and timing, transponders and atomic clocks) And you can be sure they were not making stable orbits, they started and stopped at the bottom and top of the Earth's atmosphere, not starting and ending in viable orbits. It was a once and done deal. However, they could have designed an orbit that would have gone figure 8 fashion around the earth and moon and be more or less stable but that's a loop that goes out a couple three hundred thousand Km and back, moon slowly circling the earth, mars stickiing its nose in there, Venus rubbing up against it, I don't think it would be stable long without mid-course correction, too many variables. But I am thinking simple for our toroid, it's a million light years from anything, no peturbers.
Let's take it from the start. We have to simplify.
Say we have two same planets in a fix location relative to eachother, but of some strange reason not orbiting around eachother. Is it possible to form a stable 8-shaped orbit then?
It reminds me of the Apollo XVI in a Earth-Lunar trajectory. But was it stable? I don't know. And the planets moves.
...[text shortened]... erefore I conclude that this problem lies way above my qualifications and mathematical skills.
01 Mar 07
Originally posted by FabianFnashttp://arachnoid.com/gravitation/
Let's take it from the start. We have to simplify.
Say we have two same planets in a fix location relative to eachother, but of some strange reason not orbiting around eachother. Is it possible to form a stable 8-shaped orbit then?
It reminds me of the Apollo XVI in a Earth-Lunar trajectory. But was it stable? I don't know. And the planets moves.
...[text shortened]... erefore I conclude that this problem lies way above my qualifications and mathematical skills.
Change the simulation type to three body figure of eight.
Now imagine that the two stationary bodies are arms of a torus which passes vertically through the screen at their widest point. As the force upwards is balanced by the force downwards (at all times) our orbiting body will follow the path given by the simulation (tweaking of masses would be required).
02 Mar 07
Originally posted by DeepThoughtReminds me of a Tokamak reactor.
You could do an experiment. Build a torus and charge it electrically and see if you can get electrons to orbit it in this way.
But it is magnetic and the magnetic fluid is circulating in spiral shapes inside the torus.
Perhaps not.
02 Mar 07
1 edit
Originally posted by DeepThoughtInteresting idea. The one thing that makes a decent simulation possible is the fact that electric fields are radially oriented like gravity
You could do an experiment. Build a torus and charge it electrically and see if you can get electrons to orbit it in this way.
so it would follow the same 1/R^2 law. It would undoubtedly be easier to simulate on a computer rather than build an actual model.
It would involve a beam of charged particles aimed at some angle shot through the center of the toroid and with a precise energy that would allow the opposite charged torous to attract said beam back onto itself. It should be possible. Having said that, it would probably be just as easy to simulate an actual gravitational orbit also. Not that I posess the skills to do so. One thing I see, however, is the interaction of electric field lines in the vicinity of the hole in the torous.
The lines, being like charged, would repel each other and form a splayed shape unless there wes an opposite charge dead center of the hole that would re-align the field lines to more accurately simulate a radial gravitational field. That unfortunutely would make for a perturbing force eminating from the center of the toroid which would alter the path of an incoming charged particle.
03 Mar 07
It seems to me that the simplest "orbit" would be sitting stationary in the center of the torus, and very close (in terms of simplicity) is just oscillating back and forth in a straight line in the center of the torus. My gut feel, without doing a speck of calculating, is the neither of these is stable--any perturbation towards the torus would result in the "orbiter" feeling a stronger gravitational attraction towards the (now) closer side of the torus, and the orbiter would fall into the torus. My suspicion, again without calculations to back it up, is that any figure-8 orbit would be subject to a similar instability.
Even so, it would be interesting to see what paths are possible, even if not stable. Perhaps even more interesting might be to see if paths are also possible when the torus is also allowed to rotate and/or move as a result of the gravitational attraction to the orbiter. Could the orbiter be synchronized with a rotation of the torus--I suspect there would be some interesting solutions.